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Item A closed-loop model of the ovine cardiovascular system(2003) Qian, Junhui; Clark, John W., Jr.Show more The conscious sheep is an important large animal model for the study of human cardiovascular and cardiopulmonary system. In this study we develop a closed-loop mathematical model of its cardiovascular system. A distributed approach is taken in describing the systemic circulation, which is divided into cerebral, coronary, foreleg, thoracic, abdominal, and hind-limb circulations. Nonlinear aspects of the systemic venous system are described, which include nonlinear pressure-volume characteristics of small and large veins and pressure-operated valves in large veins. The complete integrated model mimics typical steady-state hemodynamic data in the supine position. It is also used to predict the blood volume shifts and hemodynamic changes that accompany standing up. These include the short-term neurally mediated cardiovascular response to the orthostatic stress. Additional studies predict the circulatory response to an increased afterload (balloon inflation) presented to the right ventricle. This model is further used to predict the response of the ovine cardiovascular system to the implantation of the PAL (Para-corporeal Artificial Lung device and to test the putative effectiveness of different PAL device designs.Show more Item A distributed-parameter model of the myelinated nerve fiber(1989) Halter, John Alan; Clark, John W., Jr.Show more This thesis is concerned with the development of a new distributed-parameter model of the myelinated nerve fiber that includes an adequate representation of the anatomical complexity present at the node of Ranvier, considers the peri-axonal conductance pathway and includes active ionic channels in the axolemmal membrane beneath the myelin sheath. A detailed review of the current anatomical and electrophysiological literature was performed and tables containing the biophysical properties of the amphibian and mammalian myelinated nerve fibers were compiled. Recent dynamics for the mammalian sodium channel were adopted and a non-linear parameter estimation method was applied to fit the dynamics of a fast and a slow amphibian potassium channel. Membrane action potentials were computed from the new space-clamped nodal and internodal membrane models. A multi-axial electrical equivalent circuit was developed with intra-axonal, peri-axonal and extra-axonal longitudinal conduction paths and independent transverse elements for the axolemmal membrane and the myelin sheath. Non-uniform spatial step sizes were used, enabling detailed representation of the nodal region while minimizing the number of segments necessary to represent the entire fiber. An implicit integration method was developed for the resulting multiple cross-coupled parabolic partial differential equations as represented in finite difference matrix form. The solution was implemented on a Sequent Systems S81 parallel processor, dividing the solution for the component ionic currents and the matrix operations across an arbitrary number of processors. The model allowed for the detailed examination of component potentials and currents. Physiological conduction velocities of 20.2 m/s at 20$\sp\circ$C for a 15$\mu$m diameter amphibian fiber and 57.6 m/s at 37$\sp\circ$C for a 17.5$\mu$m diameter mammalian fiber were achieved. An increase in conduction velocity of 32.3% was seen for a nodal constriction of 80%, contrary to previous modeling efforts. The peri-axonal space in the paranodal region was shown to have a strong influence on conduction velocity. Restriction of the extracellular volume resulted in slower conduction velocities for radii less than 25 $\mu$m. Paranodal ionic channels were activated during conduction and there was model evidence for the possible generation of slow (0.06 m/s) propagating action potentials beneath the myelin sheath.Show more Item A MATHEMATICAL MODEL OF LEFT VENTRICULAR FUNCTION AND ITS SYMPATHETIC CONTROL(1973) GREENE, MICHAEL EDWARD; Clark, John W., Jr.Show more Item A mathematical model of the afferent stage of the mammalian baroreceptor reflex(1994) Schild, John Henry; Clark, John W., Jr.Show more The purpose of this research effort is to develop a mathematical model of the afferent portion mammalian arterial baroreceptor reflex. The entire model is comprised of a small network of Hodgkin-Huxley (HH) type membrane models representing the minimum number of anatomical structures (i.e. neurons and afferent terminations) participating in the transduction, transmission and the initial processing stage for arterial pressure information within the medullary cardiovascular control centers. The structures represented are: arterial wall and baroreceptor terminal endings (BR), which encode arterial pressure into frequency modulated action potential trains; the synaptic connection (SYN) between sensory afferent terminations and medial nucleus tractus solitorius neurons (mNTS) which are the first brainstem neurons participating