### Organizers

More than a decade after the completion of the Human Genome Project, our ability to predict important high-level phenotypes from molecular information at the cellular level remains woefully inadequate. Statistical mapping between variants identified by genome -wide association studies and complex traits such as hypertension do not effectively explain the range of phenotypes in the population, nor do they provide useful predictions of disease risk. In short, the standard machinery of statistical genetics has fallen short as a tool to understand complex disease. This provides the opportunity and motivation for a more comprehensive approach to the grand challenge of understanding the mechanistic relationships between high-level phenotypes and molecular information.

Multi-scale simulation of physiological systems represents a powerful vehicle for linking multiple levels of causality. Mathematical modeling in combination with high-performance computing and high-resolution data has led to tremendously sophisticated and reliable multi-scale multi-physics based simulations of certain physiological systems. In particular, system dynamics from the cellular to the system levels have long been studied using mathematical modeling, for example, computer models of the heart. Yet such dynamics models rarely make any use of data gathered at the molecular level, and therefore cannot capitalize on the emerging availability of patient data collected at multiple scales (e.g. genome information). This workshop will discuss the state-of-the-art mathematical techniques (and outstanding needs) for effectively synthesizing data ranging from genomic through molecular and organ up to the system level with multi-scale computational techniques. Efforts will be focused on addressing how models can be adapted to couple data measured at different scales and from different species, yet belong to the same physiological system. This question will be studied within the respiratory, cardiovascular, and renal systems. We expect that it is possible to extract common features from these systems, and that techniques applied will have applicability outside the systems studied.

This workshop will bring together domain experts from physiology, mathematics, and statistics. Physiologists and statisticians will help identify key data sets of interest and address questions related to uncertainty in data sampling, including discussion of known variation within species, and between in-vivo and in-vitro sampling. Mathematicians will bring expertise in modeling, model reduction, and solving inverse problems. The aim will be to discuss ways to combine data from multiple sources and scales with relevant models to predict patient specific responses. New techniques that have shown promise for solving these types of problems include reformulation of models using techniques from algebra, uncertainty quantification, parameter estimation, and networks. This diverse group of researchers will have potential to generate new projects and ideas for linking statistical and physics-based techniques for building multi-scale mathematical models that incorporate physiological data from multiple sources and scales, which may eventually elucidate relationships between phenotypes and the underlying physiology.

### Accepted Speakers

Monday, May 5, 2014 | |
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Time | Session |

08:00 AM | Shuttle to MBI |

08:15 AM 09:00 AM | Breakfast |

09:00 AM 09:15 AM | Welcome to MBI - Marty Golubitsky |

09:15 AM 09:35 AM | Introduction by Organizers |

09:45 AM 10:20 AM | Santiago Schnell - On the mechanisms of sensing unfolded protein in the endoplasmic reticulum. One of the main functions of the endoplasmic reticulum (ER) is to serve as the cell protein-folding factory. The ER is responsible for the synthesis, folding, assembly and modification of one third of the eukaryotic proteome. Proteins enter the ER as unfolded polypeptide chains with variable fluxes depending on the physiological state of the cell. A sudden increase in the demand for a protein or the disruption of a folding reaction causes an imbalance between protein-folding load and capacity of the ER, which can lead to the accumulation of unfolded protein in the ER lumen. The ER protein balance is regulated by several signaling pathways, which are collectively termed the unfolded protein response. The unfolded protein response is activated by three transducers, which are enzymes whose oligomerization-induced activation is linked to perturbed protein folding in the ER. Three model mechanisms have been proposed for how these enzymes sense the unfolded protein load in the ER lumen: (i) direct recognition, (ii) indirect recognition and (iii) hybrid recognition. We developed detailed reaction mechanisms for each model and analyzed their dynamical behavior. We found that some of these mechanisms have serious discrepancies with the experimental data. We suggest a set of experiments that have not been yet carried out to test a detailed novel model mechanism of protein load sensing in the ER lumen, which explains current experimental findings. Our new model could provide new insights into the mechanisms of protein homeostasis in the ER. |

10:30 AM 11:05 AM | Amina Qutub - Molecular Signatures of Cells during Hypoxic-Stimulated Tissue Growth Oxygen is fundamental to life on Earth. In diseases affecting the vasculature including cancer and neurodegenerative diseases, abberrant hypoxic response is a critical part of the disease. Limited oxygen can lead to more aggressive tumors or determine our susceptibility to dementia. On the other hand, appropriate manipulation of proteins involved in cellular hypoxic response can help restore blood vessels and regenerate tissues. A challenge lies in understanding the complex cellular response to hypoxia both across different diseases and between patients with the detail needed to develop effective therapies. In this presentation, I will share how we are developing and integrating methods in multiscale modeling, machine learning, molecular biology, and microscopy image analysis to tackle the challenge of interpreting how changes at the molecular level affect cellular response and multicellular dynamics. My lab€™s goal is to use computational systems biology methods to understand €“ and ultimately control €“biological response to oxygen across scales. |

11:10 AM 12:00 PM | Discussion: Integrating multiple-scale biophysical processes (Discussion Leader: Daniela Calvetti) |

12:00 PM 01:30 PM | Lunch Break |

01:30 PM 02:05 PM | Gheorghe Craciun - Persistence, Permanence, and Global Stability in Biological Interaction Networks Complex interaction networks are present in all areas of biology, and manifest themselves at very different spatial and temporal scales. Persistence, permanence and global stability are emergent properties of complex networks, and play key roles in the dynamics of living systems. Mathematically, a dynamical system is called persistent if, for all positive solutions, no variable approaches zero. In addition, for a permanent system, all variables are uniformly bounded. We describe criteria for persistence and permanence of solutions, and for global convergence of solutions to an unique equilibrium, in a manner that is robust with respect to initial conditions and parameter values. A thorough understanding of these properties will allow for a better understanding of essential biological processes, such as homeostasis and adaptability. |

02:15 PM 02:50 PM | Anita Layton - Assessment of Renal Autoregulatory Mechanisms A mathematical model of renal hemodynamics is used to assess the individual contributions of the tubuloglomerular feedback (TGF) mechanism and the myogenic response to glomerular filtration rate regulation in the rat kidney. The model represents an afferent arteriole segment, glomerular filtration, and a short loop of Henle. The afferent arteriole model exhibits myogenic response, which is activated by hydrostatic pressure variations to induce changes in membrane potential and vascular muscle tone. The tubule model predicts tubular fluid and Cl- transport. Macula densa Cl- concentration is sensed as the signal for TGF, which acts to constrict or dilate the afferent arteriole. With this configuration, the model afferent arteriole maintains stable glomerular filtration rate within a physiologic range of perfusion pressure (80-180 mmHg). The contribution of TGF to overall autoregulation is significant only within a narrow band of perfusion pressure values (80-110 mmHg). Model simulations of ramp-like perfusion pressure perturbations agree well with findings by Flemming et al. (J Am Soc Nephrol 12:2253-2262, 2001), which indicate that changes in vascular conductance is markedly sensitive to pressure velocity. That asymmetric response is attributed to the rate-dependent kinetics of the myogenic mechanism. Moreover, simulations of renal autoregulation in diabetes mellitus predict that, due to the impairment of the voltage-gated Ca2+ channels of the afferent arteriole smooth muscle cells, the perfusion pressure range in which SNGFR remains stable is reduced by ~70%, and that TGF gain is reduced by nearly 40%, consistent with experimental findings. |

03:00 PM 03:35 PM | Michael Reed - How Mathematicians can Contribute to Genomic Medicine Mathematical models of physiological processes allow one to study the homeostatic mechanisms that keep important phenotypic variables within certain normal ranges. When these variables leave the homeostatic range often disease processes ensue. From the models one can derive surfaces that show the relationship between genetic polymorphisms and particularly important phenotypic variables. Known gene polymorphisms correspond to particular points on the surface, some of which are located near the edge of the homeostatic region. The purpose of medical advice tailored to the patient€™s genotype is to suggest dietary changes or exercise changes that move the patient back towards the middle of the homeostatic region. |

04:00 PM 05:00 PM | COLLOQUIUM: Alberto Figueroa - Recent Advances in 3D Blood flow Simulation: From Parameter Estimation Methods to Clinical ApplicationsIn this talk we will give an overview of a series of methods for 3D blood flow modeling, ranging from Kalman filtering techniques for automatic outflow and material parameter estimation to baroreflex model for automatic control of blood pressure. We will also discuss recent progress made on the validation of CFD predictions of pressure gradients in coarctation patients at rest and stress using clinical pressure data. |

05:00 PM 06:00 PM | Reception in MBI lounge |

06:00 PM | Shuttle pick-up from MBI |

Tuesday, May 6, 2014 | |
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Time | Session |

08:00 AM | Shuttle to MBI |

08:15 AM 09:00 AM | Breakfast |

09:00 AM 09:35 AM | Hien Tran - A Stochastic Approach to Nonlinear Mixed Effects Modeling Nonlinear hierarchical or mixed effects modeling is a statistical framework involving both fixed-effects and random effects for population parameters incorporating uncertainty associated with intra- and inter-subject variability. The inter-individual variability acknowledges the fact that the subject arises from a heterogeneous population of individuals by viewing the subject parameters as random variables. In this talk, we will view the intra-individual variability as two separated types of noises: uncorrelated measurement noise due to the effects of within-subject sources such as assay error, and system noise due to model misspecifications. This setup allows a more sophisticated method for handling models with structural misspecifications using stochastic differential equations (SDE). In the talk, we will discuss the implementation of SDEs into a nonlinear-mixed effects modeling framework. Using Metformin clinical data, which is a commonly prescribed treatment for type 2 diabetes, we will compare the model development results using an SDE approach to common practice using ordinary differential equations. |

09:45 AM 10:20 AM | Daniela Calvetti - Multi-scale challenges in brain cellular metabolism We present some recent work where how phenomena which occur at the microscopic scale are captured by macroscopic models which lack the fine resolution needed to describe them. This will be illustrated in the context of cellular brain energy metabolism by comparing a spatially distributed model with the capability to account for the proximity of blood vessels and diffusion, and a lumped model which assumes well mixed compartments. |

10:30 AM 11:05 AM | Leif Hellevik - Recent advances in uncertainty quantification for material parameters in arterial network simulations In this talk we will present the recent progress in the ongoing development of a framework for the simulation of pressure and flow propagation in arterial networks. Focus will be given on how the effect of uncertainties in model parameters (correlated and uncorrelated) may be quantified. Further, the flexibility of the framework, which allows for the incorporation of organ models (e.g. renal) and multi-scale models for phenotypes such as arterial compliance, will be discussed. |

11:10 AM 12:00 PM | Discussion: Practical approaches to multi-scale physiology modeling (Discussion Leader: Alberto Figueroa) |

12:00 PM 01:30 PM | Lunch Break |

01:30 PM 02:05 PM | Carsten Wiuf - Model reduction is biochemical reaction networks In many situations we apply simplified models to complex dynamical systems, either because we are unaware of what the 'correct' model should look like, or because the 'correct' model is too complex to handle statistically/mathematically. In this talk, I will discuss model reduction for stochastic as well as deterministic biochemical reaction networks. In particular, I will focus on reduction by elimination of intermediate species, transient species that typically are consumed at a faster rate than non-intermediates and provide a number of results concerning equilibrium dynamics as well as non-equilibrium dynamics. |

02:15 PM 02:50 PM | Tarun Goswami - Modeling Biomedical Systems - An Engineering Approach Biological systems and their interactions often take place at nanometer level. However, engineering approaches, and modeling biological systems often is at macro or a global level. Examples include devices that mimic the anatomical joints and/or organs replacing them by utilizing the engineering materials in bio environments and follow them up for their durability. During the course of in vivo use of the devices new pathophysiology emerges, affecting other pathways that were not known before. Osteolysis in the case of total joint replacement arises from debris may also be initiated by metal ions. However, engineering approaches are evolving to reduce the debris from the liners in total joint replacements via new manufacturing routes and cross-linking the polymers as well as kinetics of wear rates of the liners. The presentation will show modeling methods utilized to optimize new total joint replacement models of the ankle, and others, understand the tear of anterior cruciate ligament and other injury mechanisms and develop new probabilistic methods to predict the injury occurrences. An overview of device and bone damage mechanics will be presented, at large scale. |

