Current Topic Workshop: Statistical and Mathematical Modeling of fMRI Data

(March 18,2004 - March 20,2004 )

Organizers


Thomas Santner
Department of Statistics, The Ohio State University
Jay Zweier
Davis Heart and Lung Research Institute, The Ohio State University

The Blood Oxygen Level Dependent (BOLD) image contrast provides an important mechanism for tissue characterization with Magnetic Resonance Imaging. Among the neuro-functional of applications of BOLD fMRI are fundamental assessments of the processing of motor, visual, auditory, and sensory tasks by the brain, the evaluation of various diseases including neurological disorders, the pre-surgical determination of brain function, and the evaluation of psychiatric diseases. The BOLD effect is also a dominant mechanism for imaging at an ultra-high magnetic field strength and for cardiac imaging.

Currently, the majority of neuro-functional applications use BOLD fMRI in a qualitative fashion and employ statistical analysis to extract the signal changes present in fMRI data. This task is difficult because of the highly spatially and temporally correlated nature of fMRI data and because of the small levels of the signal changes (1-4%).

For a complete understanding of the BOLD effect and its relation to neuronal activation, one must not only understand where signal changes occur but also the physiologic and physical mechanisms causing the signal change. A number of studies have addressed these issues, however many details regarding these physical and physiologic mechanism remain open questions.

The physical modeling of fMRI data involves the description of MRI signal changes due to the diffusion of tissue water molecules in the locally variable magnetic fields produced by paramagnetic deoxyhemoglobin. These spatially variable magnetic fields, on a 10-100 m scale, can be described mathematically; this knowledge can be used to estimate the signal from water proton diffusion in different tissue compartments (intra-, extra-vascular) and in different geometries (of the vascular and micro-vascular network), as well as the amount and distribution of deoxyhemoglobin. Physiological models are needed to explain the altered amount of deoxyhemoglobin during neuronal activation and its dependence on blood oxygenation, cerebral metabolic rate, oxygen extraction fraction, cerebral blood volume, and cerebral blood flow. It needs to account for the interconnectedness of these different factors under normal or pathologically altered physiologic conditions. Using this knowledge, the statistical modeling of BOLD fMRI signal changes can be improved by better descriptions of the spatial and temporal correlations present in such data, and the prior extent of activation for different tasks. This will, in turn, lead to a more accurate understanding of the physiologic and physical mechanisms causing the signal change.

This workshop will bring together researchers from the statistical, imaging, and modeling communities; it seeks to integrate their knowledge to enhance the medical and basic biomedical sciences communities' understanding of the physiologic and physical mechanisms causing BOLD fMRI signal changes.

Accepted Speakers

William Eddy
Department of Statistics, Carnegie-Mellon University
Mark Haacke
Radiology & Biomedical Engineering, Wayne State University
Fahmeed Hyder
Diagnostic Radiology & Biomed Eng, Yale University
John Kornak
Magnetic Resonance Unit, University of California, San Diego
Joe Mandeville
Department of Radiology, Harvard Medical School
Jean-Francois Mangin
INSERM U494, CHU Pitie-Salpetriere
John Mayhew
Department of Psychology, University of Sheffield
Harold Swartz
Radiology & Physiology, Dartmouth Medical School
Keith Worsley
Mathematics & Statistics, McGill University, Macdonald Campus
Thursday, March 18, 2004
Time Session
09:15 AM
10:15 AM
Joe Mandeville - CBV Contributions to BOLD: Implications for Modeling & Statistics

Significant progress has been made in last 10 years in terms of refining fMRI statistical analyses, acquiring empirical data on the relationship between BOLD signal and underlying physiology, and modeling these processes. Two questions addresses by this workshop include 1) How can we improve fMRI detection power, and 2) what do these signal changes mean in terms of hemodynamic, metabolic, and neuronal activity? In some (but not all) cases, a better understanding of the latter issue can inform statistical methods that define brain activation. One way to subdivide issues surrounding detection power and physiological modeling is to separately consider steady state and dynamic changes in fMRI signal.


fMRI between steady states: From a statistical viewpoint, long block designs have a minimal dependence on the hemodynamic response function. Pharmacological stimuli present an extreme form of the one-stimulus block design, where hemodynamic modeling is essentially irrelevant due to the slow evolution of neuronal activity. These cases limit certain options for analyses and place a premium on intrinsic sensitivity. From a modeling viewpoint, block designs and drug stimuli reduce sensitivity to BOLD transients, and help define the limits of interpretation in a simplified regime.


Numerous investigators, using the "hypercapnia calibration" methodology [1, 2], now have reported the relationship between steady state changes in CBF/CBV and CMRO2 [1-5]. The consensus appears to be that changes in CBF exceed those in CMRO2 by a factor between 2 and 3. These empirical data are not inconsistent with a diffusion-limited model of oxygen delivery [6] that includes capillary swelling, which was not included in the original model. I will argue that further refinements of both models and empirical data using fMRI techniques are limited by our uncertainties in physiological inputs.


The resting state BOLD relaxation rate amplifies changes in reactivity according to the local blood volume fraction and the magnetic field strength. The magnetic field dependence of the relaxation rate (and, hence, intrinsic BOLD sensitivity) can be investigated by 1) a "hypercapnia calibration" procedure, 2) comparisons between BOLD signal and fMRI based upon exogenous contrast agent, and 3) inferences based upon stimulus-induced changes in relaxation rates. These methods provide predictions for BOLD amplitude versus field strength. Empirical data show a regional coupling of BOLD and CBV signal changes, with a strong dependence of BOLD signal on resting state CBV [7, 8]. The BOLD dependence on resting state CBV represents a major impediment in terms of reliably and routinely translating BOLD signal to quantitative indices of neuronal activity.


