### Organizers

PSW@MBI is a week-long workshop where participating mathematical modelers tackle questions proposed by life science researchers. Similar workshops have provided fresh perspectives and new ideas to proposed questions and established new interdisciplinary collaborations between theoreticians and life scientists. The workshop gives the opportunity to practitioners and researchers in medicine and the biosciences who present problems to exploit the expertise of applied mathematical faculty, postdoctoral fellows, and graduate students in working toward solutions to their problems. Workshop Format Participants will include between 50-60 applied mathematicians, statisticians and domain experts. Problems will be presented on the first day and participants will divide into teams of 6-10 self-selected people each. The teams will collaborate and brain-storm on their problems, and present their solution on the final day of the workshop. Problem presenters have domain knowledge, which is needed throughout the workshop and will be available during the workshop to provide background information. Deliverables The teams will prepare reports for the problem sponsors shortly after the end of the workshop. Cost Accepted participants will receive partial travel support, hotel, and a small per diem.

### Accepted Speakers

Monday, July 16, 2012 | |
---|---|

Time | Session |

09:45 AM 10:15 AM | Martin Frasch - Online detection of physiological fetal distress pattern during birth This proposal is derived from our studies on changes of fetal brain electrical activity (electroenkephalogram, EEG) and heart rate (FHR) which we recorded during simulated labour in fetal sheep model of human pregnancy and fetal development. The goal is to develop mathematical models allowing online detection of physiological patterns alarming of incipient fetal distress in clinical conditions of labour. There are two major aspects of the problem: 1. A pattern of time correlated changes in EEG and FHR is now known to occur during conditions of deteriorated blood supply to the fetus as it may occur during labour. This pattern is an early predictor of immanent severe drop in fetal pH. Fetal pH under 7.00 (severe acidemia) is associated with increased risk of brain injury and sustained neurological deficits. In obstetrical care, an urgent need exists for technologies allowing the detection of such severe acidemia in fetus. We describe the phenomenon in detail in Frasch et al (2011). Question 1: Can we create a mathematical model of this phenomenon robust enough to be capable of capturing the onset of the pattern online despite varying EEG/FHR signal characteristics? 2. Certain properties of FHR variability (FHRV, higher order fluctuations in FHR on millisecond time scale) can also be used for early detection of the onset of severe acidemia. FHRV can be calculated in different signal property domains (linear, nonlinear, time and frequency or both). Different measures of FHRV are known to reflect somewhat different aspects of underlying physiological activities and probably carry a predictive value variable in time. A group of FHRV measures is likely to provide a higher positive predictive value of fetal acidemia than one particular FHRV measure alone. Please see also Frasch (2011). Question 2: Can we develop a mathematical model to allow us to 1) identify the FHRV measures that would perform best together to detect the pathophysiological mechanism of incipient acidemia and 2) incorporate such FHRV measures into the model that captures the correlated changes in EEG and FHR? In a broader sense, we hope that such approach would help create a novel paradigm for context-specific generation of mathematical models for online detection of complex physiological patterns. Ideally, this new paradigm should go beyond a purely statistical or data mining framework. For example, can we build a model that incorporates physiological mechanisms into a standard data mining approach? In order to facilitate the discussion and modeling building exercise, relevant data will be provided for workshop participants. |

10:15 AM 10:45 AM | Ewen King-Smith - The structure of the lipid layer of the tear film Dry eye disorders affect about 15% of older Americans and are poorly understood.Â Â Increased evaporation is an important contributing factor.Â Â The superficial lipid layer of the tear film is normally an excellent barrier to evaporation but its effectiveness is often reduced in dry eye disorders.Â Â This lipid, called meibum, is secreted from meibomian glands in the lids. The main components of meibum are wax esters and cholesteryl esters with smaller quantities of polar and other lipids.Â Â Also, surfactant proteins probably play an important role.Â Â The esters often contain a proportion of long, saturated hydrocarbon chains which are thought to help increase resistance to evaporation.Â Â Another important characteristic of the lipid layer is its ability to withstand the blink cycle which causes compression to a small fraction of the original area, followed by expansion.Â Â Â Lipids with long, saturated hydrocarbon chains often do not reâ€?spread to their original state after compression and expansion, so the inclusion of unsaturated hydrocarbon chains in meibum may aid in respreading after a blink. The molecular organization of the lipid layer is poorly understood.Â Â Â The team will be asked to consider and propose models of molecular structure of the lipid layer, and to evaluate their consistency with observed properties which will be presented.Â Â Â |