in the arterial baroreflex. Realistic membrane models of the peripheral and central terminations (i.e. BR and SYN) was made possible through the initial development of a comprehensive mathematical model of isolated nodose sensory neurons. Individually, the excitable membrane have all been modeled using HH-type formalisms which have been modeled using an iterative process of electrophysiological recordings, nonlinear parameter estimation, phase-plane analysis and computer simulation. Each component model provides good numerical fits to quantitative whole-cell voltage clamp and action potential data (i.e. rat) recorded both by myself and our scientific collaborators. Each membrane model, with the exception of the BR, is coupled to a lumped fluid compartment model that describes Ca$\sp{2+}$ ion concentration dynamics within the intracellular media in addition to buffering via a calmodulin-type buffer. The complete model attempts to describe the essential electrophysiological characteristics of this primary input stage of the baroreflex system in the rat.Show more Item A mathematical model of the amphibian muscarinic channel(1989) Shumaker, John Michael; Clark, John W., Jr.Show more A modification of the Osterrieder-Noma-Trautwein model of the ACh-sensitive K$\sp+$ I$\sb{K,ACh}$ current in the rabbit SA node is used to study the behavior of the ACh-sensitive K$\sp+$ channels in bullfrog atrial and sinus venosus myocytes. The parameters of the modified description of the muscarinic current are chosen to fit available data from the literature on bullfrog atrial myocytes. This model is incorporated into larger mathematical models of bullfrog myocytes that are based on quantitative whole-cell voltage clamp data and simulations are run to discern the effects of this muscarinic channel on the electrical behavior of the cell membrane. Simulations of the electrical behavior of the sinus venosus myocyte predict that the effects of ACh on the pacemaker action potential are dependent on both the phase of ACh delivery and rate of removal of the ACh. Model-generated phase response curves (PRC's), inhibition curves (IC's) and entrainment curves are produced. (Abstract shortened with permission of author.)Show more Item A mathematical model of the mammalian ventricular cell: Mechanistic explanations of long Q-T syndrome(2002) Daniel, Kimberly Nichole; Clark, John W., Jr.Show more We have developed a mathematical model of a rabbit ventricular cell based on available whole cell voltage clamp data. The model consists of three components: a Hodgkin-Huxley type membrane model describing the electrical activity of the cell membrane; and intracellular fluid compartment model; and a small extracellular cleft space. Material balances for Na+, K +, and Ca2+ provide the describing equations for the intra and extracellular spaces. A model for the sarcoplasmic reticulum is also provided in the intracellular fluid compartment model. Whole cell voltage clamp data from the rabbit ventricular myocyte was utilized to characterize the kinetics of the ionic membrane currents. Parameters associated with the ionic currents can be adjusted to yield good fits to measured action potential and Ca2+ transient waveforms recorded in our laboratory. Moreover, the model can be employed to qualitatively predict the ionic mechanisms underlying repolarization.Show more Item A mechanistic model for the study of the arterial myogenic response(2002) Yang, Jin; Clark, John W., Jr.Show more This study is concerned with the development of a multiple compartment model of the isolated cerebral artery in rat. The smooth muscle/arterial wall complex is an important component of the circulatory model and serves as a "vasomotor organ", which provides the myogenic mechanism that underlies the phenomenon of the autoregulation of blood flow. We have focused on this myogenic mechanism and have developed a model of the electrophysiological and contractile characteristics of the single smooth muscle cell of the posterior cerebral artery. This cell model is used to interrelate the topics of arterial wall stress, changes in transmembrane potential, intracellular Ca 2+ concentration and contraction. Moreover, the smooth muscle cell model is imbedded in a larger arterial wall model which converts contractile activity into changes in lumen diameter. The complete model consisting of component models of cell, wall, vessel and testing apparatus is used to provide biophysically based explanations of the myogenic mechanisms underlying the autoregulation of cerebral blood flow.Show more Item A model of lateral inhibition and directional selectivity in the crayfish compound eye(1994) Bartels, Annemarie; Clark, John W., Jr.Show more This study models the network interactions of five classes of neurons in the crayfish retina which support lateral inhibition and directional selectivity. The models approximate pulse responses and responses to drifting sinusoidal gratings in each cell type. Lateral inhibition is implemented by a shunting inhibitory feedback from lamina