Dynamic fMRI: Modeling dynamic fMRI data, such as event-related studies, requires a detailed understanding of transient features of the fMRI response and non-linearities that arise between the stimulus design and the measured output. It is now clear that a temporal mismatch between flow and volume is one of the major sources of BOLD transients. In both the anesthetized rodent [2, 9] and the awake non-human primate [10], the slow response of CBV is consistent with the time constant required to explain the BOLD post-stimulus undershoot. In each of these animal models, a detailed look at the temporal response of CBV shows 2 distinct time constants (much as BOLD signal appears to have one time constant for the dominant positive response, plus another slower time constant to describe the post-stimulus undershoot). In this section of the presentation, I will 1) review our empirical data on the responses of blood plasma and total hemoglobin [11], 2) describe models of this response [12] and discuss open questions about the physiological source of the flow-volume temporal mismatch, and 3) discuss the linearity of the CBV response, and implications for rapid event-related stimulus designs using BOLD and CBV contrast [13]. For short or rapidly presented stimuli, attempts to derive CMRO2 or ascribe significance to fine temporal features of the time course are complicated by transit time effects.


In summary, statistical refinements may yield modest improvements in BOLD sensitivity for some paradigms. Some outstanding issues remain in terms of modeling. In general, certain experimental limitations, such as the difficulty in determining the BOLD baseline, will continue to hamper quantitative interpretations of BOLD signal changes in the routine experimental setting.


References



  1. Davis, T.L., Kwong, K.K., Weisskoff, R.M., & Rosen, B.R. (1998). Calibrated functional MRI: Mapping the dynamics of oxidative metabolism. Proc. Natl. Acad. Sci. USA, 95, 1834-1839.

  2. Mandeville, J.B., Marota, J.J.A., Ayata, C., Moskowitz, M.A., Weisskoff, R.M., & Rosen, B.R. (1999). An MRI Measurement of the Temporal Evolution of Relative CMRO2 During Rat Forepaw Stimulation. Magn. Reson. Med., 42(5), 944-951.

  3. Hoge, R.D., Atkinson, J., Gill, B., Crelier, G.R., Marrett, S., & Pike, G.B. (1999). Linear coupling between cerebral blood flow and oxygen consumption in activated human cortex. Proc. Natl. Acad. Sci. USA, 96(16), 9403-9408.

  4. Kim, S.G., Rostrup, E., Larsson, H.B., Ogawa, S., & Paulson, O.B. (1999). Determination of relative CMRO2 from CBF and BOLD changes: significant increase of oxygen consumption rate during visual stimulation. Magn. Reson. Med., 41(6), 1152-1161.

  5. Kastrup, A., Kruger, G., Neumann-Haefelin, T., Glover, G.H., & Moseley, M.E. (2002). Changes of cerebral blood flow, oxygenation, and oxidative metabolism during graded motor activation. Neuroimage, 15(1), 74-82.

  6. Buxton, R.B., & Frank, L.R. (1997). A model for the coupling between cerebral blood flow and oxygen metabolism during neuronal stimulation. J. Cereb. Blood Flow Metab., 17(1), 64-72.

  7. Mandeville, J.B., Jenkins, B.G., Kosofsky, B.E., Moskowitz, M.A., Rosen, B.R., & Marota, J.J.A. (2001). Regional Sensitivity and Coupling of BOLD and CBV Changes during Stimulation of Rat Brain. Magn. Reson. Med., 45(3), 443-447.

  8. Mandeville, J.B., Jenkins, B.G., Chen, Y.I., Choi, J.-K., Kim, Y., Belen, D., et al. (2004). Exogenous contrast agent improves sensitivity of gradient-echo fMRI at 9.4 Tesla. Manuscript submitted for publication.

  9. Mandeville, J.B., Marota, J.J.A., Kosofsky, B.E., Keltner, J.R., Weissleder, R., Rosen, B.R., et al. (1998). Dynamic Functional Imaging of Relative Cerebral Blood Volume During Rat Forepaw Stimulation. Magn. Reson. Med., 39(4), 615-624.

  10. Leite, F.P., Tsao, D., Vanduffel, W., Fize, D., Sasaki, Y., Wald, L.L., et al. (2002). Repeated fMRI Using Iron Oxide Contrast Agent in Awake, Behaving Macaques at 3 Tesla. Neuroimage, 16(2), 283-94.

  11. Siegel, A.M., Culver, J.P., Mandeville, J.B., & Boas, D.A. (2003). Temporal comparison of functional brain imaging with diffuse optical tomography and fMRI during rat forepaw stimulation. Phys Med Biol, 48(10), 1391-1403.

  12. Mandeville, J.B., Marota, J.J.A., Ayata, C., Zaharchuk, G., Moskowitz, M.A., Rosen, B.R., et al. (1999). Evidence of a Cerebrovascular Post-arteriole Windkessel with Delayed Compliance. J. Cereb. Blood Flow Metab., 19(6), 679-689.

  13. Leite, F.P., & Mandeville, J.B. (2003). Event-related BOLD and IRON stimulus designs. in Int Soc Magn Reson Med. Toronto, CA.