02:50 PM 03:00 PM | Break |

03:00 PM 03:30 PM | John Gennari - Part 1: Codeword annotation for sharing and merging physiological models Hunter and Bassingthwaithe define the Physiome as a set of multiscale, interacting mathematical models of physiology. Although available model repositories are an initial step toward this vision, it is a critical next step to develop computer-readable annotation for connecting codewords across models. Current hand-crafted model-building methods must be formalized and standardized to better support knowledge interaction and sharing. In particular, we argue for semantic annotations as a way of communicating the biophysical meaning of individual model codewords. Once annotated in a computable format, we can automatically find and connect models based on the annotation semantics of the biological entities and physiological properties. In this talk, we present our approach to semantic annotation, using standard bio-ontology terms to relate physiological properties (e.g. pressure), to anatomical entities (e.g. blood). In turn, we use these annotations to semi-automatically find relevant models from repositories, and ultimately merge those models where appropriate. We present our results with SemGen, a prototype tool, for both building annotations and merging models, even across different modeling languages. If successful, our approach to develop interacting model repositories could accelerate model sharing and integration, and research that depends on the construction of complex models. |

03:30 PM 04:00 PM | Daniel Cook - Part 2: Codeword annotation for sharing and merging physiological models Hunter and Bassingthwaithe define the Physiome as a set of multiscale, interacting mathematical models of physiology. Although available model repositories are an initial step toward this vision, it is a critical next step to develop computer-readable annotation for connecting codewords across models. Current hand-crafted model-building methods must be formalized and standardized to better support knowledge interaction and sharing. In particular, we argue for semantic annotations as a way of communicating the biophysical meaning of individual model codewords. Once annotated in a computable format, we can automatically find and connect models based on the annotation semantics of the biological entities and physiological properties. In this talk, we present our approach to semantic annotation, using standard bio-ontology terms to relate physiological properties (e.g. pressure), to anatomical entities (e.g. blood). In turn, we use these annotations to semi-automatically find relevant models from repositories, and ultimately merge those models where appropriate. We present our results with SemGen, a prototype tool, for both building annotations and merging models, even across different modeling languages. If successful, our approach to develop interacting model repositories could accelerate model sharing and integration, and research that depends on the construction of complex models. |

04:00 PM 05:30 PM | Poster Session |

05:30 PM | Shuttle pick-up from MBI |

Wednesday, May 7, 2014 | |
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Time | Session |

08:00 AM | Shuttle to MBI |

08:15 AM 09:00 AM | Breakfast |

09:00 AM 09:35 AM | Kellie Archer - Ordinal Response Models for Modeling Longitudinal High-Dimensional Genomic Feature Data Ordinal scales are commonly used to measure health status and disease related outcomes. Notable examples include cancer staging, histopathological classification, adverse event rating, and severity of illness. In addition, repeated measurements are common in clinical practice for tracking and monitoring the progression of complex diseases. Classical likelihood-based ordinal modeling methods have contributed to the analysis of data in which the response categories are ordered and the number of covariates ( |

09:45 AM 10:15 AM | Klas Pettersen - Arterial Stiffening Provides Sufficient Explanation for Primary Hypertension The baroreflex is a negative feedback system for regulation of blood pressure. Its sensors, the baroreceptors located in the aortic wall and the carotid sinuses, are, however, not pressure sensors, but mechanoreceptors excited by stretch. Here we present a computational physiology model which shows that the increase in arterial stiffness that follows with age is sufficient to account for an overwhelming amount of experimental and clinical data on hypertension. We demonstrate quantitatively that the stiffening causes the baroreceptors to misinform the highly complex machinery responsible for blood pressure regulation. This misinformation occurs because the baroreceptors are strain sensitive, not pressure sensitive, and with stiffening the aortic wall strain ceases to be a good proxy for aortic blood pressure. In contrast to widely held opinions, the results suggest that primary hypertension can be attributed to a mechanogenic etiology without challenging current conceptions of renal and sympathetic nervous system function. And they support the view that a major target for treating chronic hypertension in the elderly is the reestablishment of a proper baroreflex response. |

10:30 AM 11:05 AM | Julia Arciero - Assessing vascular risk factors for glaucoma using a mathematical model of blood flow in the retina Glaucoma is the second leading cause of blindness in the world and is characterized by progressive retinal ganglion cell death and irreversible visual field loss. Although elevated intraocular pressure has been identified as the primary risk factor for glaucoma and is the main target of glaucoma treatments, several vascular risk factors that lead to impaired retinal blood flow have also been correlated with the progression and incidence of glaucoma. Here, a multi-scale mathematical model is used to investigate the relative contributions of vascular risk factors on flow regulation and tissue oxygenation in the retina. A previously-developed fluid-structure interaction system modeling the central retinal artery is coupled to a vascular wall mechanics model for the vessels of the retinal microcirculation. Under normal conditions, the model predicts a 14% decrease in retinal perfusion if oxygen demand is decreased by 50% and a 33% increase in perfusion if demand is increased by 50%. These responses are impaired significantly if the metabolic or carbon dioxide mechanisms of retinal blood flow autoregulation are impaired. Changes in oxygen saturation levels in the retinal vascular network are also assessed as levels of mean arterial pressure, oxygen demand, and intraocular pressure are varied. Overall, the model results suggest that impaired autoregulation might increase the risk of retinal ischemic damage, as would occur in glaucoma, under conditions of elevated metabolic demand or decreased mean arterial pressure. |

11:10 AM 12:00 PM | Discussion: When and how are models from different labs compatible: Is there any value in archiving and disseminating computational models? (Discussion Leader: Klas Petersen) |

12:00 PM 01:30 PM | Lunch Break |

01:30 PM 02:05 PM | Nick Hill - A structured tree model for the pulmonary circulation A novel multiscale mathematical and computational model of the pulmonary circulation is presented and used to analyse both arterial and venous pressure and flow. This work is a major advance over previous studies using structured trees to model vascular beds, e.g. Olufsen et al. (2012), which only considered the arterial circulation. For the first three generations of vessels within the pulmonary circulation, geometry is specified from patient-specific measurements obtained using magnetic resonance imaging (MRI). Blood flow and pressure in the larger arteries and veins are predicted using a nonlinear, cross-sectional-area-averaged system of equations for a Newtonian fluid in an elastic tube. Inflow into the main pulmonary artery is obtained from MRI measurements, while pressure entering the left atrium from the main pulmonary vein is kept constant at the normal mean value of 2 mmHg. Each terminal vessel in the network of `large' arteries is connected to its corresponding terminal vein via a network of vessels representing the vascular bed of smaller arteries and veins. We develop and implement an algorithm to calculate the admittance of each vascular bed, using bifurcating structured trees and recursion. The structured-tree models take into account the geometry and material properties of the `smaller' arteries and veins of radii > 50 microns. We study the effects on flow and pressure associated with three classes of pulmonary hypertension expressed via stiffening of larger and smaller vessels, and vascular rarefaction. The results of simulating these pathological conditions are in agreement with clinical observations, showing that the model has potential for assisting with diagnosis and treatment of circulatory diseases within the lung. References: Olufsen, M.S., Hill, N.A., Vaughan, G.D.A., Sainsbury, C. & Johnson, M. (2012) Rarefaction and blood pressure in systemic and pulmonary arteries. J Fluid Mech 705:280-305. Qureshi, M.U., Vaughan, G.D.A., Sainsbury, C., Johnson, M., Peskin, C.S., Olufsen, M.S. & Hill, N.A. (2014) Numerical simulation of blood flow and pressure drop in the pulmonary arterial and venous circulation, Biomechanics and Modeling in Mechanobiology. ISSN 1617-7959 (doi:10.1007/s10237-014-0563-y ) |

02:15 PM 02:50 PM | Frans van de Vosse - Personalization of 1D Wave Propagation Models of the Cardiovascular System One of the main di?culties in the translation of mathematical models to the clinic for supporting clinical decision-making is assessing patient-speci?c values for the model parameters, the boundary and the initial conditions. Measurement modalities or data are not always available for all model parameters. In addition, the precision and accuracy of clinical measurements are hampered by large (biological) variations. Consequently, a balance is needed between the uncertainty resulting from model input parameters and the uncertainty resulting from model assumptions. For this, it is essential to quantify the uncertainty resulting from model input and to determine whether the complexity of the model is su?cient for the application of interest. The aim of this study is to investigate model personalization (parameter ?xing and prioritization), model output uncertainty, and the number of runs required to reach convergence of their sensitivity estimates (i.e. computational cost) in case of a 1D pulse wave propagation model that was developed to support vascular access surgery planning [1]. The most common and straightforward method is to use crude Monte Carlo simulations in which the model is executed multiple times to estimate the sensitivity indices. This method, however, requires a lot of computational e?ort. Saltelli et al. [2] introduced a method that is computationally less demanding. This makes the method better applicable to computational expensive models or models with many model parameters. However, large computing resources are still required when applying the method to models with many model parameters. Finally, the method of Morris [3] is a global sensitivity analysis that is able to identify the few important model parameters among the many model parameters in the model with a relatively small number of model evaluations. Our specific aim was to investigate whether model personalization could be performed by ?rst applying the Morris screening method that identi?es the non-important parameters and subsequently applying the Saltelli method to the resulting subset of important parameters. As this is expected to reduce the computational cost of the uncertainty and sensitivity analysis, this might improve clinical applicability. In addition the uncertainty of the model outputs was quantified using the same data that was generated for the sensitivity analysis. The Saltelli method, which in general requires many model runs, is found to be a robust method for model personalization. Screening for the important parameters using the Morris method is found to work well for the complex cardiovascular wave propagation model for vascular access. The Morris method can therefore be used for parameter ?xing. However, it does not o?er any information in the setting of parameter prioritization, i.e. in identifying which parameters are most rewarding to measure as accurately as possible. The subsets of important parameters identi?ed for the output of interest lead to a significant complexity reduction. We conclude that for model personalization of complex models it is advised to perform a screening for the important parameters using the method of Morris ?rst, and then perform a variance-based sensitivity analysis on the subset with only important parameters. For this purpose a Saltelli method can be used. Alternative and more computationally e?cient estimation methods not presented in this study are stochastic collocation methods based on polynomial chaos expansion. [1]W. Huberts, C de Jonge, W.P.M. van der Linden, M.A Inda, J.H.M. Tordoir, F.N. van de Vosse, and E.M.H. Bosboom. A sensitivity analysis of a personalized pulse wave propagation model for arteriovenous ?stula surgery. Part A: Identi?cation of most in?uential model parameters. Med Eng Phys., 35(6):810€“26, 2013. [2]A. Saltelli. Making best use of model evaluations to compute sensitivity indices. Comp Phys Comm, 145:280€“297, 2002. [3]M.D. Morris. Factorial sampling plans for preliminary computational experiments. Technometrics, 33(2):161€“174, 1991. |

03:00 PM 03:15 PM | Break |

03:15 PM 03:50 PM | Laura Ellwein - Image-based 3D quantification and reconstruction of coronary artery morphology in the context of stenting as treatment of cardiovascular disease One in six adults in the US have some form of coronary artery disease, characterized in particular by accumulation of atherosclerotic plaque. Though stenting is the most common treatment technique, it often leads to restenosis and thrombus formation. Computational modeling of human arteries from patient-specific image-based data offers a noninvasive way to investigate geometry, hemodynamics, and vascular disease corresponding with effects of stenting. Improved strategies for stent-based patient-specific treatment of atherosclerotic lesions at coronary bifurcations require a greater understanding of normal coronary vessel morphology. We developed a method to quantify morphology in the left coronary artery for eventual use in bifurcating stent design. Computational models of the left main coronary were created from computed tomography (CT) images of 54 patients using ITK-Snap. Metrics assessed using Visualization Toolkit-based software and MATLAB included cross?sectional area, length, eccentricity, taper, curvature, branching law parameters, and bifurcation angles. Traditional statistical analysis using parametric tests for comparing and correlating means revealed significant differences both within and between bifurcations for most metrics. Image-based computational models for quantifying hemodynamic indices in stented coronary arteries often employ biplane angiography and intravascular ultrasound for 3D reconstruction, but recent advances in optical coherence tomography (OCT) suggest more precise coronary artery reconstruction may be possible. We developed a patient-specific coronary artery reconstruction method that combines OCT, an intravascular imaging modality, with techniques for imaging wire pathway reconstruction adopted from graph theory. The pathway of the imaging wire was determined with a shortest path algorithm assuming minimum bending energy, and OCT images were registered orthogonal to the pathway with appropriate rotational orientation. Segments from both OCT in the stented region and CT upstream and downstream were imported into computational fluid dynamics software to quantify indices of wall shear stress (WSS). WSS results are presented using the method applied to imaging data of a left circumflex coronary artery acquired immediately post-stenting and after a 6-month follow-up period. Findings from computational modeling studies using patient-specific imaging data may ultimately enhance our knowledge of both healthy coronary arteries and of harmful hemodynamic indices induced by stenting and could be leveraged for future stent design. |

