Core Project #1
Nonlinear
and Nonstationary Modeling of Biomedical Systems
Vasilis Z. Marmarelis,
Ph.D.
Project
Leader
This project is dedicated to the development of practical modeling methodologies using experimental or clinical data from physiological systems under natural operating conditions. This places the problem in its true operating context and requires the methodological capability to capture the dynamic nonlinearities of multi-variable interactions within a physiological system in a stochastic broadband context. Due to the complexity of this fundamental problem, we have taken a gradualist step-by-step approach, building on the rigorous and general mathematical foundation of the Volterra-Wiener approach as extended over the last thirty years. It is gratifying to note that our efforts have succeeded in developing a solid foundation for a general modeling approach that holds the promise of tackling this problem in a realistic context.
The methodological advances are tested in pilot applications -- initially with data from the six Collaborative Projects affiliated with this Core Project – which represent key applications to the nervous system (neuronal multi-unit interactions and sensory integration), the cardiovascular system (cerebral hemodynamic autoregulation) and the metabolic/endocrine system (insulin-glucose-fatty acid interactions). In addition to being the source of the requisite data, these Collaborative Projects provide valuable physiological guidance for the proper development of the methods and the critical grounds for interpretation and utilization of the obtained models.
These applications have demonstrated the efficacy of the developed methodologies and have allowed important advances in model interpretation by assigning physiological significance to the obtained model components in a manner that deepens the scientific understanding of the system under study and enables improvements in diagnostic as well as therapeutic procedures.
The current aims of this project are clustered into two areas of development of advanced modeling methodologies for the dynamic interrelationships among multiple observed variables under realistic operating conditions (i.e. not constrained paradigms) for:
- multi-unit neuronal dynamics using data from single (encoding/decoding) or multiple (inter-ensemble transformations) multi-electrode arrays in the hippocampus of behaving rats;
- nested-loop homeostatic/homeodynamic autoregulatory systems (endocrine-metabolic or neural-cardiovascular) observed through multiple variables in spontaneous physiological operation -- with or without external stimulation exerting control action.
To maximize the impact of the developed methodologies on the peer community, we will develop, test, distribute and support the requisite user-friendly software in a manner consistent with the mission of a National Resource. It must be emphasized that the advanced modeling methodologies developed and disseminated by this Core Project address problems of great complexity and, therefore, represent the “cutting edge” of research in this field. The development and testing/validation of such modeling methodologies, as well as the requisite software, will help the peer community overcome a critical barrier that has impeded rapid progress in these important scientific fields.
Selected Publications
Marmarelis, V.Z., T.P. Zanos and T.W. Berger. Boolean modeling of neural systems with point-process inputs and outputs. Part I: Theory and simulations. Annals of Biomedical Engineering (submitted).
Marmarelis, V.Z., G.D. Mitsis, K. Huecking and R. Bergman. Nonlinear modeling of the closed-loop dynamic interrelationships between spontaneous variations of plasma insulin and glucose in dogs. Annals of Biomedical Engineering (submitted).
Zanos, T.P., R.E. Hampson, S.A. Deadwyler, T.W. Berger and V.Z. Marmarelis. Boolean modeling of neural systems with point-process inputs and outputs. Part II: Application to the rat hippocampus. Annals of Biomedical Engineering (submitted).
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 Engineering (submitted).
Dimoka, A., S.H. Courellis, V.Z. Marmarelis and T.W. Berger. Modeling the nonlinear dynamic interactions of afferent pathways into the dentate gyrus of the rat hippocampus. Annals of Biomedical Engineering (in press).
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 Neural Engineering (in press).
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 – 601 KB]
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 – 1,008 KB]
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 – 534 KB]
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 – 670 KB]
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 - 301 KB]
Marmarelis, V.Z. Nonlinear Dynamic Modeling of Physiological Systems, Wiley, New York, 2004.
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 - 717 KB]
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 - 606 KB]
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 21(2):111-127, 2002. [PDF - 531KB]
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 - 434 KB]
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 - 155 KB]
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 - 498 KB]
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 - 468 KB]
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 - 668 KB]
Shehada, R.W., V.Z. Marmarelis, H.N. Mansour & W.S. Grundfest. Laser-induced fluorescence attenuation spectroscopy: Detection of hypoxia. IEEE Transactions on Biomedical Engineering 47(3):301-312, 2000. [PDF - 184 KB]
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 Engineering27(5):581-591, 1999. [PDF - 158 KB]
Marmarelis, V.Z., M. Juusola & A.S. French. Principal dynamic mode analysis of nonlinear transduction in a spider mechanoreceptor. Annals of Biomedical Engineering27:391-402, 1999.
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.
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.
Marmarelis, V.Z. & X. Zhao. Volterra models and three-layer perceptrons. IEEE Transactions on Biomedical Engineering 8(6):1421-1433, 1997.
Marmarelis, V.Z. Modeling methodology for nonlinear physiological systems. Annals of Biomedical Engineering 25:239-251, 1997.
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.
Marmarelis, V.Z. Identification of nonlinear biological systems using Laguerre expansions of kernels. Annals of Biomedical Engineering 21:573-589, 1993.
Marmarelis, V.Z. Wiener analysis of nonlinear feedback in sensory system. Annals of Biomedical Engineering 19:345-382, 1991.
Marmarelis, V.Z. Signal transformation and coding in neural systems. IEEE Transactions on Biomedical Engineering 36(1):15-24, 1989.
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.