02:00 PM
03:00 PM
Mark Haacke - High Resolution SWI and Complex Analysis in fMRI

Functional MRI can be accomplished with a high resolution gradient echo scan. The disadvantages of this approach are that the acquisition time can be many minutes. A further disadvantage is that as the resolution increases, the signal-to-noise (SNR) decreases. However, the data can be complex filtered back down to an equivalent lower resolution EPI like image to regain SNR. A simple subtraction can be performed rather than a correlation analysis. We also examine the role of using the complex data in the subtraction process rather than just the magnitude data. This approach may prove useful when studying activated tissue near tumors for example where the high resolution information may prove most useful. We test this approach using a conventional motor cortex fMRI paradigm involving finger tapping with and without the use of caffeine as an enhancer of the BOLD effect.

Friday, March 19, 2004
Time Session
09:00 AM
10:00 AM
Harold Swartz - Integrating Data Obtained by In Vivo Spectroscopy and Imaging with Modeling of Oxygen Distribution in Tissues: Concept and Approach

Our aim is to conceptualize the complex physiology/pathophysiology that is involved in changes of oxygen in tissue and then apply advanced computational methods to develop a comprehensive physiological model that describes the distribution and changes of oxygen in tissue and the metabolic and signaling events associated with oxygen. This will be done using data from several different and complimentary methods for making measurements in vivo. Because the distribution of oxygen in tissues is very heterogeneous, even at cellular dimensions, such measurements and the resulting model are important but challenging tasks.


The need and opportunities for developing a comprehensive model for oxygen in tissues that is consistent with and validated by direct measurements, arose from studies that began as validation of EPR oximetry. As the "new" method, it was desirable to show that the measurements obtained with EPR oximetry "gave the same results" as other methods for measuring oxygen in tissues. We therefore initiated studies to make careful simultaneous or sequential measurements with EPR and one or more other modalities to determine the relationships between the results obtained with the various methods, taking into account the parameters on which the measurements are based.


As we began to carry out these experiments, however, we became acutely aware that the idea that we could do this via simple direct comparisons was an illusion. For example, it seemed logical to make direct measurements of oxygen in tumors simultaneously with EPR oximetry and the "gold standard", the Eppendorf Histograph. But the measurements are not really directly comparable even though they both measure the partial pressure of oxygen. This is because the volume measured with the EPR oximetry technique that we used is much larger than the volume probed with a single point with the Eppendorf. Even if we aggregate the volumes probed with the Eppendorf to make the total volume comparable to that with EPR oximetry, the Eppendorf measurements are spatially different and inevitably should record extremes of values that would not be recorded with the EPR method, because of the heterogeneity of the oxygen in real tissues, especially tumors. Therefore, even if both methods were technically perfect and valid, the results would be different. This conclusion, of course, applies to comparisons of essentially all types of measurements of oxygen and related parameters.


The relationship of measurements made with the BOLD effect to those made with other modalities is especially interesting, because the BOLD technique is widely available and it can be used to make measurements in virtually any part of an animal or human subject. The data obtained with BOLD, however, are very non-specific, reflecting principally the amount of deoxyhemoglobin. These data can be made more useful if they are combined with another type of related measurement, e.g. direct measurements of oxygen.


While data comparing results with two or more different modalities are valuable, these experiments have made us aware that it would be possible to develop a much more thorough and useful understanding of oxygen in tissue if we developed methods and models that can incorporate the different measurements into a physiologically based model that is based on the nature of the data from the different types of measurements. The oxygen concentration at any point is affected by the delivery, distribution, and consumption of oxygen locally, regionally, and systemically. These parameters are affected by many different processes including perfusion, diffusion, metabolism, the anatomy of the microcirculation, and the function of the macrocirculatory system. There are methods available to measure parameters that can be affected by most or all of the processes, but because each measured parameter is affected by multiple processes, multiple types of measurements are desirable. It also is desirable to have a logical basis to relate the measurements to each other; i.e., appropriate models of the processes. This would not only enhance the value of the data from the various types of measurements but, most importantly, also could lead to an optimized model that much more fully describes oxygenation in tissues, at levels ranging from the subcellular to the whole organism.


This is a challenging task, requiring input from several different disciplines, with multiple iterations to feed back the results of measurements into the model, then to modify the model appropriately and carry out measurements under different conditions to test the validity of the alterations to the model. We believe that such an effort is feasible and desirable.

10:30 AM
11:30 AM
John Kornak - Modeling Spatial Variation in the Shape of the BOLD Response

Several statistical approaches exist to compensate for the temporal smoothing effect inherent when using the BOLD response as a proxy for neural activation. Commonly used BOLD correction methods, such as convolving a stimulus function with a hemodynamic response kernel, inevitably make assumptions restricting the possible shapes of the BOLD response. Furthermore, the BOLD response shape is typically restricted so that only the response magnitude can vary spatially.


These assumptions were examined by fitting a range of parametric "shape" functions to voxel averaged BOLD response cycles using least squares estimation. The results imply that the shape of the BOLD response can vary spatially in a coherent fashion which, if ignored, could have implications on the detection and interpretation of activation patterns.