04:00 PM 04:35 PM | Alessandro Veneziani - Patient-specific parameter estimation in computational hemodynamics: from simulations to assimilations With the progressive inclusion of numerical simulations in medical research and clinical practice, accuracy and reliability of patient-specific computational analyses need to be properly certified. This raises new challenges when estimating patient-specific parameters that may be too difficult or even impossible to measure in practice. On the other hand, these parameters represent a macroscale synthesis of molecular or mesoscale dynamics, but their practical individual-based quantification based on modeling arguments is extremely difficult. Data assimilation techniques are required to merge available data and numerical models to assess the reliability of a quantitative analysis. In this talk, variational procedures will be considered to estimate (a) vascular compliance from available measures of displacement; (b) cardiac conductivities from available measures of cardiac potentials. Some theoretical as well as practical aspects of the numerical solution of these problems will be addressed. In particular, we pursue variational techniques based on a constrained minimization approach, the constraint being represented by the fluid-structure interaction vascular problem or by the Bidomain equations for electrocardiology. We will discuss several technical details of this approach. In general, these techniques lead to high computational costs and proper methods for the sake of computational efficiency need to be adopted. We consider in particular both methods based on simplified models for the forward problem (like the Monodomain equation) or on surrogate solutions obtained on the basis of the offline/online paradigm, like the Proper Orthogonal Decomposition method (POD). We will illustrate both succesfull experiences as well as pitfalls of these approaches. |

04:35 PM 04:45 PM | Discussion/Day's Wrap-up [Dan Beard] |

04:45 PM | Shuttle pick-up from MBI |

Thursday, May 8, 2014 | |
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Time | Session |

08:00 AM | Shuttle to MBI |

08:15 AM 09:00 AM | Breakfast |

09:00 AM 09:35 AM | Mette Olufsen - Modeling blood pressure and heart rate dynamics in patients with orthostatic intolerance Orthostatic intolerance occurs when a transition to standing upright causes an imbalance in blood pressure and flow. It affects an estimated 500,000 Americans in particular young women (the female-to-male ratio is approximately 5:1). Symptoms of this disorder range from lightheadedness to fainting. Because many diseases exhibit these symptoms, this disorder can be difficult to diagnose. Moreover, several competing hypotheses have been put forward to explain this disorder, including imbalance of the blood volume regulation and reduced efficacy of the baroreflex control system. The most common tests performed to assess a patient's health are the head-up-tilt and sit-to-stand tests. These tests are designed to stimulate the cardiovascular control system via a simple change of body posture from supine to sitting or standing position. In response to the postural change, blood volume is pooled in the legs leading to a drop in blood pressure in the upper body. The blood pressure drop stimulates baroreceptor neurons, which, via sympathetic stimulation and parasympathetic withdrawal, regulate the heart pumping function and vessel properties facilitating return of blood flow and pressure to their homeostatic levels. This regulation is often disrupted in patients with orthostatic intolerance, often experienced by patients with diabetes, hypertension, and other neurological diseases of which Parkinson€™s disease is the most prevalent. The autonomic nervous system is composed of many interacting components, yet measurements done to assess the system are typically limited to heart rate and blood pressure. One way to gain more understanding of the system is via mathematical modeling. This talk will demonstrate what insights can be learned using multiscale models predicting cardiovascular dynamics and the associated autonomic control. |

09:45 AM 10:20 AM | John Schild - The arterial baroreceptor reflex: a model system for multi scale modeling with clinical significance In its simplest form, the arterial baroreceptor reflex (BRx) is a negative feedback controller of heart rate and an essential component of cardiovascular autonomic control. Clinical measures of autonomic function such as BRx sensitivity and heart rate variability (HRV) are gaining recognition as potentially reliable indicators of cardiac health and disease progression but considerable controversy remains. Our experimental and computational work strives to enhance knowledge concerning the cellular level mechanisms underlying the neural coding and signal integration of arterial pressure dynamics and the manner in which these may impact the unique functional properties of the BRx. Transduction of the magnitude and time course of arterial pressure begins at mechanosensitive nerve terminals (baroreceptors) that can be neuroanatomically classified as either myelinated or unmyelinated sensory afferents, with each phenotype exhibiting strikingly different patterns of neural discharge. Results from whole animal BRx studies suggest that the more sensitive, lower threshold myelinated baroreceptors may function more toward buffering acute changes in arterial blood pressure whereas the less sensitive, higher threshold unmyelinated baroreceptors may function more toward controlling mean arterial pressure. More recently, our experimental studies have been guided by the increasing clinical evidence for sexual dimorphism in cardiovascular health and disease and in particular BRx function. Using female rats, we previously identified a distinct myelinated baroreceptor phenotype that exhibits functional dynamics and ionic currents that are a mix of those observed in barosensory afferents functionally identified as myelinated (A-type) or unmyelinated (C-type). Interestingly, these €œAh-type€? myelinated afferents constitute nearly 50% of the total population of myelinated aortic baroreceptors in female but less than 2% in male rat. We hypothesize that the observed sexual dimorphism in BRx function may be a result of, at least in part, differences in the population of myelinated baroreceptor afferents between males and females. Subsequent whole animal, in situ BRx studies have demonstrated that females (n = 16) exhibit significantly greater BRx responses as compared to males (n =17) at stimulus intensities selective for activation of A-type and Ah-type myelinated afferents (P < 0.05). Collectively, our results provide evidence that in females, two anatomically distinct myelinated afferent pathways contribute to integrated BRx function whereas in males there is only a single pathway with a far more uniform population of myelinated afferents. These functional and neuroanatomical differences may account for, at least in part, the well documented enhanced parasympathetic control of blood pressure in females. |

10:30 AM 11:05 AM | Johnny Ottesen - Patient specific modelling of the endocrine HPA-axis and its relation to depression: Ultradian and circadian oscillations Depression is a widely spread disease: In the Western world approximately 10% of the population experience severe depression at least once in their lifetime and many more experience a mild form of depression. We establish a statistical significant correlation between depression and a recently defined index characterising the hypothalamus-pituitary-adrenal (HPA) axis. The relation supports the common belief that depression is caused by malfunctions in the HPA-axis. We suggest a novel model capable of showing both circadian as well as ultradian oscillations of the hormone concentrations related to the HPA-axis. The fast ultradian rhythm is generated in the hippocampus whereas the slower circadian rhythm is caused by the circadian clock. We show that these patterns fit data from 29 subjects. We demonstrate that patient-specific modelling is capable of making more precise diagnostics and offers a tool for individual treatment plans and more effective design of pharmaceutical molecules as a consequence. Three parameters related to depression are identified by non-linear mixed effects modelling and statistical hypothesis testing. These parameters represent underlying physiological mechanisms controlling the average levels as well as the ultradian frequency and amplitudes of the hormones ACTH and cortisol. The results are promising since they offer an exact aetiology for depression going from molecular level to systems physiology. |

11:10 AM 12:00 PM | Discussion: What can/should models be used for? To fit data? To make discoveries? To cure disease? (Discussion Leader: Stig Omholt) |

12:00 PM 01:30 PM | Lunch Break |

01:30 PM 02:05 PM | Robert Moss - Regulation of renal function: building a detailed and coherent mathematical model Among its many functions, the kidney regulates water and sodium excretion, both of which have significant consequences for whole-body homeostasis. A failure to conserve water can lead to death due to dehydration, and a failure to excrete sufficient quantities of sodium can lead to hypertension. To date, mathematical models of renal function have typically treated the kidney as either a "black box", or as a single (homogeneous) nephron. In either case, such models are ill-equipped to predict the consequences of functional changes in the kidney, which may arise in response to neurohumoral regulation, genetic disorders, gene knockouts, the onset of a renal or extra-renal pathology, or the administration of pharmacological interventions. I will discuss our efforts to build a whole-kidney model that explicitly represents the tubular and vascular architecture of the kidney, and which can accurately predict renal water and sodium excretion over a range of physiological conditions. |

02:15 PM 02:50 PM | Brian Carlson - Mechanisms of blood flow regulation and methods of integration into multiscale cardiovascular system models The vasculature dynamically responds to a myriad of acute signals reflecting local mechanical conditions, concentrations of neurohumoral substances and metabolic demand in the downstream tissue. The most well known of these mechanisms is the local response of vessels to their intraluminal pressure otherwise know as the myogenic response. Other mechanisms are more global in nature such as the delivery of norepinephrine through sympathetic enervation. In concert with these stimuli we have the conducted response, which is a mechanism acting remotely to convey metabolic state of the downstream tissue to the upstream supply vessels. The common thread of all these regulatory response mechanisms is that the end effectors are the circumferentially oriented vascular smooth muscle cells in the vessel wall that control the dilation and constriction of the vessel. This talk will present several theoretical models of mechanisms of blood flow regulation some developed at cell level and some at single vessel level resolution, show how these model can be defined from experimental data and then describe how these theoretical models may be utilized in comprehensive models of the cardiovascular system. |

02:50 PM 03:15 PM | Break |

03:15 PM 03:50 PM | Alison Hu - Modeling autonomic and metabolic dysfunction in sleep-disordered breathing using PNEUMA There is increasing recognition that sleep-disordered breathing (SDB), which is quite prevalent in obese subjects, can play an independent role in facilitating the development of autonomic and metabolic dysfunction. These abnormalities can lead to the emergence of metabolic syndrome, and subsequently with disease progression, to overt Type 2 diabetes (T2DM). The causal pathways linking SDB to T2DM remain controversial and relatively unexplored. We are developing a large-scale simulation model that would enable competing hypotheses of these causal pathways to be tested at the organ systems level. Our current efforts are based on an integrative model of respiratory, cardiovascular and sleep state control (€œPNEUMA€?) that was developed by us to characterize the underlying mechanisms that lead to SDB and to determine the effects of SDB on autonomic control of the cardiovascular system and sleep-wake control. We have extended PNEUMA by incorporating a metabolic component, representing the regulation of glucose, insulin, glucagon and free fatty acids using a multi-compartment model. An additional feature is the incorporation of the dynamics of beta-cell regulation. Changes in sympathetic output from the cardiorespiratory portion of PNEUMA, as well as changes in sleep-wake state, lead to changes in epinephrine output and blood flow to the tissues, in turn affecting the metabolism of glucose, insulin and FFA. €œMetabolic feedback€? takes the form of changes in insulin level, which lead to changes in sympathetic tone through stimulation of the alpha-sympathetic receptors. Consistent with clinical observations, the model predicts that increased severity of sleep apnea, as reflected in an increase in apnea-hypopnea index, leads to higher levels of fasting plasma insulin. Ongoing efforts are aimed at incorporating biological and biochemical processes that occur at the cellular or sub-cellular level, that would enable PNEUMA to simulate disease progression. |

04:00 PM 04:35 PM | Adam Mahdi - Stability and identifiability of biological models The study of various dynamic properties of biological models is of fundamental importance. The analysis of the local stability is usually studied by considering the linear part of a differential model and examining its set of eigenvalues. Unfortunately, when at least one of the eigenvalues has a zero real part (and the rest are negative) this method fails to provide the answer regarding the local stability as higher order terms of the system must be taken into account. In this talk we will discuss some alternative and computationally efficient approaches for determining the local stability of a steady state for multi-parameter differential systems. Another important tool for model analysis are methods for determining the structural identifiability, which can be viewed as necessary condition for the "stability" of the parameter estimation procedures. We will show some of our recent results related to structural identifiability of viscoelastic models and present some challenges in obtaining similar results for more general systems used in cardiovascular modeling. |

