Core Project #2

Nonlinear Modeling of Complex Biomedical Systems

Vasilis Z. Marmarelis, Ph.D.
Project Leader

The term“complex” in the project title indicates that the goal of this project is the analysis of the dynamic interrelationships among multiple interconnected variables (e.g. multi-unit neural activity, variables of cerebral hemodynamics or metabolic-endocrine variables under natural operating conditions).

The motivation and overall objective of this project is two-fold:

  1. development and testing of practicable, yet general and rigorous, methodologies for data-based nonlinear modeling of the dynamic interrelationships among multiple observed biological/physiological variables in order to advance scientific knowledge in the study of biological and physiological functional dynamics;
  2. application and translation of the developed methodologies to clinical problems of critical importance in order to improve diagnosis and treatment in a broad spectrum of disease (neurological, cardiovascular, neurovascular, metabolic, endocrine).

Specific recent advances on the methodological front include: (a) the optimization of a general methodology for multi-input/multi-output modeling in order to obtain compact, reliable and interpretable nonlinear dynamic models for the interactions of neuronal ensembles in the brain (using our novel concept of PMDs: Principal Dynamic Modes); (b) the development of a general methodology for the design of optimal patterns of neurostimulation for cognitive neuroprostheses; (c) a general methodology for closed-loop modeling of the dynamic interrelationships between mutually-dependent physiological variables, suitable for the analysis of physiological autoregulation and homeostatic systems – upon which life critically depends.

Specific examples of recent model-based clinical applications are: (a) model-based “functional biomarkers” for improved diagnosis of early-stage Alzheimer’s disease and prognosis in patients with Mild Cognitive Impairment or cognitive/executive dysfunction; (b) optimized neuro-stimulation patterns for the prevention of epileptic seizures; (c) model-based diagnosis of Type 2 diabetes, prognosis of gestational diabetes and blood glucose regulation.

Our efforts in model-based clinical diagnosis and treatment are continuing and expanding at a rapid pace as the “comfort zone” of our clinical collaborators widens with increasing exposure to our modeling methodologies/approach and our own understanding, as well as confidence, rises with broadening experience. As the broad gamut of potential clinical benefits emerges through this discovery process, this translational effort becomes the main thrust of our current and future efforts.

The development and testing of the requisite software for implementing the modeling methodologies in an efficient and user-friendly manner, so that they can be easily adopted by the broader peer community, remains one of our indispensable objectives in the context of the Service activities of the BMSR.

The aforementioned efforts are enriched and, in fact, enabled by our collaborative projects which have been the source of valuable data and background knowledge in various scientific or clinical applications through the years. For this reason, we are placing increasing emphasis on such collaborations in the direction of translational efforts in important clinical domains (neurological, cardiovascular, neurovascular, metabolic, endocrine).

 

Selected Publications

PubMed

Marmarelis V.Z., D.C. Shin, M.E. Orme, and R. Zhang. Closed-loop dynamic modeling of cerebral hemodynamics. Annals of Biomedical Engineering 41(5):1029-48, 2013. [PMC3625507]

Marmarelis V.Z., D.C. Shin, D. Song, R.E. Hampson, S.A. Deadwyler, and T.W. Berger. Nonlinear modeling of dynamic interactions within neuronal ensembles using Principal Dynamic Modes. Journal of Computational Neuroscience 34(1):73-87, 2013. [PMC3531564]

Marmarelis V.Z., D.C. Shin, D. Song, R.E. Hampson, S.A. Deadwyler, and T.W. Berger. Design of optimal stimulation patterns for neuronal ensembles based on Volterra-type hierarchical modeling. Journal of Neural Engineering 9(6):066003, 2012. [PMC3538881]

Eikenberry S.E. and V.Z. Marmarelis. A nonlinear autoregressive Volterra-type model of the Hodgkin-Huxley equations. Journal of Computational Neuroscience 34(1):163-83, 2013. [PubMed – In Process]

