Research Topics
Department of Nuclear, Plasma and Radiological Engineering
Ph.D. (1987) University of Illinois
Research Topics
Research Interests
My biotechnology related research is focused around mathematical model development, simulation and computational biology. This exercise often leads toward laboratory and clinical data analysis, nonlinear dynamical systems and chaos, and complex systems. Recent specific interests have been in three areas: heart rate variability (HRV) data analysis, modeling the sino atrial node, and simulation of tumor growth.
We have analyzed numerical and clinical cardiac data using methods developed in the field of modern nonlinear dynamical systems and deterministic chaos. The goal is to identify quantifiers that can be used as clinical measures to identify and possibly predict the state of a patient. This work can be classified into two groups. First, the series of RR intervals are classified using quantifiers like, correlation dimension, embedding dimension, Lyapunov exponent and others, to classify chaotic and non- chaotic attractors obtained in experimental, clinical and theoretical (numerical) studies. Epochs of series of RR intervals from heart transplant patients are analyzed. In the second series of work, certain characteristic features of neonatal HRV are evaluated and compared with those of adult HRV to identify key differences in the pattern of interbeat increments in healthy and sick newborn infants vs. healthy and sick adults. This suggested that very low-frequency elements of neonatal and adult heart rate variability rise from fundamentally different mechanisms. That work was recently extended to probe the reasons why the HRV falls during neonatal illness. We calculated predictability and regularity of RR interval time series that showed different degrees of HRV. It was concluded that neonatal RR interval time series are ordered by periodic processes with frequencies over a large spectrum, and that the amount of order is less during illness when HRV is low.
The Sino Atrial (SA) node modeling problem was approached by first improving an existing model. We developed a new continuous model based on a modified Poincaré oscillator, which is able to capture essentially all the characteristic features observed in the SA node culture experiments reported in literature without going to a complex model of the Hodgkin-Huxley (H-H) type. The new model leads to a transient in response to a single stimulus, and subsequently returns to periodic behavior with the original frequency, but with a phase shift as observed in experiments. We extended this model of the sinus node to account for overdrive suppression. This required the addition of one more ordinary differential equation to the model to account for different rates of decay of the normalized intrinsic cycle length after application of different number of stimuli, leading to excellent agreement between experimental results and our extended model. We have also developed a Hodgkin-Huxley type model by successfully modifying an existing model to include a phase-dependent response of external stimuli. This has resulted in simulated phase response curves that are identical to those measured in laboratories.
We are studying the encapsulation and lobulation mechanism of tumors in a virtual (numerical simulation) environment. Recent studies have analyzed the impact of the geometry -- Cartesian, cylindrical or spherical -- on the growth and encapsulation process of a tumor. We have introduced in a 1-D model of tumor growth, a modified generation term that represents the population pressure on growth, and consequently leads to nodular tumors. Simulations in spherical geometry show that the lobes (nodules) near the center of the tumor to be larger than those near the capsule well.
Key Words Mathematical and Computational Biology, Heart Rate Variability
(HRV), Nonlinear dynamics and Chaos, Complex Systems, Sino Atrial Node Modeling,
Modeling of Tumor Structure and Growth
Current Research Funding: DOE