04:35 PM 04:45 PM | Discussion/Day's Wrap-up [Laura Ellwein] |

04:45 PM | Shuttle pick-up from MBI |

06:00 PM 07:00 PM | Cash Bar |

07:00 PM 09:00 PM | Banquet in the Fusion Room at Crowne Plaza |

Friday, May 9, 2014 | |
---|---|

Time | Session |

08:00 AM | Shuttle to MBI |

08:15 AM 09:00 AM | Breakfast |

09:00 AM 09:35 AM | Daniel Beard - Multi-scale modular modeling of cardiovascular function to probe the etiology of complex cardiovascular disease It is increasingly recognized that multifactorial diseases arise from interaction between genetic and environmental factors, and physiological systems. Examples of particular relevance to human health include the major health burdens that we face: cardiovascular disease and heart failure; metabolic syndrome and type 2 diabetes; and cancer. In all of these examples, acute and chronic (mal)adaptions of specific molecular mechanism and pathways in disease states occur against a background of physiological regulation. Since processes involved in complex disease operate in the context of physiological regulatory mechanisms, an understanding of a disease process builds upon an understanding of the associated physiological systems. The Virtual Physiological Rat (VPR) is a multi-national research program combining model-driven experiments and experimentally validated multi-scale models to develop theoretical and computational framework explaining: (1.) the long-term regulation of arterial pressure; and (2.) the etiology and sequelae of hypertensive heart disease, spanning molecular genetic to whole-body function. Recent results elucidating novel hypotheses for the mechanisms underlying primary hypertension and the role of metabolic alterations in heart failure will we presented. |

09:45 AM 10:20 AM | Naomi Chesler - Toward more comprehensive and data-driven mathematical models of the heart and circulations According to Claude Bernard, €œthe application of mathematics to natural phenomena is the aim of all science, because the expression of the laws of phenomena should always be mathematical.€? While much progress has been made in understanding natural phenomena since 1865 when Bernard made this statement and developing mathematical models of these phenomena, much work remains to be done. Whether these models range from the genome to the whole body or are more focused on a particular length-scale, time-scale and organ system, development and validation of physiological, mathematical models still require close collaboration between the theoretician and the experimentalist. An achievable goal in mathematical modeling today is a model of the cardiovascular system that describes the ejection of blood from the heart, from cross-bridge cycling dynamics to ventricular contraction; incorporates the anatomy, morphometry and biomechanics of the pulmonary and systemic circulations; and is able to connect these systems into one integrated system dependent on and responsible for oxygen delivery, waste removal, and homeostasis. In this presentation, I will share my perspective as an experimentalist. In particular, I will show a set of experimental data that are being used to validate a mathematical model of the heart, pulmonary and systemic circulations and preliminary modeling results. I will also present a vision for more in-depth experimental work that will enable development and validation of a more detailed model with shorter length scales, smaller time scales and better integration between the organ systems with the eventual and lofty goal of the application of mathematics to all cardiovascular phenomena. |

10:30 AM 10:45 AM | Break |

10:45 AM 11:20 AM | Jefferson Frisbee - A loss of system flexibility in the microcirculation: the critical contributor to poor organ performance in the metabolic syndrome? With metabolic syndrome (MS) in obese Zucker rats (OZR), the ability of in situ skeletal muscle to resist fatigue is compromised well before muscle function; implicating microvascular or perfusion-based impairments as playing a causal role. However, our results suggest that bulk flow to muscle is not sufficiently constrained to explain the poor performance, and indices such as dilator/constrictor reactivity, vessel wall mechanics and capillary density are not strong predictors of functional outcomes. We have determined that altered RBC distribution at arteriolar bifurcations (?) is increasingly heterogeneous in OZR muscle, iterating to produce a wide heterogeneity of pre-capillary flow distribution vs. controls. This increased spatial heterogeneity of perfusion at bifurcations is not compensated for via temporal switching, rather it is exacerbated owing to blunted temporal activity. The combined effect of these behaviors is that microvascular hematocrit becomes increasingly heterogeneous and fixed, compromising perfusion:demand matching and muscle performance. The magnitude of the deviation of ? from 0.5, and its temporal stability are the strongest predictors of muscle performance to date and reflect a striking loss of system flexibility for microvascular responses to imposed challenges under the setting of elevated cardiovascular disease risk. |

11:30 AM 12:05 PM | Jon Olav Vik - The virtues of virtual experiments in multiscale modelling Virtual experiments are essential in specifying, assaying, and comparing the behavioural repertoires of computational physiological models. This has applications in model composition, which is crucial for integrative research programmes such as the Virtual Physiological Human and the Human Brain Project. By clearly specifying (sub-) model requirements in terms of expected behaviours under standardised experiments, we envision that model composition could be made much more straightforward, focused and reliable, achieving the industry-level quality management that computational modelling needs to enter the clinical mainstream. A key step is that models and experimental protocols should be represented separately, but annotated so as to facilitate the linking of models to experiments and data. The rigorous, streamlined confrontation between experimental datasets and candidate (sub-) models would enable a "continuous integration" of biological knowledge, in clinical application as well as in model development and basic research. |

12:05 PM 12:30 PM | Discussion and wrap-up [Mette Olufsen] |

12:30 PM | Shuttle pick-up from MBI |

Name | Affiliation | |
---|---|---|

Archer, Kellie | kjarcher@vcu.edu | Biostatistics, Virginia Commonwealth University |

Arciero, Julia | jarciero@math.iupui.edu | Mathematics, Indiana University--Purdue University |

Battista, Christina | cbattis2@ncsu.edu | Department of Mathematics, North Carolina State University |

Beard, Daniel | beardda@gmail.com | Department of Physiology, Medical College of Wisconsin |

Bilinsky, Lydia | bilinsky@math.duke.edu | Mathematics, Duke University |

Calvetti, Daniela | daniela.calvetti@case.edu | Mathematics, Applied Mathematics and Statistics, Case Western Reserve University |

Cao, Yang | ycao@cs.vt.edu | Computer Science, Virginia Tech |

Carlson, Brian | Molecular and Integrative Physiology, University of Michigan | |

Chesler, Naomi | chesler@engr.wisc.edu | Biomedical Engineering, University of Wisconsin |

Cook, Daniel | dCook@uw.edu | Department of Biological Structure, University of Washington |

Craciun, Gheorghe | craciun@math.wisc.edu | Mathematics and Biomolecular Chemistry, University of Wisconsin-Madison |

Dunn, Robert | rrdunn@ncsu.edu | Biology, North Carolina State University |

Ellwein, Laura | Mathematics, Virginia Commonwealth University | |

Figueroa, C. Alberto | alberto.figueroa@kcl.ac.uk | Department of Biomedical Engineering, King's College |

Ford Versypt, Ashlee | ashleefv@mit.edu | Chemical Engineering, Massachusetts Institute of Technology |

Frisbee, Jefferson | Physiology and Pharmacology, West Virginia University | |

Fry, Brendan | yrfnadnerb@hotmail.com | Mathematics, Duke University |

Gennari, John | gennari@uw.edu | Biomedical Informatics and Medical Education, University of Washington |

Goswami, Tarun | tarun.goswami@wright.edu | Biomedical, Industrial and Human Factors Engineering, Wright State University |

Hellevik, Leif Rune | leif.r.hellevik@ntnu.no | Structural Engimeering, Norwegian University of Science and Technology |

Hill, Nicholas | Nicholas.Hill@maths.gla.ac.uk | School of Mathematics and Statistics, University of Glasgow |

Hu, Wen-Hsin | wenhsin@usc.edu | Biomedical Engineering, University of Southern California |

Joo, Jaewook | jjoo1@utk.edu | Physics, University of Tennessee |

Kim, Jae Kyoung | kim.5052@mbi.osu.edu | Mathematical Biosciences Institute, The Ohio State University |

Layton, Anita | alayton@math.duke.edu | Mathematics, Duke University |

Lee, Namyong | nlee@mnsu.edu | Department of Mathematics, Minnesota State University |

Lee, Pilhwa | pilee@med.umich.edu | Department of Molecular and Integrative Physiology, University of Michigan |

Liu, Aiping | aliu26@wisc.edu | Biomedical Engineering, University of Wisconsin-Madison |

Mahdi, Adam | adam.mahdi@gmail.com | Mathematics, North Carolina State University |

Makrides, Elizabeth | elizabeth_makrides@brown.edu | Division of Applied Mathematics, Brown University |

Malka, Roy | Roy_Malka@hms.harvard.edu | Systems Biology, Harvard Medical School |

Moss, Robert | robm@math.duke.edu | Mathematics, Duke University |

Olsen, Christian | chaarga@ncsu.edu | Biomathematics, North Carolina State University |

Olufsen, Mette | msolufse@ncsu.edu | Department of Mathematics, North Carolina State University |

Ottesen, Johnny | Johnny@ruc.dk | Department of Mathematics and Physics, Roskilde University Center |

Pantea, Casian | cpantea@math.wvu.edu | Mathematics, West Virginia University |

Pettersen, Klas | Centre for Molecular Medicine Norway, University of Oslo | |

Qutub, Amina | aminaq@rice.edu | Bioengineering, Rice University |

Reed, Michael | reed@math.duke.edu | Mathematics, Duke University |

Schild, John | jschild@iupui.edu | Department of Biomedical Engineering, Indiana University--Purdue University |

Schnell, Santiago | schnells@umich.edu | Department of Molecular & Integrative Biology, University of Michigan Medical School |

Sturdy, Jacob | jsturdy@ncsu.edu | Mathematics, North Carolina State University |

Temamogullari, Nihal | ezgitamam@yahoo.com | Mathematics, Duke University |

Tran, Hien | tran@ncsu.edu | Mathematics, North Carolina State University |

van de Vosse, Frans | F.N.v.d.Vosse@tue.nl | Department of Biomedical Engineering, Technische Universiteit Eindhoven |

Veneziani, Alessandro | ale@mathcs.emory.edu | Department of Mathematics and Computer Science, Emory University |

Vik, Jon Olav | jonovik@gmail.com | Department of Animal and Aquacultural Sciences, Norwegian University of Life Sciences |

Wiuf, Carsten | wiuf@math.ku.dk | Department of Mathematical Sciences, University of Copenhagen |

Zuhr, Erica | ezuhr@highpoint.edu | Mathematics, High Point University |

Ordinal scales are commonly used to measure health status and disease related outcomes. Notable examples include cancer staging, histopathological classification, adverse event rating, and severity of illness. In addition, repeated measurements are common in clinical practice for tracking and monitoring the progression of complex diseases. Classical likelihood-based ordinal modeling methods have contributed to the analysis of data in which the response categories are ordered and the number of covariates (*p*) is smaller than the sample size (*n*). With the emergence of genomic technologies being increasingly applied to identify molecular markers associated with complex disease phenotypes and outcomes, many research studies now include high dimensional feature data where* p >> n*, so that traditional methods cannot be applied. To fill this void we have developed an innovative penalized random coefficient ordinal response model for classifying and predicting disease progression along with time. Specifically our method extends the Generalized Monotone Incremental Forward Stagewise method (Hastie et al, 2007) to the ordinal response setting in combination with classical mixed effects modeling methods. We demonstrate our method using data from the Inflammation and the Host Response to Injury study in which Affymetrix gene expression profiles and Marshall Multiple Organ Dysfunction Score on six body systems were longitudinally collected at hospitalization day 1 up to day 30 in 169 patients.