02:00 PM
03:00 PM
Fahmeed Hyder - Neuroenergetic Basis of fMRI

The conventional functional MRI (fMRI) map offers information indirectly about localized changes in neural activity because it reflects changes in blood oxygenation, not the actual neural activity. To provide neural basis of fMRI researchers have combined electrophysiology and various optical methods to show correlations between fMRI and surrogate signals associated with neural activity. But quantitative interpretation of "How much has the neural activity changed by?" still cannot be made from conventional fMRI data. The fMRI signal (S) has two partitions, one that describes the correlation between oxidative metabolism (CMRO2) and blood flow (CBF) which supports the bioelectric work to sustain neuronal excitability and the other is the requisite dilation of blood vessels (CBV) which is the mechanical response involved in removal of waste while providing nutrients. Since changes in energy metabolism is related to bioelectric work, we tested if spiking frequency of a large neuronal ensemble (v) in the cerebral cortex is reflected by local energy metabolism (CMRO2) in rat brain. We used extracellular recordings to measure dv/v and calibrated fMRI (using S, CBF, and CBV maps) to measure CMRO2/CMRO2 during sensory stimulation. We found that dCMRO2/CMRO2 ~ dv/v, which suggests efficient energy use during brain work. Thus calibrated fMRI can be used to provide data on where and by how much the neural activity has changed. We have probed the oxygenated environment of neural cells using fluorescence quenching methods. The localized oxygen partial pressure (pO2) measurements combined with quantitative measurements of oxidative metabolism (CMRO2) and blood perfusion (CBF) provide insights about oxygen back flux from brain to blood. The degree of oxygen back flux has bearings on the 'balloon' model, which is often used to describe the hemodynamic components of the stimulation-induced fMRI response. Since the results suggest that there is negligible oxygen back flux (from brain to blood), the oxygen transport process (from blood to brain) is believed to be far more efficient than assumed by the 'balloon' model. Recently we have also probed local temperature (T) changes in the brain and have begun to understand these changes with respect to quantitative changes in oxidative metabolism (CMRO2) and blood perfusion (CBF) during functional activation. The results suggest that the stimulation-induced temperature dynamics are heavily dependent on biophysical properties of heat transfer across different media and depend heavily on cooling and warming affects caused by blood flow and tissue metabolism, respectively. These combined multi-modal studies reveal the neuroenergetic basis of fMRI which is often an ignored aspect of the physiological makeup of the image contrast.

Saturday, March 20, 2004
Time Session
09:00 AM
10:00 AM
John Mayhew - An Examination of Biophysical Models of the BOLD fMRI Signal Using

The talk will describe recent work developing a biophysical model linking the neural responses to stimulation, through the hemodynamic changes in blood oxygenation flow and volume, to the BOLD fMRI signal. In particular the major focus will be on the use of optical imaging spectroscopy and LDF measurements made concurrently with the BOLD and cbv-MRI measurements to examine the predictions of what is sometimes known as the Massachusetts General Hospital model of the BOLD signal (eg Boxerman, Davis, Hoge etc). Some even more recent work will be described in which IVIM crushing is used to explore the predictions of the 'Yablonskiy Haacke' (1994) model of the contribution of the extravascular static regime to the BOLD signal. The topic for discussion is this : despite the fact that the spectroscopy and the LDF (using Grubb's 'law') data is commensurate with the MRI measurements of the changes in blood volume, the measured BOLD signal is much larger than that predicted by the models (using generally accepted assumptions of baseline values) and the concurrent optical imaging measurements of changes in Hbr and Hbt.

10:30 AM
11:30 AM
Keith Worsley - A General Statistical Analysis of fMRI Data

Our proposed method for the statistical analysis of fMRI data seeks a compromise between validity, generality, simplicity and execution speed. The method is based on linear models with local AR(p) errors. The AR(p) model is fitted via the Yule-Walker equations with a simple bias correction that is similar to the first step in the Fisher scoring algorithm for finding ReML estimates. The resulting effects are then combined across runs in the same session, across sessions in the same subject, and across subjects within a population by a simple mixed effects model. The model is fitted by ReML using the EM algorithm after re-parameterization to reduce bias, at the expense of negative variance components. The residual degrees of freedom are boosted using a form of pooling by spatial smoothing. Activation is detected using Bonferroni, False Discovery Rate, and non-isotropic random field methods for local maxima and spatial extent. We briefly look at an alternative method based on conjunctions. Finally, we use a simple method to estimate and make inference about the delay of the hemodynamic response function at every voxel. We conclude with some suggestions for the optimal design of fMRI experiments.