Hampson, R.E., G.A. Gerhardt, V.Z. Marmarelis, D. Song, I. Opris, L. Santos, T.W. Berger, and S.A. Deadwyler. Facilitation and restoration of cognitive function in primate prefrontal cortex by a neuroprosthesis that utilizes minicolumn-specific neural firing. Journal of Neural Engineering 9(5):056012, 2012. [PMC3505670]

Hampson R.E., D. Song, R.H.M. Chan, A.J. Sweatt, J. Fuqua, G.A. Gerhardt, D. Shin, V.Z. Marmarelis, T.W. Berger, and S.A. Deadwyle. A nonlinear model for hippocampal cognitive prosthesis: Memory facilitation by hippocampal ensemble stimulation. IEEE Transactions on Neural Systems & Rehabilitation Engineering 20(2):184-197, 2012. [PMC3397311]

Berger T.W., D. Song, R.H.M. Chan, V.Z. Marmarelis, R.E. Hampson, S.A. Deadwyler, J. LaCoss, J. Wills, and J.J. Granacki. A hippocampal cognitive prosthesis: Multi-Input, Multi-Output nonlinear modeling and VLSI implementation. IEEE Transactions on Neural Systems & Rehabilitation Engineering 20(2):198-211, 2012. [PMC3395724]

Zanos S., T.P. Zanos, V. Z. Marmarelis, G. A. Ojemann, E.E. Fetz. Relationships between spike-free local field potentials and spike timing in human temporal cortex. J. Neurophysiology 107:1808-1821, 2012. [PMC3331669]

Hampson, R.E., D. Song, R.H.M. Chan, A.J. Sweatt, M.R. Riley, A.V. Goonawardena, V.Z. Marmarelis, G.A. Gerhardt, T.W. Berger, and S.A. Deadwyler. Closing the loop for memory prostheses: Detecting the role of hippocampal neural ensembles using nonlinear models IEEE Transactions on Neural Systems & Rehabilitation Engineering 20(4):510-525, 2012. [PMC3395725]

Marmarelis V.Z., D.C. Shin, and R. Zhang. Linear and nonlinear modeling of cerebral flow autoregulation using principal dynamic modes. Open Biomedical Engineering Journal 6:42-55, 2012. [PMC3377891]

Berger, T.W. R.E. Hampson, D. Song, A. Goonawardena, V.Z. Marmarelis, and S.A. Deadwyler. A cortical neural prosthesis for restoring and enhancing memory. Journal of Neural Engineering 8(4): 1-12, 2011. [PMC3141091]

Hampson R.E., A.J. Sweatt, A.V. Goonawardena, D. Song, R.H.M. Chan, V.Z. Marmarelis, V. Z., T.W. Berger and S.A. Deadwyler. Memory encoding in hippocampal ensembles is negatively influenced by cannabinoid CB1 receptors. Behavioral Pharmacology 22(4):335-346, 2011. [PMC3135765]

Markakis, M. G., G. D. Mitsis, G. P. Papavassilopoulos, P. A. Ioannou and V. Z. Marmarelis. A switching control strategy for the attenuation of blood glucose disturbances. Optimal Control Applications and Methods 32(2):85-195, 2011. [PDF][PMC3081193]

Berger, T.W., S. Dong, R. Chan and V.Z. Marmarelis. The Neurobiological Basis of Cognition: Identification by Multi-Input, Multioutput Nonlinear Dynamic Modeling. Proceedings of the IEEE 98(3):356-374, 2010. [PDF][PMC2917726]

Chaniotis A.K., L. Kaiktsis, D. Katritsis, E. Efstathopoulos, I. Pantos and V. Marmarellis. Computational study of pulsatile blood flow in prototype vessel geometries of coronary segments. Physica Medica 17:1-17, 2009. [PDF]

Mitsis, G.D., R. Zhang, B.D. Levine, E. Tzanalaridou, D.G. Katritsis and V.Z. Marmarelis. Autonomic neural control of cerebral hemodynamics. IEEE Engineering in Medicine & Biology Magazine 28(6):54-62, 2009. [PMC2917725]