Glaucoma is the second leading cause of blindness in the world and is characterized by progressive retinal ganglion cell death and irreversible visual field loss. Although elevated intraocular pressure has been identified as the primary risk factor for glaucoma and is the main target of glaucoma treatments, several vascular risk factors that lead to impaired retinal blood flow have also been correlated with the progression and incidence of glaucoma. Here, a multi-scale mathematical model is used to investigate the relative contributions of vascular risk factors on flow regulation and tissue oxygenation in the retina. A previously-developed fluid-structure interaction system modeling the central retinal artery is coupled to a vascular wall mechanics model for the vessels of the retinal microcirculation. Under normal conditions, the model predicts a 14% decrease in retinal perfusion if oxygen demand is decreased by 50% and a 33% increase in perfusion if demand is increased by 50%. These responses are impaired significantly if the metabolic or carbon dioxide mechanisms of retinal blood flow autoregulation are impaired. Changes in oxygen saturation levels in the retinal vascular network are also assessed as levels of mean arterial pressure, oxygen demand, and intraocular pressure are varied. Overall, the model results suggest that impaired autoregulation might increase the risk of retinal ischemic damage, as would occur in glaucoma, under conditions of elevated metabolic demand or decreased mean arterial pressure.

It is increasingly recognized that multifactorial diseases arise from interaction between genetic and environmental factors, and physiological systems. Examples of particular relevance to human health include the major health burdens that we face: cardiovascular disease and heart failure; metabolic syndrome and type 2 diabetes; and cancer. In all of these examples, acute and chronic (mal)adaptions of specific molecular mechanism and pathways in disease states occur against a background of physiological regulation. Since processes involved in complex disease operate in the context of physiological regulatory mechanisms, an understanding of a disease process builds upon an understanding of the associated physiological systems.

The Virtual Physiological Rat (VPR) is a multi-national research program combining model-driven experiments and experimentally validated multi-scale models to develop theoretical and computational framework explaining: (1.) the long-term regulation of arterial pressure; and (2.) the etiology and sequelae of hypertensive heart disease, spanning molecular genetic to whole-body function. Recent results elucidating novel hypotheses for the mechanisms underlying primary hypertension and the role of metabolic alterations in heart failure will we presented.

We present some recent work where how phenomena which occur at the microscopic scale are captured by macroscopic models which lack the fine resolution needed to describe them. This will be illustrated in the context of cellular brain energy metabolism by comparing a spatially distributed model with the capability to account for the proximity of blood vessels and diffusion, and a lumped model which assumes well mixed compartments.

According to Claude Bernard, â€œthe application of mathematics to natural phenomena is the aim of all science, because the expression of the laws of phenomena should always be mathematical.â€? While much progress has been made in understanding natural phenomena since 1865 when Bernard made this statement and developing mathematical models of these phenomena, much work remains to be done. Whether these models range from the genome to the whole body or are more focused on a particular length-scale, time-scale and organ system, development and validation of physiological, mathematical models still require close collaboration between the theoretician and the experimentalist.

An achievable goal in mathematical modeling today is a model of the cardiovascular system that describes the ejection of blood from the heart, from cross-bridge cycling dynamics to ventricular contraction; incorporates the anatomy, morphometry and biomechanics of the pulmonary and systemic circulations; and is able to connect these systems into one integrated system dependent on and responsible for oxygen delivery, waste removal, and homeostasis. In this presentation, I will share my perspective as an experimentalist. In particular, I will show a set of experimental data that are being used to validate a mathematical model of the heart, pulmonary and systemic circulations and preliminary modeling results. I will also present a vision for more in-depth experimental work that will enable development and validation of a more detailed model with shorter length scales, smaller time scales and better integration between the organ systems with the eventual and lofty goal of the application of mathematics to all cardiovascular phenomena.

Hunter and Bassingthwaithe define the Physiome as a set of multiscale, interacting mathematical models of physiology. Although available model repositories are an initial step toward this vision, it is a critical next step to develop computer-readable annotation for connecting codewords across models. Current hand-crafted model-building methods must be formalized and standardized to better support knowledge interaction and sharing. In particular, we argue for semantic annotations as a way of communicating the biophysical meaning of individual model codewords. Once annotated in a computable format, we can automatically find and connect models based on the annotation semantics of the biological entities and physiological properties.

In this talk, we present our approach to semantic annotation, using standard bio-ontology terms to relate physiological properties (e.g. pressure), to anatomical entities (e.g. blood). In turn, we use these annotations to semi-automatically find relevant models from repositories, and ultimately merge those models where appropriate. We present our results with SemGen, a prototype tool, for both building annotations and merging models, even across different modeling languages. If successful, our approach to develop interacting model repositories could accelerate model sharing and integration, and research that depends on the construction of complex models.

Complex interaction networks are present in all areas of biology, and manifest themselves at very different spatial and temporal scales. Persistence, permanence and global stability are emergent properties of complex networks, and play key roles in the dynamics of living systems.

Mathematically, a dynamical system is called persistent if, for all positive solutions, no variable approaches zero. In addition, for a permanent system, all variables are uniformly bounded. We describe criteria for persistence and permanence of solutions, and for global convergence of solutions to an unique equilibrium, in a manner that is robust with respect to initial conditions and parameter values.

A thorough understanding of these properties will allow for a better understanding of essential biological processes, such as homeostasis and adaptability.

One in six adults in the US have some form of coronary artery disease, characterized in particular by accumulation of atherosclerotic plaque. Though stenting is the most common treatment technique, it often leads to restenosis and thrombus formation. Computational modeling of human arteries from patient-specific image-based data offers a noninvasive way to investigate geometry, hemodynamics, and vascular disease corresponding with effects of stenting.

Improved strategies for stent-based patient-specific treatment of atherosclerotic lesions at coronary bifurcations require a greater understanding of normal coronary vessel morphology. We developed a method to quantify morphology in the left coronary artery for eventual use in bifurcating stent design. Computational models of the left main coronary were created from computed tomography (CT) images of 54 patients using ITK-Snap. Metrics assessed using Visualization Toolkit-based software and MATLAB included cross?sectional area, length, eccentricity, taper, curvature, branching law parameters, and bifurcation angles. Traditional statistical analysis using parametric tests for comparing and correlating means revealed significant differences both within and between bifurcations for most metrics.

Image-based computational models for quantifying hemodynamic indices in stented coronary arteries often employ biplane angiography and intravascular ultrasound for 3D reconstruction, but recent advances in optical coherence tomography (OCT) suggest more precise coronary artery reconstruction may be possible. We developed a patient-specific coronary artery reconstruction method that combines OCT, an intravascular imaging modality, with techniques for imaging wire pathway reconstruction adopted from graph theory. The pathway of the imaging wire was determined with a shortest path algorithm assuming minimum bending energy, and OCT images were registered orthogonal to the pathway with appropriate rotational orientation. Segments from both OCT in the stented region and CT upstream and downstream were imported into computational fluid dynamics software to quantify indices of wall shear stress (WSS). WSS results are presented using the method applied to imaging data of a left circumflex coronary artery acquired immediately post-stenting and after a 6-month follow-up period.

Findings from computational modeling studies using patient-specific imaging data may ultimately enhance our knowledge of both healthy coronary arteries and of harmful hemodynamic indices induced by stenting and could be leveraged for future stent design.

In this talk we will give an overview of a series of methods for 3D blood flow modeling, ranging from Kalman filtering techniques for automatic outflow and material parameter estimation to baroreflex model for automatic control of blood pressure. We will also discuss recent progress made on the validation of CFD predictions of pressure gradients in coarctation patients at rest and stress using clinical pressure data.

With metabolic syndrome (MS) in obese Zucker rats (OZR), the ability of in situ skeletal muscle to resist fatigue is compromised well before muscle function; implicating microvascular or perfusion-based impairments as playing a causal role. However, our results suggest that bulk flow to muscle is not sufficiently constrained to explain the poor performance, and indices such as dilator/constrictor reactivity, vessel wall mechanics and capillary density are not strong predictors of functional outcomes. We have determined that altered RBC distribution at arteriolar bifurcations (?) is increasingly heterogeneous in OZR muscle, iterating to produce a wide heterogeneity of pre-capillary flow distribution vs. controls. This increased spatial heterogeneity of perfusion at bifurcations is not compensated for via temporal switching, rather it is exacerbated owing to blunted temporal activity. The combined effect of these behaviors is that microvascular hematocrit becomes increasingly heterogeneous and fixed, compromising perfusion:demand matching and muscle performance. The magnitude of the deviation of ? from 0.5, and its temporal stability are the strongest predictors of muscle performance to date and reflect a striking loss of system flexibility for microvascular responses to imposed challenges under the setting of elevated cardiovascular disease risk.

Biological systems and their interactions often take place at nanometer level. However, engineering approaches, and modeling biological systems often is at macro or a global level. Examples include devices that mimic the anatomical joints and/or organs replacing them by utilizing the engineering materials in bio environments and follow them up for their durability. During the course of in vivo use of the devices new pathophysiology emerges, affecting other pathways that were not known before. Osteolysis in the case of total joint replacement arises from debris may also be initiated by metal ions. However, engineering approaches are evolving to reduce the debris from the liners in total joint replacements via new manufacturing routes and cross-linking the polymers as well as kinetics of wear rates of the liners. The presentation will show modeling methods utilized to optimize new total joint replacement models of the ankle, and others, understand the tear of anterior cruciate ligament and other injury mechanisms and develop new probabilistic methods to predict the injury occurrences. An overview of device and bone damage mechanics will be presented, at large scale.

In this talk we will present the recent progress in the ongoing development of a framework for the simulation of pressure and flow propagation in arterial networks. Focus will be given on how the effect of uncertainties in model parameters (correlated and uncorrelated) may be quantified. Further, the flexibility of the framework, which allows for the incorporation of organ models (e.g. renal) and multi-scale models for phenotypes such as arterial compliance, will be discussed.

A novel multiscale mathematical and computational model of the pulmonary circulation is presented and used to analyse both arterial and venous pressure and flow. This work is a major advance over previous studies using structured trees to model vascular beds, e.g. Olufsen et al. (2012), which only considered the arterial circulation. For the first three generations of vessels within the pulmonary circulation, geometry is specified from patient-specific measurements obtained using magnetic resonance imaging (MRI). Blood flow and pressure in the larger arteries and veins are predicted using a nonlinear, cross-sectional-area-averaged system of equations for a Newtonian fluid in an elastic tube. Inflow into the main pulmonary artery is obtained from MRI measurements, while pressure entering the left atrium from the main pulmonary vein is kept constant at the normal mean value of 2 mmHg. Each terminal vessel in the network of `large' arteries is connected to its corresponding terminal vein via a network of vessels representing the vascular bed of smaller arteries and veins. We develop and implement an algorithm to calculate the admittance of each vascular bed, using bifurcating structured trees and recursion. The structured-tree models take into account the geometry and material properties of the `smaller' arteries and veins of radii > 50 microns. We study the effects on flow and pressure associated with three classes of pulmonary hypertension expressed via stiffening of larger and smaller vessels, and vascular rarefaction. The results of simulating these pathological conditions are in agreement with clinical observations, showing that the model has potential for assisting with diagnosis and treatment of circulatory diseases within the lung.

References:

Olufsen, M.S., Hill, N.A., Vaughan, G.D.A., Sainsbury, C. & Johnson, M. (2012) Rarefaction and blood pressure in systemic and pulmonary arteries. J Fluid Mech 705:280-305.

Qureshi, M.U., Vaughan, G.D.A., Sainsbury, C., Johnson, M., Peskin, C.S., Olufsen, M.S. & Hill, N.A. (2014) Numerical simulation of blood flow and pressure drop in the pulmonary arterial and venous circulation, Biomechanics and Modeling in Mechanobiology. ISSN 1617-7959 (doi:10.1007/s10237-014-0563-y )

There is increasing recognition that sleep-disordered breathing (SDB), which is quite prevalent in obese subjects, can play an independent role in facilitating the development of autonomic and metabolic dysfunction. These abnormalities can lead to the emergence of metabolic syndrome, and subsequently with disease progression, to overt Type 2 diabetes (T2DM). The causal pathways linking SDB to T2DM remain controversial and relatively unexplored. We are developing a large-scale simulation model that would enable competing hypotheses of these causal pathways to be tested at the organ systems level. Our current efforts are based on an integrative model of respiratory, cardiovascular and sleep state control (â€œPNEUMAâ€?) that was developed by us to characterize the underlying mechanisms that lead to SDB and to determine the effects of SDB on autonomic control of the cardiovascular system and sleep-wake control. We have extended PNEUMA by incorporating a metabolic component, representing the regulation of glucose, insulin, glucagon and free fatty acids using a multi-compartment model. An additional feature is the incorporation of the dynamics of beta-cell regulation. Changes in sympathetic output from the cardiorespiratory portion of PNEUMA, as well as changes in sleep-wake state, lead to changes in epinephrine output and blood flow to the tissues, in turn affecting the metabolism of glucose, insulin and FFA. â€œMetabolic feedbackâ€? takes the form of changes in insulin level, which lead to changes in sympathetic tone through stimulation of the alpha-sympathetic receptors. Consistent with clinical observations, the model predicts that increased severity of sleep apnea, as reflected in an increase in apnea-hypopnea index, leads to higher levels of fasting plasma insulin. Ongoing efforts are aimed at incorporating biological and biochemical processes that occur at the cellular or sub-cellular level, that would enable PNEUMA to simulate disease progression.