Name Affiliation
Abduljalil, Amir amir@justice.med.ohio-state.edu Department of Radiology, The Ohio State University
Algaze, Antonio algaze.1@osu.edu Physics & Radiology, University of Puerto Rico - Bayamon
Bazaliy, Boris Mathematical Biosciences Institute, The Ohio State University
Beattie, Michael beattie.2@osu.edu Department of Neuroscience, The Ohio State University
Best, Janet jbest@mbi.osu.edu Mathematics, The Ohio State University
Beversdorf, David beversdorf.2@osu.edu Department of Neurology, The Ohio State University
Borisyuk, Alla borisyuk@mbi.osu.edu Mathematical Biosciences Institute, The Ohio State University
Bourekas, Eric bourekas.1@osu.edu Department of Radiology, The Ohio State University
Carmack, Patrick pcarmack@mail.smu.edu Statistical Science, Southern Methodist University
Clymer, Bradley clymer.1@osu.edu Electrical & Computer Engineering, The Ohio State University
Cracium, Gheorghe craciun@math.wisc.edu Dept. of Mathematics, University of Wisconsin-Madison
Cressie, Noel ncressie@stat.ohio-state.edu Department of Statistics, The Ohio State University
Danthi, Sanjay danthi.1@osu.edu Staff Scientist II, Genzyme Corporation
Deng, Yuanmu deng.40@osu.edu College of Medicine & Public Health, The Ohio State University
Dougherty, Daniel dpdoughe@mbi.osu.edu Mathematical Biosciences Institute, The Ohio State University
Eddy, William OR Department of Statistics, Carnegie-Mellon University
Goel, Pranay goelpra@helix.nih.gov NIDDK, Indian Institute of Science Education and Research
Guo, Yixin yixin@math.drexel.edu Department of Mathematics, The Ohio State University
Haacke, Mark rdmlaze@yahoo.com Radiology & Biomedical Engineering, Wayne State University
He, Guanglong he.86@osu.edu Biological Spectoscopy & Imaging, The Ohio State University
Heverhagen, Johannes heverhagen.1@osu.edu Department of Radiology, The Ohio State University
Hillier, Ashleigh hillier.9@osu.edu Department of Neurology, The Ohio State University
Hoffmann, Raymond hoffmann@mcw.edu Department of Biostatistics, Medical College of Wisconsin
Hyder, Fahmeed fahmeed.hyder@yale.edu Diagnostic Radiology & Biomed Eng, Yale University
Ibinson, James ibinson.1@osu.edu Department of Radiology, The Ohio State University
Kangarlu, Alayar kangarlu.1@osu.edu Department of Radiology, The Ohio State University
Karunanayaka, Prasanna kar4rp@cchmc.org Dept. of Radiology, Cincinnati Children's Hospital Medical Center
Khan, Asadullah Biomedical Engineering, Wayne State University
Kim, Seong-Gi kimsg@pitt.edu Brain Imaging Research Center, University of Pittsburgh
Knopp, Michael knopp-1@medctr.ohio-state.edu Department of Radiology, The Ohio State University
Kornak, John kornak@itsa.ucsf.edu Magnetic Resonance Unit, University of California, San Diego
Lewis, Jennifer lewis.792@osu.edu William H. Havener Eye Center, The Ohio State University
Lim, Sookkyung limsk@math.uc.edu Department of Mathematical Sciences, University of Cincinnati
Lolas, Georgios mpokos@hotmail.com Mathematics, University of Dundee
Lou, Yuan lou@math.ohio-state.edu Department of Mathematics, The Ohio State University
Mandeville, Joe jbm@nmr.mgh.harvard.edu Department of Radiology, Harvard Medical School
Mangin, Jean-Francois mangin@shfj.cea.fr INSERM U494, CHU Pitie-Salpetriere
Martindale, Anthony John martindate@sheffield.ac.uk Psychology Department, University of Sheffield
Mayhew, John j.e.mayhew@sheffield.ac.uk Department of Psychology, University of Sheffield
Meda, Shashwath Ashok Biomedical Engineering, Wayne State University
Mitchell, Chad ltcamitchell@yahoo.com Department of Radiology, The Ohio State University
Myers, Kary kary@stat.cmu.edu Department of Statistics, Carnegie-Mellon University
Neff, Maria neff.6@osu.edu Psychiatry and Pharmacology, The Ohio State University
Nichols, Thomas nichols@umich.edu Department of Biostatistics, University of Michigan
Ogden, Todd to166@columbia.edu Department of Biostatistics, Columbia University
Pan, Hong hop2001@med.cornell.edu Psychiatry; Weill Medical College, Cornell University
Pate, Ed edpate@hotmail.com Department of Mathematics, Washington State University
Pavlicova, Martina pavlicov@stat.ohio-state.edu Department of Statistics, The Ohio State University
Posse, Stefan sposse@unm.edu MIND Imaging Center, University of New Mexico
Raman, Subha raman.1@osu.edu Davis Heart and Lung Research Institute, The Ohio State University
Rejniak, Katarzyna rejniak@mbi.osu.edu Mathematical Biosciences Institute, The Ohio State University
Saltz, Joel Joel.Saltz@osumc.edu. Biomedical Information, The Ohio State University
Sandstede, Bjorn sandsted@math.ohio-state.edu Department of Mathematics, The Ohio State University
Santner, Thomas tjs@stat.ohio-state.edu Department of Statistics, The Ohio State University
Schamalbrock, Petra schmalbrock.1@osu.edu Department of Radiology, The Ohio State University
Sneyd, James sneyd@mbi.osu.edu Mathematics, The University of Auckland
Swartz, Harold harold.swartz@dartmouth.edu Radiology & Physiology, Dartmouth Medical School
Taylor, Jonathan jonathan.taylor@stanford.edu Department of Statistics, Stanford University
Terman, David terman@math.ohio-state.edu Mathemathics Department, The Ohio State University
Tivarus, Madalina tivarus.2@osu.edu Department of Neurology, The Ohio State University
Truong, Trong-Kha truong.31@osu.edu Department of Radiology, The Ohio State University
Tsai, Chih-Chiang tsaijc@mbi.osu.edu Department of Mathematics, National Taiwan Normal University
Wassenaar, Peter wassenaar.3@osu.edu Department of Radiology, The Ohio State University
Wechselberger, Martin wm@mbi.osu.edu Mathematical Biosciences Insitute, The Ohio State University
Whitaker, Chastity chastity@justice.med.ohio-state.edu Department of Radiology, The Ohio State University
Worsley, Keith worsley@math.mcgill.ca; Mathematics & Statistics, McGill University, Macdonald Campus
Wright, Geraldine wright.572@osu.edu School of Biology, Newcastle University
Zweier, Jay jay.zweier@osumc.edu Davis Heart and Lung Research Institute, The Ohio State University
High Resolution SWI and Complex Analysis in fMRI

Functional MRI can be accomplished with a high resolution gradient echo scan. The disadvantages of this approach are that the acquisition time can be many minutes. A further disadvantage is that as the resolution increases, the signal-to-noise (SNR) decreases. However, the data can be complex filtered back down to an equivalent lower resolution EPI like image to regain SNR. A simple subtraction can be performed rather than a correlation analysis. We also examine the role of using the complex data in the subtraction process rather than just the magnitude data. This approach may prove useful when studying activated tissue near tumors for example where the high resolution information may prove most useful. We test this approach using a conventional motor cortex fMRI paradigm involving finger tapping with and without the use of caffeine as an enhancer of the BOLD effect.