11:00 AM 11:30 AM | Thomas Rosal - Mathematical model of blood ionized calcium concentration The blood ionized calcium concentration (Ca2+, iCa) is tightly regulated in animals ranging from the most primitive fishes and nonvertebrates to humans. This is because iCa is utilized by diverse cell types as a transcellular and intracellular signaling molecule, such as in the nervous system, cardiac and skeletal muscle, epithelial cells, endocrine cells, blood cells, among others. The blood ionized calcium concentration is approximately 1.5 mM in all animals. If the concentration changes by as little as 10-20% dysregulation of body systems (such as the neuromuscular system) will result and can be fatal. Therefore, there are multiple, redundant regulatory systems that exist to maintain blood calcium in a narrow biological range. Terrestrial animals live in a calcium poor environment and are dependent upon calcium absorption from the gastrointestinal tract to provide calcium as a regulatory ion and component of bones. In contrast, sea animals live in a calcium rich environment (since seawater has 10 mM calcium) and excretion of calcium is important. |

11:30 AM 12:00 PM | Matthew Doyle - Development of a mathematical model for microindentation of aortic valve leaflets to aid in the determination of local micromechanical properties Calcific aortic valve disease (CAVD) is the most common heart valve disease, affecting over 25% of the population in developed countries. The hallmark of early CAVD is focal changes in the mechanical properties of the extracellular matrix (ECM) in the valve leaflets. In particular, proteoglycan-rich lesions begin to form on the surface of the fibrosa layer of these leaflets. Maladaptive remodeling of the ECM is hypothesized to negatively influence valve cell function, ultimately resulting in stiffened leaflets that do not function properly. To date, the local micromechanical properties of healthy and diseased valve leaflets have not been characterized. The objectives of the present study are to measure local micromechanical properties of the three layers of porcine aortic valve leaflets (fibrosa, spongiosa, and ventricularis), and of these proteoglycan-rich lesions, and to develop material models for these layers and the lesions that take into account material non-linearity and heterogeneity. Leaflets will be obtained from healthy swine as well as those with early stage CAVD; comparison between the material models developed for the two cases will help identify changes in the local micromechanical properties of the aortic valve leaflets during the onset of CAVD. To obtain the experimental data, a microindenter will be used to deform the surface of the leaflets. From these experiments, we will obtain the indenter depth and the corresponding force. We will also know the shape and size of the indenter and the shape and size of the tissue region deformed by the indentation. |

12:00 PM 12:30 PM | Masami Tatsuno - Information geometric analysis for multi-neuronal spike trains - Estimation of directional interaction and direct/indirect synaptic connections Understanding how the brain works is one of the most challenging questions of modern science. It is important not only for expanding the frontier of our scientific knowledge, but also for developing a more effective treatment for neuronal diseases. The brain is composed of a large number of neurons. Most neurons interact with other neurons via action potentials (spikes), and have the tendency to form cell-assemblies (1) that can be organized dynamically through information processing in the brain. To study these group dynamics and their role in cognitive functions, it is important to record simultaneously from as many neurons as possible from behaving animals (2). Due to recent technological developments, multi-electrode recordings have become an increasingly widespread tool in electrophysiology, enabling the recording of spiking activity from tens to hundreds of neurons simultaneously |

Tuesday, July 17, 2012 | |
---|---|

Time | Session |

Wednesday, July 18, 2012 | |
---|---|

Time | Session |

Thursday, July 19, 2012 | |
---|---|

Time | Session |

Friday, July 20, 2012 | |
---|---|

Time | Session |

09:10 AM 09:35 AM | Ewen King-Smith - The structure of the lipid layer of the tear film (report) Summary Report from The structure of the lipid layer of the tear film problem solving workshop |