A mathematical model of renal hemodynamics is used to assess the individual contributions of the tubuloglomerular feedback (TGF) mechanism and the myogenic response to glomerular filtration rate regulation in the rat kidney. The model represents an afferent arteriole segment, glomerular filtration, and a short loop of Henle. The afferent arteriole model exhibits myogenic response, which is activated by hydrostatic pressure variations to induce changes in membrane potential and vascular muscle tone. The tubule model predicts tubular fluid and Cl- transport. Macula densa Cl- concentration is sensed as the signal for TGF, which acts to constrict or dilate the afferent arteriole. With this configuration, the model afferent arteriole maintains stable glomerular filtration rate within a physiologic range of perfusion pressure (80-180 mmHg). The contribution of TGF to overall autoregulation is significant only within a narrow band of perfusion pressure values (80-110 mmHg). Model simulations of ramp-like perfusion pressure perturbations agree well with findings by Flemming et al. (J Am Soc Nephrol 12:2253-2262, 2001), which indicate that changes in vascular conductance is markedly sensitive to pressure velocity. That asymmetric response is attributed to the rate-dependent kinetics of the myogenic mechanism. Moreover, simulations of renal autoregulation in diabetes mellitus predict that, due to the impairment of the voltage-gated Ca2+ channels of the afferent arteriole smooth muscle cells, the perfusion pressure range in which SNGFR remains stable is reduced by ~70%, and that TGF gain is reduced by nearly 40%, consistent with experimental findings.

The study of various dynamic properties of biological models is of fundamental importance. The analysis of the local stability is usually studied by considering the linear part of a differential model and examining its set of eigenvalues. Unfortunately, when at least one of the eigenvalues has a zero real part (and the rest are negative) this method fails to provide the answer regarding the local stability as higher order terms of the system must be taken into account. In this talk we will discuss some alternative and computationally efficient approaches for determining the local stability of a steady state for multi-parameter differential systems.

Another important tool for model analysis are methods for determining the structural identifiability, which can be viewed as necessary condition for the "stability" of the parameter estimation procedures. We will show some of our recent results related to structural identifiability of viscoelastic models and present some challenges in obtaining similar results for more general systems used in cardiovascular modeling.

Among its many functions, the kidney regulates water and sodium excretion, both of which have significant consequences for whole-body homeostasis. A failure to conserve water can lead to death due to dehydration, and a failure to excrete sufficient quantities of sodium can lead to hypertension. To date, mathematical models of renal function have typically treated the kidney as either a "black box", or as a single (homogeneous) nephron. In either case, such models are ill-equipped to predict the consequences of functional changes in the kidney, which may arise in response to neurohumoral regulation, genetic disorders, gene knockouts, the onset of a renal or extra-renal pathology, or the administration of pharmacological interventions. I will discuss our efforts to build a whole-kidney model that explicitly represents the tubular and vascular architecture of the kidney, and which can accurately predict renal water and sodium excretion over a range of physiological conditions.

Orthostatic intolerance occurs when a transition to standing upright causes an imbalance in blood pressure and flow. It affects an estimated 500,000 Americans in particular young women (the female-to-male ratio is approximately 5:1). Symptoms of this disorder range from lightheadedness to fainting. Because many diseases exhibit these symptoms, this disorder can be difficult to diagnose. Moreover, several competing hypotheses have been put forward to explain this disorder, including imbalance of the blood volume regulation and reduced efficacy of the baroreflex control system. The most common tests performed to assess a patient's health are the head-up-tilt and sit-to-stand tests. These tests are designed to stimulate the cardiovascular control system via a simple change of body posture from supine to sitting or standing position. In response to the postural change, blood volume is pooled in the legs leading to a drop in blood pressure in the upper body. The blood pressure drop stimulates baroreceptor neurons, which, via sympathetic stimulation and parasympathetic withdrawal, regulate the heart pumping function and vessel properties facilitating return of blood flow and pressure to their homeostatic levels. This regulation is often disrupted in patients with orthostatic intolerance, often experienced by patients with diabetes, hypertension, and other neurological diseases of which Parkinsonâ€™s disease is the most prevalent. The autonomic nervous system is composed of many interacting components, yet measurements done to assess the system are typically limited to heart rate and blood pressure. One way to gain more understanding of the system is via mathematical modeling. This talk will demonstrate what insights can be learned using multiscale models predicting cardiovascular dynamics and the associated autonomic control.

Depression is a widely spread disease: In the Western world approximately 10% of the population experience severe depression at least once in their lifetime and many more experience a mild form of depression. We establish a statistical significant correlation between depression and a recently defined index characterising the hypothalamus-pituitary-adrenal (HPA) axis. The relation supports the common belief that depression is caused by malfunctions in the HPA-axis. We suggest a novel model capable of showing both circadian as well as ultradian oscillations of the hormone concentrations related to the HPA-axis. The fast ultradian rhythm is generated in the hippocampus whereas the slower circadian rhythm is caused by the circadian clock. We show that these patterns fit data from 29 subjects. We demonstrate that patient-specific modelling is capable of making more precise diagnostics and offers a tool for individual treatment plans and more effective design of pharmaceutical molecules as a consequence. Three parameters related to depression are identified by non-linear mixed effects modelling and statistical hypothesis testing. These parameters represent underlying physiological mechanisms controlling the average levels as well as the ultradian frequency and amplitudes of the hormones ACTH and cortisol. The results are promising since they offer an exact aetiology for depression going from molecular level to systems physiology.

The baroreflex is a negative feedback system for regulation of blood pressure. Its sensors, the baroreceptors located in the aortic wall and the carotid sinuses, are, however, not pressure sensors, but mechanoreceptors excited by stretch. Here we present a computational physiology model which shows that the increase in arterial stiffness that follows with age is sufficient to account for an overwhelming amount of experimental and clinical data on hypertension. We demonstrate quantitatively that the stiffening causes the baroreceptors to misinform the highly complex machinery responsible for blood pressure regulation. This misinformation occurs because the baroreceptors are strain sensitive, not pressure sensitive, and with stiffening the aortic wall strain ceases to be a good proxy for aortic blood pressure. In contrast to widely held opinions, the results suggest that primary hypertension can be attributed to a mechanogenic etiology without challenging current conceptions of renal and sympathetic nervous system function. And they support the view that a major target for treating chronic hypertension in the elderly is the reestablishment of a proper baroreflex response.

Oxygen is fundamental to life on Earth. In diseases affecting the vasculature including cancer and neurodegenerative diseases, abberrant hypoxic response is a critical part of the disease. Limited oxygen can lead to more aggressive tumors or determine our susceptibility to dementia. On the other hand, appropriate manipulation of proteins involved in cellular hypoxic response can help restore blood vessels and regenerate tissues. A challenge lies in understanding the complex cellular response to hypoxia both across different diseases and between patients with the detail needed to develop effective therapies. In this presentation, I will share how we are developing and integrating methods in multiscale modeling, machine learning, molecular biology, and microscopy image analysis to tackle the challenge of interpreting how changes at the molecular level affect cellular response and multicellular dynamics. My labâ€™s goal is to use computational systems biology methods to understand â€“ and ultimately control â€“biological response to oxygen across scales.

Mathematical models of physiological processes allow one to study the homeostatic mechanisms that keep important phenotypic variables within certain normal ranges. When these variables leave the homeostatic range often disease processes ensue. From the models one can derive surfaces that show the relationship between genetic polymorphisms and particularly important phenotypic variables. Known gene polymorphisms correspond to particular points on the surface, some of which are located near the edge of the homeostatic region. The purpose of medical advice tailored to the patientâ€™s genotype is to suggest dietary changes or exercise changes that move the patient back towards the middle of the homeostatic region.

One of the main functions of the endoplasmic reticulum (ER) is to serve as the cell protein-folding factory. The ER is responsible for the synthesis, folding, assembly and modification of one third of the eukaryotic proteome. Proteins enter the ER as unfolded polypeptide chains with variable fluxes depending on the physiological state of the cell. A sudden increase in the demand for a protein or the disruption of a folding reaction causes an imbalance between protein-folding load and capacity of the ER, which can lead to the accumulation of unfolded protein in the ER lumen. The ER protein balance is regulated by several signaling pathways, which are collectively termed the unfolded protein response. The unfolded protein response is activated by three transducers, which are enzymes whose oligomerization-induced activation is linked to perturbed protein folding in the ER. Three model mechanisms have been proposed for how these enzymes sense the unfolded protein load in the ER lumen: (i) direct recognition, (ii) indirect recognition and (iii) hybrid recognition. We developed detailed reaction mechanisms for each model and analyzed their dynamical behavior. We found that some of these mechanisms have serious discrepancies with the experimental data. We suggest a set of experiments that have not been yet carried out to test a detailed novel model mechanism of protein load sensing in the ER lumen, which explains current experimental findings. Our new model could provide new insights into the mechanisms of protein homeostasis in the ER.

Aortic baroreceptors are stretch sensitive neurons that generate afferent input to the baroreflex system. The system operates via negative feedback mediated by the autonomic nervous system. Changes in blood pressure stimulate the endings of the neurons via changes in arterial wall deformation, which stimulate mechanosensitive ion channels in the cell membrane of the neuron. The current through these serves to initiate action potentials along the baroreceptor axons. We model this process using a conductance based neuron model based on electrophysiological characterizations of the ion channels present in the baroreceptors. We consider patterns observed in baroreceptor firing rates and use model reduction, simulation, and parameter estimation methods to investigate possible physiological differences implied by variations in model parameters for each firing rate type.

Nonlinear hierarchical or mixed effects modeling is a statistical framework involving both fixed-effects and random effects for population parameters incorporating uncertainty associated with intra- and inter-subject variability. The inter-individual variability acknowledges the fact that the subject arises from a heterogeneous population of individuals by viewing the subject parameters as random variables. In this talk, we will view the intra-individual variability as two separated types of noises: uncorrelated measurement noise due to the effects of within-subject sources such as assay error, and system noise due to model misspecifications. This setup allows a more sophisticated method for handling models with structural misspecifications using stochastic differential equations (SDE). In the talk, we will discuss the implementation of SDEs into a nonlinear-mixed effects modeling framework. Using Metformin clinical data, which is a commonly prescribed treatment for type 2 diabetes, we will compare the model development results using an SDE approach to common practice using ordinary differential equations.

One of the main di?culties in the translation of mathematical models to the clinic for supporting clinical decision-making is assessing patient-speci?c values for the model parameters, the boundary and the initial conditions. Measurement modalities or data are not always available for all model parameters. In addition, the precision and accuracy of clinical measurements are hampered by large (biological) variations. Consequently, a balance is needed between the uncertainty resulting from model input parameters and the uncertainty resulting from model assumptions. For this, it is essential to quantify the uncertainty resulting from model input and to determine whether the complexity of the model is su?cient for the application of interest.

The aim of this study is to investigate model personalization (parameter ?xing and prioritization), model output uncertainty, and the number of runs required to reach convergence of their sensitivity estimates (i.e. computational cost) in case of a 1D pulse wave propagation model that was developed to support vascular access surgery planning [1].

The most common and straightforward method is to use crude Monte Carlo simulations in which the model is executed multiple times to estimate the sensitivity indices. This method, however, requires a lot of computational e?ort. Saltelli et al. [2] introduced a method that is computationally less demanding. This makes the method better applicable to computational expensive models or models with many model parameters. However, large computing resources are still required when applying the method to models with many model parameters. Finally, the method of Morris [3] is a global sensitivity analysis that is able to identify the few important model parameters among the many model parameters in the model with a relatively small number of model evaluations.