Neuroenergetic Basis of fMRI

The conventional functional MRI (fMRI) map offers information indirectly about localized changes in neural activity because it reflects changes in blood oxygenation, not the actual neural activity. To provide neural basis of fMRI researchers have combined electrophysiology and various optical methods to show correlations between fMRI and surrogate signals associated with neural activity. But quantitative interpretation of "How much has the neural activity changed by?" still cannot be made from conventional fMRI data. The fMRI signal (S) has two partitions, one that describes the correlation between oxidative metabolism (CMRO2) and blood flow (CBF) which supports the bioelectric work to sustain neuronal excitability and the other is the requisite dilation of blood vessels (CBV) which is the mechanical response involved in removal of waste while providing nutrients. Since changes in energy metabolism is related to bioelectric work, we tested if spiking frequency of a large neuronal ensemble (v) in the cerebral cortex is reflected by local energy metabolism (CMRO2) in rat brain. We used extracellular recordings to measure dv/v and calibrated fMRI (using S, CBF, and CBV maps) to measure CMRO2/CMRO2 during sensory stimulation. We found that dCMRO2/CMRO2 ~ dv/v, which suggests efficient energy use during brain work. Thus calibrated fMRI can be used to provide data on where and by how much the neural activity has changed. We have probed the oxygenated environment of neural cells using fluorescence quenching methods. The localized oxygen partial pressure (pO2) measurements combined with quantitative measurements of oxidative metabolism (CMRO2) and blood perfusion (CBF) provide insights about oxygen back flux from brain to blood. The degree of oxygen back flux has bearings on the 'balloon' model, which is often used to describe the hemodynamic components of the stimulation-induced fMRI response. Since the results suggest that there is negligible oxygen back flux (from brain to blood), the oxygen transport process (from blood to brain) is believed to be far more efficient than assumed by the 'balloon' model. Recently we have also probed local temperature (T) changes in the brain and have begun to understand these changes with respect to quantitative changes in oxidative metabolism (CMRO2) and blood perfusion (CBF) during functional activation. The results suggest that the stimulation-induced temperature dynamics are heavily dependent on biophysical properties of heat transfer across different media and depend heavily on cooling and warming affects caused by blood flow and tissue metabolism, respectively. These combined multi-modal studies reveal the neuroenergetic basis of fMRI which is often an ignored aspect of the physiological makeup of the image contrast.

Modeling Spatial Variation in the Shape of the BOLD Response

Several statistical approaches exist to compensate for the temporal smoothing effect inherent when using the BOLD response as a proxy for neural activation. Commonly used BOLD correction methods, such as convolving a stimulus function with a hemodynamic response kernel, inevitably make assumptions restricting the possible shapes of the BOLD response. Furthermore, the BOLD response shape is typically restricted so that only the response magnitude can vary spatially.


These assumptions were examined by fitting a range of parametric "shape" functions to voxel averaged BOLD response cycles using least squares estimation. The results imply that the shape of the BOLD response can vary spatially in a coherent fashion which, if ignored, could have implications on the detection and interpretation of activation patterns.

CBV Contributions to BOLD: Implications for Modeling & Statistics

Significant progress has been made in last 10 years in terms of refining fMRI statistical analyses, acquiring empirical data on the relationship between BOLD signal and underlying physiology, and modeling these processes. Two questions addresses by this workshop include 1) How can we improve fMRI detection power, and 2) what do these signal changes mean in terms of hemodynamic, metabolic, and neuronal activity? In some (but not all) cases, a better understanding of the latter issue can inform statistical methods that define brain activation. One way to subdivide issues surrounding detection power and physiological modeling is to separately consider steady state and dynamic changes in fMRI signal.


fMRI between steady states: From a statistical viewpoint, long block designs have a minimal dependence on the hemodynamic response function. Pharmacological stimuli present an extreme form of the one-stimulus block design, where hemodynamic modeling is essentially irrelevant due to the slow evolution of neuronal activity. These cases limit certain options for analyses and place a premium on intrinsic sensitivity. From a modeling viewpoint, block designs and drug stimuli reduce sensitivity to BOLD transients, and help define the limits of interpretation in a simplified regime.


Numerous investigators, using the "hypercapnia calibration" methodology [1, 2], now have reported the relationship between steady state changes in CBF/CBV and CMRO2 [1-5]. The consensus appears to be that changes in CBF exceed those in CMRO2 by a factor between 2 and 3. These empirical data are not inconsistent with a diffusion-limited model of oxygen delivery [6] that includes capillary swelling, which was not included in the original model. I will argue that further refinements of both models and empirical data using fMRI techniques are limited by our uncertainties in physiological inputs.