Zanos, T., R. Hampson, S. Deadwyler, T. Berger and V. Marmarelis. Boolean Modeling of Neural Systems with Point-Process Inputs and Outputs. Part II: Application to the Rat Hippocampus. Annals of Biomedical Engineering 37(8):1668-1682, 2009. [PDF][PMC2917724]

Marmarelis, V., T. Zanos and T. Berger. Boolean Modeling of Neural Systems with Point-Process Inputs and Outputs. Part I: Theory and Simulations. Annals of Biomedical Engineering 37(8):1654-1667, 2009. [PDF][PMC2917726]

Song, D., Z. Wang, V.Z. Marmarelis and T.W. Berger. Parametric versus non-parametric modeling of short-term synaptic plasticity. Part I: Computational study. Journal of Computational Neuroscience 26: 1-19, 2009. [PDF][PMC2770349]

Song, D., Z. Wang, V.Z. Marmarelis and T.W. Berger. Parametric versus non-parametric modeling of short-term synaptic plasticity in the hippocampus. Part II: Experimental study. Journal of Computational Neuroscience 26: 21-37, 2009. [PDF][PMC2749717]

Zanos T.P., S.H. Courellis, R.E. Hampson, S.A. Deadwyler, T.W. Berger and V.Z. Marmarelis. Nonlinear modeling of causal interrelationships in neuronal ensembles. IEEE Transactions on Neural Systems & Rehabilitation Engineering 16(4): 336-352, 2008. [PDF][PMC2729787]

Dimoka, A., S.H. Courellis, V.Z. Marmarelis and T.W. Berger. Modeling the nonlinear dynamic interactions of afferent pathways in the dentate gyrus of the hippocampus. Annals of Biomedical Engineering 36(5): 852-864, 2008. [PDF][PMC2749714]

Dimoka, A., S.H. Courellis, G. Gholmieh, V.Z. Marmarelis and T.W. Berger. Modeling the nonlinear properties of the in vitro hippocampal perforant path-dentate system using multi-electrode array technology. IEEE Transactions on Biomedical Engineering 55: 693-702, 2008. [PDF][PMC2749727]

Mitsis, G.D., A.S. French, U. Höger, S. Courellis, and V Z. Marmarelis. Principal dynamic mode analysis of action potential firing in a spider mechanoreceptor. Cybernetics 96(1):113-127, 2007. [PDF]

Song D., R.H.M. Chan, V.Z. Marmarelis, R.E. Hampson, S.A. Deadwyler and T. W. Berger. Nonlinear dynamic modeling of spike train transformation for hippocampal-cortical prostheses. IEEE Transactions on Biomedical Engineering 54(6):1053-1065, 2007. [PDF]

Gholmieh, G., S. Courellis, V.Z. Marmarelis and T.W. Berger. Nonlinear dynamic model of CA1 short-term plasticity using random impulse train stimulation. Annals of Biomedical Engineering 35(5):847-857, 2007. [PDF]

Mitsis, G.D., R. Zhang, B.D. Levine and V.Z. Marmarelis. Cerebral hemodynamics during orthostatic stress assessed by nonlinear modeling. Journal of Applied Physiology 101:354-366, 2006. [PDF]

Marmarelis, V.Z. and T.W. Berger. General methodology for nonlinear modeling of neural systems with Poisson point-process inputs. Mathematical Biosciences 196:1-13, 2005. [PDF]

Marmarelis, V.Z. Nonlinear Dynamic Modeling of Physiological Systems, Wiley Interscience & IEEE Press, New Jersey, 2004. [PDF]

Mitsis, G.D., M.J. Poulin, P.A. Robbins, and V.Z. Marmarelis. Nonlinear modeling of the dynamic effects of arterial pressure and CO2 variations on cerebral blood flow in healthy humans. IEEE Transactions on Biomedical Engineering 51(11):1932-1943, 2004. [PDF]

Gholmieh G., S.H. Courellis, V.Z. Marmarelis and T.W. Berger. Detection and classification of neurotoxins using a novel short-term plasticity quantification method. Biosensors & Bioelectronics 18(12):1467-1478, 2003.[PDF]