Our specific aim was to investigate whether model personalization could be performed by ?rst applying the Morris screening method that identi?es the non-important parameters and subsequently applying the Saltelli method to the resulting subset of important parameters. As this is expected to reduce the computational cost of the uncertainty and sensitivity analysis, this might improve clinical applicability. In addition the uncertainty of the model outputs was quantified using the same data that was generated for the sensitivity analysis.

The Saltelli method, which in general requires many model runs, is found to be a robust method for model personalization. Screening for the important parameters using the Morris method is found to work well for the complex cardiovascular wave propagation model for vascular access. The Morris method can therefore be used for parameter ?xing. However, it does not o?er any information in the setting of parameter prioritization, i.e. in identifying which parameters are most rewarding to measure as accurately as possible. The subsets of important parameters identi?ed for the output of interest lead to a significant complexity reduction.

We conclude that for model personalization of complex models it is advised to perform a screening for the important parameters using the method of Morris ?rst, and then perform a variance-based sensitivity analysis on the subset with only important parameters. For this purpose a Saltelli method can be used. Alternative and more computationally e?cient estimation methods not presented in this study are stochastic collocation methods based on polynomial chaos expansion.

[1]W. Huberts, C de Jonge, W.P.M. van der Linden, M.A Inda, J.H.M. Tordoir, F.N. van de Vosse, and E.M.H. Bosboom. A sensitivity analysis of a personalized pulse wave propagation model for arteriovenous ?stula surgery. Part A: Identi?cation of most in?uential model parameters. Med Eng Phys., 35(6):810â€“26, 2013.

[2]A. Saltelli. Making best use of model evaluations to compute sensitivity indices. Comp Phys Comm, 145:280â€“297, 2002.

[3]M.D. Morris. Factorial sampling plans for preliminary computational experiments. Technometrics, 33(2):161â€“174, 1991.

With the progressive inclusion of numerical simulations in medical research and clinical practice, accuracy and reliability of patient-specific computational analyses need to be properly certified. This raises new challenges when estimating patient-specific parameters that may be too difficult or even impossible to measure in practice. On the other hand, these parameters represent a macroscale synthesis

of molecular or mesoscale dynamics, but their practical individual-based quantification based on

modeling arguments is extremely difficult.

Data assimilation techniques are required to merge available data and numerical models to assess the reliability of a quantitative analysis. In this talk, variational procedures will be considered to estimate

(a) vascular compliance from available measures of displacement;

(b) cardiac conductivities from available measures of cardiac potentials.

Some theoretical as well as practical aspects of the numerical solution of these problems will

be addressed.

In particular, we pursue variational techniques based on a constrained minimization approach,

the constraint being represented by the fluid-structure interaction vascular problem

or by the Bidomain equations for electrocardiology.

We will discuss several technical details of this approach.

In general, these techniques lead to high computational costs and proper methods

for the sake of computational efficiency need to be adopted.

We consider in particular both methods based on simplified models for the forward problem

(like the Monodomain equation)

or on surrogate solutions obtained on the basis of the offline/online paradigm, like the Proper Orthogonal Decomposition method (POD). We will illustrate both succesfull experiences as well as pitfalls of these approaches.

Virtual experiments are essential in specifying, assaying, and comparing the behavioural repertoires of computational physiological models. This has applications in model composition, which is crucial for integrative research programmes such as the Virtual Physiological Human and the Human Brain Project. By clearly specifying (sub-) model requirements in terms of expected behaviours under standardised experiments, we envision that model composition could be made much more straightforward, focused and reliable, achieving the industry-level quality management that computational modelling needs to enter the clinical mainstream. A key step is that models and experimental protocols should be represented separately, but annotated so as to facilitate the linking of models to experiments and data. The rigorous, streamlined confrontation between experimental datasets and candidate (sub-) models would enable a "continuous integration" of biological knowledge, in clinical application as well as in model development and basic research.

In many situations we apply simplified models to complex dynamical systems, either because we are unaware of what the 'correct' model should look like, or because the 'correct' model is too complex to handle statistically/mathematically. In this talk, I will discuss model reduction for stochastic as well as deterministic biochemical reaction networks. In particular, I will focus on reduction by elimination of intermediate species, transient species that typically are consumed at a faster rate than non-intermediates and provide a number of results concerning equilibrium dynamics as well as non-equilibrium dynamics.

### Posters

An understanding of pressure and flow pulse wave propagation in conjunction with wall mechanics in the cardiovascular system via means of patient-specific vascular modeling can lead to better treatment of cardiovascular diseases and can have a lasting impact on diagnostic techniques. Computational models are playing a significant role in this area of research. This work discusses an arterial network, containing fourteen segments, which is fabricated by averaging single artery pressure-area data sets from eleven male Merino sheep. We employ a four-parameter viscoelastic Kelvin model to analyze ex vivo experimental measurements of blood pressure and cross-sectional area in a single vessel and determine an appropriate, realistic flow waveform. This flow waveform is then imposed upon the larger network using a simple two-parameter elastic wall model that predicts arterial wall deformation and a fluids model based on the 1-D Navier-Stokes equations. The results using the elastic wall and 1-D fluids model are compared to those found in the aforementioned data. The relationship between elastic and viscoelastic wall parameters associated with several large ovine arteries is discussed, and it is evident that the parameters associated with each artery, as well as the pressure-area curves, vary among the locations in a network. An overview of the experimental and numerical results is shown where both wall models demonstrate that smaller arteries are stiffer than larger arteries, a physiologically known phenomena. A novel approach to calculating zero-strain radius from measurable data is identified, and a relationship between arterial stiffness and zero-strain radius is discussed.

Christina Battista1, Daniel Bia Santana2, Yanina Zócalo Germán2, Ricardo L. Armentano2, Mansoor A. Haider1, Mette S. Olufsen1

1Department of Mathematics, North Carolina State University, 2Department of Physiology, Universidad de la Republica

The vasculature dynamically responds to a myriad of acute signals reflecting local mechanical conditions, concentrations of neurohumoral substances and metabolic demand in the downstream tissue. The most well known of these mechanisms is the local response of vessels to their intraluminal pressure otherwise know as the myogenic response. Other mechanisms are more global in nature such as the delivery of norepinephrine through sympathetic enervation. In concert with these stimuli we have the conducted response, which is a mechanism acting remotely to convey metabolic state of the downstream tissue to the upstream supply vessels. The common thread of all these regulatory response mechanisms is that the end effectors are the circumferentially oriented vascular smooth muscle cells in the vessel wall that control the dilation and constriction of the vessel.

This talk will present several theoretical models of mechanisms of blood flow regulation some developed at cell level and some at single vessel level resolution, show how these model can be defined from experimental data and then describe how these theoretical models may be utilized in comprehensive models of the cardiovascular system.

Ranjan K. Pradhan, Pilhwa Lee, Daniel A. Beard and Brian E. Carlson

Department of Molecular and Integrative Physiology, University of Michigan, Ann Arbor, Michigan

Vascular smooth muscle cell contraction and relaxation is central to the local regulation of blood flow to tissue. At the arteriolar level, interactions between vascular endothelial cells and smooth muscle cells play a critical role in determining the level of vascular tone. During mechanical and/or agonist stimulations, vascular Ca^{2+} dynamics are finely adjusted via a number of signaling pathways and the Ca^{2+} levels in the smooth muscle cells determine the level of contraction. To quantify how cellular Ca^{2+} dynamics are transformed into changes in vascular tone, we have constructed a cellular-based model of isolated resistance vessel by integrating models of vessel wall mechanics, smooth muscle force generation, smooth muscle Ca^{2+} handling and electrophysiology with an endothelial electrophysiology and Ca^{2+} handling model. The dose-response vasodilation and vasoconstriction data of different sizes of vessels in response to pharmacological vasoconstrictors and vasodilators, measured using a novel isovolumic myograph developed by Lu and Kassab are analyzed. The model simulates how the changes in intraluminal pressure result from the maintenance of a constant vessel diameter during application of phenylephrine and acetylcholine. In order to simulate these sets of experimental data the model captures integrated vessel behavior including ionic (Ca^{2+}, K^{+}, Na^{+}, etc.), nitric oxide and IP_{3} myoendothelial transport. Model analysis shows that Î±-adrenergic pathways in the smooth muscle and NO pathways in endothelial cells are sufficient to capture the experimentally observed vasodilation and constriction.

Note: This poster is reused from a faculty candidate poster session at a chemical engineering conference.

I am interested in research at the intersection of chemical engineering, computational science and engineering, applied mathematics, and biology. Many applications with great societal impact lie within the intersection of these disciplines, such as advanced pharmaceutical and medical technologies. The current pharmaceutical drug discovery and approval pipeline averages 13 years, has an attrition rate of 95%, costs more than $1 billion per approved drug, and has major impacts on clinical patient care. Predictive mathematical modeling has the potential to make significant improvements on this pipeline in several domains that often involve reacting systems with mass and energy transport on multiple length and time scales making them particularly challenging to understand mechanistically from experiments alone. Specifically, I am interested in modeling downstream processes related to how candidate drug compounds are put into formulations for dosing (manufacturing), how the drugs are released from the formulations inside patients (drug delivery), how the drugs are distributed throughout the human body and tissues (pharmacokinetics), and how the drugs dynamically affect physiological functions (pharmacodynamics).

In my research program, I aim to develop mechanistic models of dynamic physiological processes, including metabolism and transport in biological tissues, that consider the effects of pharmaceutical treatments across multiple time and length scales to translate cellular- and tissue-level insights to clinical application. These models offer ways to predict the pharmacokinetic and pharmacodynamic interactions between drugs and their distribution and impact on the human body, the impact of controlled-release drug delivery dosages on tissue-level responses, and role of therapeutics and metabolites in the pathology of diseased populations. In the poster, I offer snapshots of applications of these types of models applied to drug delivery, dosage manufacturing, and multiscale physiology.

A theoretical model is presented to analyze the impact on oxygen distribution of the heterogeneous organization of the rat outer and inner medulla revealed in anatomical studies. The present study extends the region-based mathematical model of the rat renal medulla developed by Layton (AJP Renal 300: F356-F371, 2011), which was formulated to represent sodium chloride (NaCl) and urea, to include transport of red blood cells (RBCs), deoxyhemoglobin (Hb), oxyhemoglobin (HbO2), and free oxygen (O2). Both basal cellular oxygen consumption throughout the whole medulla and active oxygen consumption via active NaCl transport in medullary ascending and descending limbs are considered. Model equations are based on conservation of water and solutes, as well as transmural transport, and are solved to steady state. Results from the model suggest that the structural organization of the outer and inner medulla produces significant axial and radial PO2 gradients, and impacts the effectiveness of the medullary urine concentrating mechanism.

In biochemical networks, reactions often occur on disparate timescales and can be characterized as either “fast” or “slow.” The quasi-steady state approximation (QSSA) utilizes timescale separation to project models of biochemical networks onto lower-dimensional slow manifolds. As a result, fast elementary reactions are not modeled explicitly, and their effect is captured by non-elementary reaction rate functions (e.g. Hill functions). The accuracy of the QSSA applied to deterministic systems depends on how well timescales are separated. Recently, it has been proposed to use the non-elementary rate functions obtained via the deterministic QSSA to define propensity functions in stochastic simulations of biochemical networks. In this approach, termed the stochastic QSSA, fast reactions that are part of non-elementary reactions are not simulated, greatly reducing computation time. However, it is unclear when the stochastic QSSA provides an accurate approximation of the original stochastic simulation. We show that, unlike the deterministic QSSA, the validity of the stochastic QSSA does not follow from timescale separation alone, but also depends on the sensitivity of the non-elementary reaction rate functions to changes in the slow species. The stochastic QSSA becomes more accurate when this sensitivity is small. Different types of QSSAs result in non-elementary functions with different sensitivities, and the total QSSA results in less sensitive functions than the standard or the pre-factor QSSA. We prove that, as a result, the stochastic QSSA becomes more accurate when non-elementary reaction functions are obtained using the total QSSA. Our work provides a novel condition for the validity of the QSSA in stochastic simulations of biochemical reaction networks with disparate timescales.