The resting state BOLD relaxation rate amplifies changes in reactivity according to the local blood volume fraction and the magnetic field strength. The magnetic field dependence of the relaxation rate (and, hence, intrinsic BOLD sensitivity) can be investigated by 1) a "hypercapnia calibration" procedure, 2) comparisons between BOLD signal and fMRI based upon exogenous contrast agent, and 3) inferences based upon stimulus-induced changes in relaxation rates. These methods provide predictions for BOLD amplitude versus field strength. Empirical data show a regional coupling of BOLD and CBV signal changes, with a strong dependence of BOLD signal on resting state CBV [7, 8]. The BOLD dependence on resting state CBV represents a major impediment in terms of reliably and routinely translating BOLD signal to quantitative indices of neuronal activity.


Dynamic fMRI: Modeling dynamic fMRI data, such as event-related studies, requires a detailed understanding of transient features of the fMRI response and non-linearities that arise between the stimulus design and the measured output. It is now clear that a temporal mismatch between flow and volume is one of the major sources of BOLD transients. In both the anesthetized rodent [2, 9] and the awake non-human primate [10], the slow response of CBV is consistent with the time constant required to explain the BOLD post-stimulus undershoot. In each of these animal models, a detailed look at the temporal response of CBV shows 2 distinct time constants (much as BOLD signal appears to have one time constant for the dominant positive response, plus another slower time constant to describe the post-stimulus undershoot). In this section of the presentation, I will 1) review our empirical data on the responses of blood plasma and total hemoglobin [11], 2) describe models of this response [12] and discuss open questions about the physiological source of the flow-volume temporal mismatch, and 3) discuss the linearity of the CBV response, and implications for rapid event-related stimulus designs using BOLD and CBV contrast [13]. For short or rapidly presented stimuli, attempts to derive CMRO2 or ascribe significance to fine temporal features of the time course are complicated by transit time effects.


In summary, statistical refinements may yield modest improvements in BOLD sensitivity for some paradigms. Some outstanding issues remain in terms of modeling. In general, certain experimental limitations, such as the difficulty in determining the BOLD baseline, will continue to hamper quantitative interpretations of BOLD signal changes in the routine experimental setting.


References



  1. Davis, T.L., Kwong, K.K., Weisskoff, R.M., & Rosen, B.R. (1998). Calibrated functional MRI: Mapping the dynamics of oxidative metabolism. Proc. Natl. Acad. Sci. USA, 95, 1834-1839.

  2. Mandeville, J.B., Marota, J.J.A., Ayata, C., Moskowitz, M.A., Weisskoff, R.M., & Rosen, B.R. (1999). An MRI Measurement of the Temporal Evolution of Relative CMRO2 During Rat Forepaw Stimulation. Magn. Reson. Med., 42(5), 944-951.

  3. Hoge, R.D., Atkinson, J., Gill, B., Crelier, G.R., Marrett, S., & Pike, G.B. (1999). Linear coupling between cerebral blood flow and oxygen consumption in activated human cortex. Proc. Natl. Acad. Sci. USA, 96(16), 9403-9408.

  4. Kim, S.G., Rostrup, E., Larsson, H.B., Ogawa, S., & Paulson, O.B. (1999). Determination of relative CMRO2 from CBF and BOLD changes: significant increase of oxygen consumption rate during visual stimulation. Magn. Reson. Med., 41(6), 1152-1161.

  5. Kastrup, A., Kruger, G., Neumann-Haefelin, T., Glover, G.H., & Moseley, M.E. (2002). Changes of cerebral blood flow, oxygenation, and oxidative metabolism during graded motor activation. Neuroimage, 15(1), 74-82.

  6. Buxton, R.B., & Frank, L.R. (1997). A model for the coupling between cerebral blood flow and oxygen metabolism during neuronal stimulation. J. Cereb. Blood Flow Metab., 17(1), 64-72.

  7. Mandeville, J.B., Jenkins, B.G., Kosofsky, B.E., Moskowitz, M.A., Rosen, B.R., & Marota, J.J.A. (2001). Regional Sensitivity and Coupling of BOLD and CBV Changes during Stimulation of Rat Brain. Magn. Reson. Med., 45(3), 443-447.

  8. Mandeville, J.B., Jenkins, B.G., Chen, Y.I., Choi, J.-K., Kim, Y., Belen, D., et al. (2004). Exogenous contrast agent improves sensitivity of gradient-echo fMRI at 9.4 Tesla. Manuscript submitted for publication.

  9. Mandeville, J.B., Marota, J.J.A., Kosofsky, B.E., Keltner, J.R., Weissleder, R., Rosen, B.R., et al. (1998). Dynamic Functional Imaging of Relative Cerebral Blood Volume During Rat Forepaw Stimulation. Magn. Reson. Med., 39(4), 615-624.

  10. Leite, F.P., Tsao, D., Vanduffel, W., Fize, D., Sasaki, Y., Wald, L.L., et al. (2002). Repeated fMRI Using Iron Oxide Contrast Agent in Awake, Behaving Macaques at 3 Tesla. Neuroimage, 16(2), 283-94.

  11. Siegel, A.M., Culver, J.P., Mandeville, J.B., & Boas, D.A. (2003). Temporal comparison of functional brain imaging with diffuse optical tomography and fMRI during rat forepaw stimulation. Phys Med Biol, 48(10), 1391-1403.

  12. Mandeville, J.B., Marota, J.J.A., Ayata, C., Zaharchuk, G., Moskowitz, M.A., Rosen, B.R., et al. (1999). Evidence of a Cerebrovascular Post-arteriole Windkessel with Delayed Compliance. J. Cereb. Blood Flow Metab., 19(6), 679-689.

  13. Leite, F.P., & Mandeville, J.B. (2003). Event-related BOLD and IRON stimulus designs. in Int Soc Magn Reson Med. Toronto, CA.