09:35 AM 10:00 AM | Thomas Rosal - Mathematical model of blood ionized calcium concentration (report) Summary Report on Mathematical model of blood ionized calcium concentration |

10:00 AM 10:25 AM | Masami Tatsuno - Information geometric analysis for multi-neuronal spike trains - Estimation of directional interaction and direct/indirect synaptic connections (report) Summary Report for Information geometric analysis for multi-neuronal spike trains - Estimation of directional interaction and direct/indirect synaptic connections |

10:40 AM 11:05 AM | Martin Frasch - Online detection of physiological fetal distress pattern during birth (report) Summary Report for Online detection of physiological fetal distress pattern during birth |

11:05 AM 11:30 AM | Matthew Doyle - Development of a mathematical model for microindentation of aortic valve leaflets to aid in the determination of local micromechanical properties (report) Summary Report for Development of a mathematical model for microindentation of aortic valve leaflets to aid in the determination of local micromechanical properties |

11:30 AM 11:55 AM | Nicanor Moldovan - Using magnetic force to colonize fibrillar scaffolds with stem/progenitor cells (report) Summary Report for Using magnetic force to colonize fibrillar scaffolds with stem/progenitor cells |

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

Bell, Jonathan | jbell@math.umbc.edu | Department of Mathematics & Statistics, University of Maryland Baltimore County |

Bohun, Sean | sean.bohun@uoit.ca | Science, University of Ontario Institute of Technology |

Braun, Richard | braun@math.udel.edu | Department of Mathematical Sciences, University of Delaware |

Breward, Chris | breward@maths.ox.ac.uk | Mathematical Institute, University of Oxford |

Byrne, Helen | helen.byrne@nottingham.ac.uk | Centre for Mathematical Medicine and Biology, University of Nottingham |

Chou, Thomas | tomchou@ucla.edu | Biomathematics, University of California, Los Angeles |

Chugunova, Marina | chugunom@math.utoronto.ca | Mathematics, University of Toronto |

Cui, Kai | kc52@stat.duke.edu | Statistical Science, Duke University |

Cytrynbaum, Eric | cytryn@math.ubc.ca | Mathematics, University of British Columbia |

Doyle, Matthew | mg.doyle@utoronto.ca | Department of Mechanical and Industrial Engineering, University of Toronto |

Fok, Pak-Wing | pakwing@udel.edu | Mathematical Sciences, University of Delaware |

Frasch, Martin | mg.frasch@umontreal.ca | Centre de recherche en reproduction animale, CHU Sainte-Justine |

Gevertz, Jana | gevertz@tcnj.edu | Mathematics and Statistics, The College of New Jersey |

Gewecke, Nicholas | ngewecke@math.udel.edu | Department of Mathematical Sciences, University of Delaware |

Hinkelmann, Franziska | fhinkel@vt.edu | Mathematical Biosciences Institute, The Ohio State University |

Huang, Huaxiong | hhuang@yorku.ca | Mathematics and Statistics, York University |

King-Smith, Ewen | EKing-smith@optometry.osu.edu | College of Optometry, The Ohio State University |

Ledder, Glenn | gledder@math.unl.edu | Mathematics, University of Nebraska |

Lewis, Gregory | greg.lewis@uoit.ca | Faculty of Science, UOIT |

Louzoun, Yoram | louzouy@math.biu.ac.il | |

Matamba Messi, Leopold | lmatamba@gmail.com | Department of Mathematics, University of Georgia |

Miakonkana, Guy-vanie | gmm0006@auburn.edu | Mathematics and Statistics, Auburn University |

Moldovan, Nicanor | moldovan.6@osu.edu | Internal Medicine, Disease Pathways, LLC |

Moulton, Derek | moulton@maths.ox.ac.uk | OCCAM, Mathematical Institute, University of Oxford |

Newby, Jay | newby@maths.ox.ac.uk | Mathematics, University of Oxford |

O'Keeffe, Stephen | stephen.okeeffe@hertford.ox.ac.uk | OCCAM, Mathematical Institute, University of Oxford |

Peercy, Bradford | bpeercy@umbc.edu | Mathematics and Statistics, University of Maryland Baltimore County |