A bidomain formulation was developed to simulate propagation of electrical signals in endothelial cells of microvascular networks. The method is used to stimulate spatiotemporal signal propagation and attenuation in arterioles and capillaries, and analyze data from experiments on isolated vessels. A single-vessel (capillary) segment model is parameterized based on conducted response data of isolated endothelial cells tube from mouse skeletal muscle feed arteries on changes in endothelial cell membrane voltages in response graded electrical stimulation. Simulation of the resulting model facilitates determination of appropriate boundary conditions to apply along the length in simulating signal propagation in whole capillary network. The model fits well to the observed spatial attenuation of the depolarization of endothelial cells, with activated/inactivated calcium-activated potassium channels of the membrane, and predicts the electrical length constant dependency on acetylcholine. Simulations of realistic network topologies are then conducted to determine the effective time and space scales for metabolic signaling in the microvascular networks, especially with the vasodilator acetylcholine. This framework is a foundation for further study of spatiotemporal aspects of the electrical conduction in various microvascular networks.

This study presents a mathematical model of the baroreflex regulation of heart rate to changes in blood pressure during head-up tilt. Changes in posture from supine to upright position causes gravitational pool of blood in the lower extremities reducing blood pressure in the upper body, while blood pressure in the lower extremities go up. In response the baroreflex system is activated restoring blood pressure in the upper body. The system operates via activation of pressure sensitive baroreceptor neurons located in the carotid arteries, signals emanating in these neurons are integrated in the autonomic nervous system (ANS), which activate the parasympathetic and sympathetic nervous systems accordingly. The parasympathetic signal is mediated by the vagus nerve and at the synapse causes the release of acetylcholine, effectively slowing the heart through its effect on the ion-influx of the pacemaker cells. The sympathetic signal is mediated through the ganglia and cause release of noradrenaline, that through the pacemaker cells increases heart rate. In addition it is believed that respiration plays an important role in the short term regulation through a direct effect from the respiratory center on the parasympathetic activity, in turn affecting heart rate.

In its simplest form, the arterial baroreceptor reflex (BRx) is a negative feedback controller of heart rate and an essential component of cardiovascular autonomic control. Clinical measures of autonomic function such as BRx sensitivity and heart rate variability (HRV) are gaining recognition as potentially reliable indicators of cardiac health and disease progression but considerable controversy remains. Our experimental and computational work strives to enhance knowledge concerning the cellular level mechanisms underlying the neural coding and signal integration of arterial pressure dynamics and the manner in which these may impact the unique functional properties of the BRx. Transduction of the magnitude and time course of arterial pressure begins at mechanosensitive nerve terminals (baroreceptors) that can be neuroanatomically classified as either myelinated or unmyelinated sensory afferents, with each phenotype exhibiting strikingly different patterns of neural discharge. Results from whole animal BRx studies suggest that the more sensitive, lower threshold myelinated baroreceptors may function more toward buffering acute changes in arterial blood pressure whereas the less sensitive, higher threshold unmyelinated baroreceptors may function more toward controlling mean arterial pressure. More recently, our experimental studies have been guided by the increasing clinical evidence for sexual dimorphism in cardiovascular health and disease and in particular BRx function. Using female rats, we previously identified a distinct myelinated baroreceptor phenotype that exhibits functional dynamics and ionic currents that are a mix of those observed in barosensory afferents functionally identified as myelinated (A-type) or unmyelinated (C-type). Interestingly, these â€œAh-typeâ€? myelinated afferents constitute nearly 50% of the total population of myelinated aortic baroreceptors in female but less than 2% in male rat. We hypothesize that the observed sexual dimorphism in BRx function may be a result of, at least in part, differences in the population of myelinated baroreceptor afferents between males and females. Subsequent whole animal, in situ BRx studies have demonstrated that females (n = 16) exhibit significantly greater BRx responses as compared to males (n =17) at stimulus intensities selective for activation of A-type and Ah-type myelinated afferents (P < 0.05). Collectively, our results provide evidence that in females, two anatomically distinct myelinated afferent pathways contribute to integrated BRx function whereas in males there is only a single pathway with a far more uniform population of myelinated afferents. These functional and neuroanatomical differences may account for, at least in part, the well documented enhanced parasympathetic control of blood pressure in females.

Grace C. Santa Cruz Chavez and John H. Schild

Stark Neurosciences Research Institute and Department of Biomedical Engineering,

Indiana University Purdue University Indianapolis, IN

Sex differences in autonomic basal cardiovascular control are well documented. Consistent baroreflex studies demonstrate that women have greater tonic parasympathetic cardiac control than men. Sex hormones may partly account for such sex bias, however, physiological mechanism(s) that mediate their effects remain poorly understood. We previously showed that female rats have a unique and functionally distinct class of low threshold, myelinated (Ah-type) aortic baroreceptor afferents that are rarely observed in males. These Ah-type afferents exhibit functional dynamics and ionic currents that are a mix of those observed in barosensory afferents functionally identified as myelinated (A-type) or unmyelinated (C-type). We hypothesized that an afferent basis for sexual dimorphism in baroreflex function exists and investigated the functional impact Ah-type afferents have upon the aortic baroreflex. Whole nerve conduction study of the left aortic depressor nerve in male (n = 9) and female (n = 7) rats showed that the recruitment and conduction velocity profiles of myelinated barosensory axons are sexually dimorphic. Subsequent baroreflex studies demonstrated that females (n = 16) exhibit significantly greater (P < 0.05) depressor responses compared to males (n =17) at stimulus intensities selective for myelinated afferents. Collectively, our results provide evidence that, in females, two distinct myelinated afferent pathways contribute to the integrated baroreflex function whereas in males there is a single pathway due to a far more uniform population of myelinated afferents. These functional differences may account for, at least in part, the enhanced control of blood pressure in females.

**The virtues of virtual experiments in multiscale modelling**

Jon Olav Vik

Virtual experiments are essential in specifying, assaying, and comparing the behavioural repertoires of computational physiological models. This has applications in model composition, which is crucial for integrative research programmes such

**A loss of system flexibility in the microcirculation: the critical contributor to poor organ performance in the metabolic syndrome?**

Jefferson Frisbee

With metabolic syndrome (MS) in obese Zucker rats (OZR), the ability of in situ skeletal muscle to resist fatigue is compromised well before muscle function; implicating microvascular or perfusion-based impairments as playing a causal role.

**Toward more comprehensive and data-driven mathematical models of the heart and circulations**

Naomi Chesler

According to Claude Bernard, €œthe application of mathematics to natural phenomena is the aim of all science, because the expression of the laws of phenomena should always be mathematical.€? While much progress

**Multi-scale modular modeling of cardiovascular function to probe the etiology of complex cardiovascular disease**

Daniel Beard

It is increasingly recognized that multifactorial diseases arise from interaction between genetic and environmental factors, and physiological systems. Examples of particular relevance to human health include the major health burdens that we

**Modeling autonomic and metabolic dysfunction in sleep-disordered breathing using PNEUMA**

Wen-Hsin Hu

There is increasing recognition that sleep-disordered breathing (SDB), which is quite prevalent in obese subjects, can play an independent role in facilitating the development of autonomic and metabolic dysfunction. These abnormalities can l

**Mechanisms of blood flow regulation and methods of integration into multiscale cardiovascular system models**

Brian Carlson

The vasculature dynamically responds to a myriad of acute signals reflecting local mechanical conditions, concentrations of neurohumoral substances and metabolic demand in the downstream tissue. The most well known of these mechanisms is the

**Regulation of renal function: building a detailed and coherent mathematical model**

Robert Moss

Among its many functions, the kidney regulates water and sodium excretion, both of which have significant consequences for whole-body homeostasis. A failure to conserve water can lead to death due to dehydration, and a failure to excrete suf

**Patient specific modelling of the endocrine HPA-axis and its relation to depression: Ultradian and circadian oscillations**

Johnny Ottesen

Depression is a widely spread disease: In the Western world approximately 10% of the population experience severe depression at least once in their lifetime and many more experience a mild form of depression. We establish a statistical signi

**Modeling blood pressure and heart rate dynamics in patients with orthostatic intolerance**

Mette Olufsen

Orthostatic intolerance occurs when a transition to standing upright causes an imbalance in blood pressure and flow. It affects an estimated 500,000 Americans in particular young women (the female-to-male ratio is approximately 5:1). Symptom

**Patient-specific parameter estimation in computational hemodynamics: from simulations to assimilations**

Alessandro Veneziani

With the progressive inclusion of numerical simulations in medical research and clinical practice, accuracy and reliability of patient-specific computational analyses need to be properly certified. This raises new challenges when estimating

One in six adults in the US have some form of coronary artery disease, characterized in particular by accumulation of atherosclerotic plaque. Though stenting is the most common treatment technique, it often leads to restenosis and thrombus f

**Personalization of 1D Wave Propagation Models of the Cardiovascular System**

Frans van de Vosse

One of the main di?culties in the translation of mathematical models to the clinic for supporting clinical decision-making is assessing patient-speci?c values for the model parameters, the boundary and the initial conditions. Measurement mod

**A structured tree model for the pulmonary circulation**

Nicholas Hill

A novel multiscale mathematical and computational model of the pulmonary circulation is presented and used to analyse both arterial and venous pressure and flow. This work is a major advance over previous studies using structured trees to mo

**Assessing vascular risk factors for glaucoma using a mathematical model of blood flow in the retina**

Julia Arciero

Glaucoma is the second leading cause of blindness in the world and is characterized by progressive retinal ganglion cell death and irreversible visual field loss. Although elevated intraocular pressure has been identified as the primary risk

**Arterial Stiffening Provides Sufficient Explanation for Primary Hypertension**

Klas Pettersen

The baroreflex is a negative feedback system for regulation of blood pressure. Its sensors, the baroreceptors located in the aortic wall and the carotid sinuses, are, however, not pressure sensors, but mechanoreceptors excited by stretch. He

**Ordinal Response Models for Modeling Longitudinal High-Dimensional Genomic Feature Data**

Kellie Archer

Ordinal scales are commonly used to measure health status and disease related outcomes. Notable examples include cancer staging, histopathological classification, adverse event rating, and severity of illness. In addition, repeated measureme

**Part 2: Codeword annotation for sharing and merging physiological models**

Daniel Cook

Hunter and Bassingthwaithe define the Physiome as a set of multiscale, interacting mathematical models of physiology. Although available model repositories are an initial step toward this vision, it is a critical next step to develop compute

**Part 1: Codeword annotation for sharing and merging physiological models**

John Gennari

Hunter and Bassingthwaithe define the Physiome as a set of multiscale, interacting mathematical models of physiology. Although available model repositories are an initial step toward this vision, it is a critical next step to develop compute

**Modeling Biomedical Systems - An Engineering Approach**

Tarun Goswami

Biological systems and their interactions often take place at nanometer level. However, engineering approaches, and modeling biological systems often is at macro or a global level. Examples include devices that mimic the anatomical joints an

**Recent advances in uncertainty quantification for material parameters in arterial network simulations**

Leif Rune Hellevik

In this talk we will present the recent progress in the ongoing development of a framework for the simulation of pressure and flow propagation in arterial networks. Focus will be given on how the effect of uncertainties in model parameters (

**Multi-scale challenges in brain cellular metabolism**

Daniela Calvetti

We present some recent work where how phenomena which occur at the microscopic scale are captured by macroscopic models which lack the fine resolution needed to describe them. This will be illustrated in the context of cellular brain energy

**Recent Advances in 3D Blood flow Simulation: From Parameter Estimation Methods to Clinical Applications**

C. Alberto Figueroa

In this talk we will give an overview of a series of methods for 3D blood flow modeling, ranging from Kalman filtering techniques for automatic outflow and material parameter estimation to baroreflex model for automatic control of blood pres

**Persistence, Permanence, and Global Stability in Biological Interaction Networks**

Gheorghe Craciun

Complex interaction networks are present in all areas of biology, and manifest themselves at very different spatial and temporal scales. Persistence, permanence and global stability are emergent properties of complex networks, and play key r