An Examination of Biophysical Models of the BOLD fMRI Signal Using

The talk will describe recent work developing a biophysical model linking the neural responses to stimulation, through the hemodynamic changes in blood oxygenation flow and volume, to the BOLD fMRI signal. In particular the major focus will be on the use of optical imaging spectroscopy and LDF measurements made concurrently with the BOLD and cbv-MRI measurements to examine the predictions of what is sometimes known as the Massachusetts General Hospital model of the BOLD signal (eg Boxerman, Davis, Hoge etc). Some even more recent work will be described in which IVIM crushing is used to explore the predictions of the 'Yablonskiy Haacke' (1994) model of the contribution of the extravascular static regime to the BOLD signal. The topic for discussion is this : despite the fact that the spectroscopy and the LDF (using Grubb's 'law') data is commensurate with the MRI measurements of the changes in blood volume, the measured BOLD signal is much larger than that predicted by the models (using generally accepted assumptions of baseline values) and the concurrent optical imaging measurements of changes in Hbr and Hbt.

Integrating Data Obtained by In Vivo Spectroscopy and Imaging with Modeling of Oxygen Distribution in Tissues: Concept and Approach

Our aim is to conceptualize the complex physiology/pathophysiology that is involved in changes of oxygen in tissue and then apply advanced computational methods to develop a comprehensive physiological model that describes the distribution and changes of oxygen in tissue and the metabolic and signaling events associated with oxygen. This will be done using data from several different and complimentary methods for making measurements in vivo. Because the distribution of oxygen in tissues is very heterogeneous, even at cellular dimensions, such measurements and the resulting model are important but challenging tasks.


The need and opportunities for developing a comprehensive model for oxygen in tissues that is consistent with and validated by direct measurements, arose from studies that began as validation of EPR oximetry. As the "new" method, it was desirable to show that the measurements obtained with EPR oximetry "gave the same results" as other methods for measuring oxygen in tissues. We therefore initiated studies to make careful simultaneous or sequential measurements with EPR and one or more other modalities to determine the relationships between the results obtained with the various methods, taking into account the parameters on which the measurements are based.


As we began to carry out these experiments, however, we became acutely aware that the idea that we could do this via simple direct comparisons was an illusion. For example, it seemed logical to make direct measurements of oxygen in tumors simultaneously with EPR oximetry and the "gold standard", the Eppendorf Histograph. But the measurements are not really directly comparable even though they both measure the partial pressure of oxygen. This is because the volume measured with the EPR oximetry technique that we used is much larger than the volume probed with a single point with the Eppendorf. Even if we aggregate the volumes probed with the Eppendorf to make the total volume comparable to that with EPR oximetry, the Eppendorf measurements are spatially different and inevitably should record extremes of values that would not be recorded with the EPR method, because of the heterogeneity of the oxygen in real tissues, especially tumors. Therefore, even if both methods were technically perfect and valid, the results would be different. This conclusion, of course, applies to comparisons of essentially all types of measurements of oxygen and related parameters.


The relationship of measurements made with the BOLD effect to those made with other modalities is especially interesting, because the BOLD technique is widely available and it can be used to make measurements in virtually any part of an animal or human subject. The data obtained with BOLD, however, are very non-specific, reflecting principally the amount of deoxyhemoglobin. These data can be made more useful if they are combined with another type of related measurement, e.g. direct measurements of oxygen.


While data comparing results with two or more different modalities are valuable, these experiments have made us aware that it would be possible to develop a much more thorough and useful understanding of oxygen in tissue if we developed methods and models that can incorporate the different measurements into a physiologically based model that is based on the nature of the data from the different types of measurements. The oxygen concentration at any point is affected by the delivery, distribution, and consumption of oxygen locally, regionally, and systemically. These parameters are affected by many different processes including perfusion, diffusion, metabolism, the anatomy of the microcirculation, and the function of the macrocirculatory system. There are methods available to measure parameters that can be affected by most or all of the processes, but because each measured parameter is affected by multiple processes, multiple types of measurements are desirable. It also is desirable to have a logical basis to relate the measurements to each other; i.e., appropriate models of the processes. This would not only enhance the value of the data from the various types of measurements but, most importantly, also could lead to an optimized model that much more fully describes oxygenation in tissues, at levels ranging from the subcellular to the whole organism.


This is a challenging task, requiring input from several different disciplines, with multiple iterations to feed back the results of measurements into the model, then to modify the model appropriately and carry out measurements under different conditions to test the validity of the alterations to the model. We believe that such an effort is feasible and desirable.

A General Statistical Analysis of fMRI Data

Our proposed method for the statistical analysis of fMRI data seeks a compromise between validity, generality, simplicity and execution speed. The method is based on linear models with local AR(p) errors. The AR(p) model is fitted via the Yule-Walker equations with a simple bias correction that is similar to the first step in the Fisher scoring algorithm for finding ReML estimates. The resulting effects are then combined across runs in the same session, across sessions in the same subject, and across subjects within a population by a simple mixed effects model. The model is fitted by ReML using the EM algorithm after re-parameterization to reduce bias, at the expense of negative variance components. The residual degrees of freedom are boosted using a form of pooling by spatial smoothing. Activation is detected using Bonferroni, False Discovery Rate, and non-isotropic random field methods for local maxima and spatial extent. We briefly look at an alternative method based on conjunctions. Finally, we use a simple method to estimate and make inference about the delay of the hemodynamic response function at every voxel. We conclude with some suggestions for the optimal design of fMRI experiments.