Pugh, Mary | mpugh@math.utoronto.ca | Mathematics, University of Toronto |

Radunskaya, Ami | aradunskaya@pomona.edu | Mathematics, Pomona College |

Roberts, Paul | paul.roberts@univ.ox.ac.uk | Mathematics Department and Computer Science Department, University of Oxford |

Rosol, Thomas | rosol.1@osu.edu | Veterinary Biosciences, The Ohio State University |

Schwendeman, Donald | schwed@rpi.edu | Mathematical Sciences, Rensselaer Polytechnic Institute |

Shipley, Rebecca | rebecca.shipley@ucl.ac.uk | Department of Mechanical Engineering, University College London |

Siggers, Jennifer | j.siggers@imperial.ac.uk | Department of Bioengineering, |

Sivaloganathan, Siv | ssivalog@math.uwaterloo.ca | Applied Mathematics, University of Waterloo |

Solomon, Bill | billsolo@sbcglobal.net | Blue Valley High School |

Stamper, Johanna | jstamper@uab.edu | Physics, University of Alabama at Birmingham |

Stepien, Tracy | tls52@pitt.edu | Mathematics, University of Pittsburgh |

Strawbridge, Eva | emstrawbridge@gmail.com | Mathematics, University of Chicago |

Tatsuno, Masami | tatsuno@uleth.ca | Neuroscience, University of Lethbridge |

Tseng, Yu-Hau | yhtseng@math.nctu.edu.tw | DEPARTMENT OF MATHEMATICS AND STATISTICS, York University |

Vandiver, Becky | vandiver@stolaf.edu | Mathematics and Computer Science, St. Olaf College |

Vats, Divyanshu | dvats@ima.umn.edu | Institute for Mathematics and its Applications, University of Minnesota |

Wang, Steven | stevenw@mathstat.yorku.ca | Mathematics and Statistics, York University |

Ward, John | John.Ward@lboro.ac.uk | Mathematical Sciences, |

Washington, Talitha | talitha.washington@howard.edu | Mathematics, Howard University |

Wattis, Jonathan | Jonathan.Wattis@nottingham.ac.uk | School of Mathematical Sciences, University of Nottingham |

Witelski, Thomas | witelski@math.duke.edu | Mathematics, Duke University |

25% of the population in developed countries. The hallmark of early CAVD is focal changes in

the mechanical properties of the extracellular matrix (ECM) in the valve leaflets. In particular,

proteoglycan-rich lesions begin to form on the surface of the fibrosa layer of these leaflets.

Maladaptive remodeling of the ECM is hypothesized to negatively influence valve cell function,

ultimately resulting in stiffened leaflets that do not function properly. To date, the local

micromechanical properties of healthy and diseased valve leaflets have not been characterized.

The objectives of the present study are to measure local micromechanical properties of the three

layers of porcine aortic valve leaflets (fibrosa, spongiosa, and ventricularis), and of these

proteoglycan-rich lesions, and to develop material models for these layers and the lesions that

take into account material non-linearity and heterogeneity. Leaflets will be obtained from

healthy swine as well as those with early stage CAVD; comparison between the material models

developed for the two cases will help identify changes in the local micromechanical properties of

the aortic valve leaflets during the onset of CAVD.

To obtain the experimental data, a microindenter will be used to deform the surface of the

leaflets. From these experiments, we will obtain the indenter depth and the corresponding force.

We will also know the shape and size of the indenter and the shape and size of the tissue region

deformed by the indentation.

(electroenkephalogram, EEG) and heart rate (FHR) which we recorded during simulated labour

in fetal sheep model of human pregnancy and fetal development.

The goal is to develop mathematical models allowing online detection of physiological

patterns alarming of incipient fetal distress in clinical conditions of labour.

There are two major aspects of the problem:

1. A pattern of time correlated changes in EEG and FHR is now known to occur during

conditions of deteriorated blood supply to the fetus as it may occur during labour. This pattern is

an early predictor of immanent severe drop in fetal pH. Fetal pH under 7.00 (severe acidemia) is

associated with increased risk of brain injury and sustained neurological deficits. In obstetrical

care, an urgent need exists for technologies allowing the detection of such severe acidemia in

fetus. We describe the phenomenon in detail in Frasch et al (2011).