Gholmieh, G., S.H. Courellis, V.Z. Marmarelis and T.W. Berger. An efficient method for studying short-term plasticity with random impulse train stimuli. Journal of Neuroscience Methods 121:111-127, 2002.[PDF]

Mitsis G.D., R. Zhang, B.D. Levine and V.Z. Marmarelis. Modeling of nonlinear physiological systems with fast and slow dynamics. II. Application to cerebral autoregulation. Annals of Biomedical Engineering 30(4):555-565, 2002. [PDF]

Mitsis G.D. and V.Z. Marmarelis. Modeling of nonlinear physiological systems with fast and slow dynamics. I. Methodology. Annals of Biomedical Engineering 30(2):272-281, 2002. [PDF]

Berger, T.W., M. Baudry, R.D. Brinton, J-S. Liaw, V.Z. Marmarelis, Y. Park, B.J. Sheu and A.R. Tanguay, Jr. Brain-implantable biomimetic electronics as the next era in neural prosthetics. Proceedings of the IEEE, 89:993-1012, 2001. [PDF]

Gholmieh, G., W. Soussou, S.H. Courellis, V.Z. Marmarelis, T.W. Berger and M. Baudry. A biosensor for detecting changes in cognitive processing based on nonlinear systems analysis. Biosensors and Bioelectronics, 16(7-8): 491-501, 2001. [PDF]

Alataris, K., T.W. Berger & V.Z. Marmarelis. A novel network for nonlinear modeling of neural systems with arbitrary point-process inputs. Neural Networks, 13(2):255-266, 2000. [PDF]

Iatrou, M., T.W. Berger & V.Z. Marmarelis. Application of a novel modeling method to the nonstationay properties of potentiation in the rabbit hippocampus. Annals of Biomedical Engineering 27(5):581-591, 1999. [PDF]

Marmarelis, V.Z., M. Juusola & A.S. French. Principal dynamic mode analysis of nonlinear transduction in a spider mechanoreceptor. Annals of Biomedical Engineering 27:391-402, 1999.[PDF]

Marmarelis, V.Z., K.H. Chen, N.H. Holstein-Rathlou & D.J. Marsh. Nonlinear analysis of renal autoregulation in rats using principal dynamic modes. Annals of Biomedical Engineering 27:23-31, 1999.[PDF]

Iatrou, M., T.W. Berger and V.Z. Marmarelis. Application of a novel modeling method to the nonstationary properties of potentiation in the rabbit hippocampus. Annals of Biomedical Engineering 27:581-591, 1999.[PDF]

Marmarelis, V.Z. & X. Zhao. Volterra models and three-layer perceptrons. IEEE Transactions on Neural Networks 8(6):1421-1433, 1997. [PDF]

Marmarelis, V.Z. Modeling methodology for nonlinear physiological systems. Annals of Biomedical Engineering 25:239-251, 1997. [PDF]

Marmarelis, V.Z. (Ed.) Advanced Methods of Physiological System Modeling: Volume III., Plenum, New York, 1994.

Marmarelis, V.Z. & M.E. Orme. Modeling of neural systems by use of neuronal modes. IEEE Transactions on Biomedical Engineering 40(11):1149-1158, 1993.[PDF]

Marmarelis, V.Z. Identification of nonlinear biological systems using Laguerre expansions of kernels. Annals of Biomedical Engineering 21:573-589, 1993.[PDF]

Marmarelis, V.Z. Wiener analysis of nonlinear feedback in sensory system. Annals of Biomedical Engineering 19(4):345-382, 1991.[PDF]

Marmarelis, V.Z. Signal transformation and coding in neural systems. IEEE Transactions on Biomedical Engineering 36(1):15-24, 1989.[PDF]

Marmarelis, V.Z. (Ed.) Advanced Methods of Physiological System Modeling: Volume II., Plenum, New York, 1989.

Marmarelis, V.Z. Advanced Methods of Physiological System Modeling: Volume I., Biomedical Simulations Resource, Los Angeles, California, 1987.