Question 1: Can we create a mathematical model of this phenomenon robust enough to be

capable of capturing the onset of the pattern online despite varying EEG/FHR signal

characteristics?

2. Certain properties of FHR variability (FHRV, higher order fluctuations in FHR on millisecond

time scale) can also be used for early detection of the onset of severe acidemia.

FHRV can be calculated in different signal property domains (linear, nonlinear, time and

frequency or both). Different measures of FHRV are known to reflect somewhat different

aspects of underlying physiological activities and probably carry a predictive value variable in

time. A group of FHRV measures is likely to provide a higher positive predictive value of fetal

acidemia than one particular FHRV measure alone. Please see also Frasch (2011).

Question 2: Can we develop a mathematical model to allow us to 1) identify the FHRV

measures that would perform best together to detect the pathophysiological mechanism of

incipient acidemia and 2) incorporate such FHRV measures into the model that captures the

correlated changes in EEG and FHR?

In a broader sense, we hope that such approach would help create a novel paradigm for

context-specific generation of mathematical models for online detection of complex

physiological patterns. Ideally, this new paradigm should go beyond a purely statistical or data

mining framework. For example, can we build a model that incorporates physiological

mechanisms into a standard data mining approach?

In order to facilitate the discussion and modeling building exercise, relevant data will be

provided for workshop participants.

evaporation is an important contributing factor.Ã‚Â Ã‚Â The superficial lipid layer of the tear film is normally an

excellent barrier to evaporation but its effectiveness is often reduced in dry eye disorders.Ã‚Â Ã‚Â This lipid,

called meibum, is secreted from meibomian glands in the lids.

The main components of meibum are wax esters and cholesteryl esters with smaller quantities of polar

and other lipids.Ã‚Â Ã‚Â Also, surfactant proteins probably play an important role.Ã‚Â Ã‚Â The esters often contain a

proportion of long, saturated hydrocarbon chains which are thought to help increase resistance to

evaporation.Ã‚Â Ã‚Â Another important characteristic of the lipid layer is its ability to withstand the blink cycle

which causes compression to a small fraction of the original area, followed by expansion.Ã‚Â Ã‚Â Ã‚Â Lipids with

long, saturated hydrocarbon chains often do not reÃ¢â‚¬?spread to their original state after compression and

expansion, so the inclusion of unsaturated hydrocarbon chains in meibum may aid in respreading after a

blink.

The molecular organization of the lipid layer is poorly understood.Ã‚Â Ã‚Â Ã‚Â The team will be asked to consider

and propose models of molecular structure of the lipid layer, and to evaluate their consistency with

observed properties which will be presented.Ã‚Â Ã‚Â Ã‚Â

ranging from the most primitive fishes and nonvertebrates to humans. This is because

iCa is utilized by diverse cell types as a transcellular and intracellular signaling

molecule, such as in the nervous system, cardiac and skeletal muscle, epithelial cells,

endocrine cells, blood cells, among others. The blood ionized calcium concentration is

approximately 1.5 mM in all animals. If the concentration changes by as little as 10-20%

dysregulation of body systems (such as the neuromuscular system) will result and can

be fatal. Therefore, there are multiple, redundant regulatory systems that exist to

maintain blood calcium in a narrow biological range.

Terrestrial animals live in a calcium poor environment and are dependent upon calcium

absorption from the gastrointestinal tract to provide calcium as a regulatory ion and

component of bones. In contrast, sea animals live in a calcium rich environment (since

seawater has 10 mM calcium) and excretion of calcium is important.

important not only for expanding the frontier of our scientific knowledge, but also for developing a

more effective treatment for neuronal diseases.

The brain is composed of a large number of neurons. Most neurons interact with other neurons via

action potentials (spikes), and have the tendency to form cell-assemblies (1) that can be organized

dynamically through information processing in the brain. To

study these group dynamics and their role in cognitive

functions, it is important to record simultaneously from as

many neurons as possible from behaving animals (2). Due to

recent technological developments, multi-electrode recordings

have become an increasingly widespread tool in

electrophysiology, enabling the recording of spiking activity

from tens to hundreds of neurons simultaneously