amacrine cells to the photoreceptor terminals. This mechanism determines the range of possible spatial and temporal frequencies of the synaptic input signals to the transmedullary and tangential cells. Tangential cells implement a delay and compare operation via competitive binding of GABA and ACh to ligand-gated membrane channels. The delay and compare operation can account for the directional selectivity which is observed experimentally in the tangential cells but not in any of the cells which form its input pathway. The models presented are nonlinear. They can reproduce the observed pulse responses over wide range of light intensities.Show more Item A model of normal and depressed conduction in cardiac strands(1988) Murphey, Carey Richard; Clark, John W., Jr.Show more Mathematical modeling of the electrical activity of a single cardiac cell and of strands of cardiac cells are problems of fundamental interest in the area of electrophysiology. New and increasingly comprehensive data on the electrophysiological behavior of single, isolated cardiac myocytes have facilitated the development of more 'complete' models and are used here for the development of mathematical characterizations of cells exhibiting 'normal' electrophysiologic behavior as well as those exhibiting 'depressed' activity. Simulation and parameter estimation techniques are utilized to investigate model-generated single cell electrical behavior and to adjust this behavior to best fit observed responses. Suitably 'identified' models may be used in further simulations of electrical activity in linear strands of resistively coupled cardiac cells. It is hoped that together with advances in experimental methods, these methods for analysis and adjustment of model behavior will provide new and meaningful insight into the mechanisms of cardiac electrical activity.Show more Item A model of sarcolemmal calcium(2+) currents and cytosolic calcium(2+) transients in a rat ventricular cell(2000) Sun, Liang; Clark, John W., Jr.Show more We have developed a mathematical model of the L-type Ca2+ current and cytosolic Ca2+ transient, which is based on data from whole-cell voltage clamp experiments on rat ventricular myocytes. Modified Goldman-Hodgkin-Katz (GHK) equations are provided to account for the different ion selectivity of the DHP-sensitive Ca2+ current channel. The decay of whole cell currents obtained by maintained depolarization is characterized by means of voltage and Ca2+-dependent inactivation embedded in a 5-state dynamic DHP channel model. To characterize a reduced amount of steady-state inactivation of DHP channel in the presence of [Ca 2+]o, a mechanism is used in the model whereby Ca 2+ also inhibits the voltage-dependent inactivation pathway. The 5-state DHP model is also used to simulate single-channel activity. Cytosolic Ca 2+ transients are studied as well. They derive mainly from secondary Calcium-Induced-Calcium-Release (CICR) from the Sarcoplasmic Reticulum (SR). We have developed a 4-state RyR-sensitive Ca2+ model that describes the kinetics of the release channel. This model provides close fitting of cytosolic Ca2+-transient data and mimics the high gain, graded Ca2+ release behavior of the channel. Overall, the model provides a quantitative description of the Ca2+ subsystem in the mammalian heart.Show more Item A model of the aortic baroreceptor in rat(1997) Alfrey, Karen D.; Clark, John W., Jr.Show more The baroreceptor, a stretch-sensitive neuron, senses static and dynamic arterial blood pressure and responds by producing a frequency-modulated train of action potentials. The size and anatomy of baroreceptor nerve endings precludes direct experimental study of the details of baroreceptor behavior; however, studies of output firing frequency in response to arterial pressure changes reveal a highly nonlinear input-output characteristic. While many models of the baroreceptor have been developed, most of these models have failed to provide a comprehensive view of the mechanisms under-lying baroreceptor function. We present a new baroreceptor model which provides a physiologically-based, comprehensive description of all aspects of the system. This model combines a mechanical model of the arterial wall with Hodgkin-Huxley-type models of the transducer and encoder sections of the neuron. The complete model not only mimics a wide range of experimental results, it also provides a means of making predictions about baroreceptor behavior and of examining the mechanisms underlying baroreceptor function.Show more Item A model of the rate dependence of the atrial action potential in rabbit(1994) Lindblad, Douglas S.; Clark, John W., Jr.Show more We have developed a mathematical model of the rabbit atrial myocyte in order to investigate the ionic bases of rate dependent changes in action potential (AP) wave-shape. Postulated mediators of such changes include rate dependencies of ionic currents (incomplete reactivation) and ionic concentration gradients. The model utilizes biophysical data to quantify the specific morphology and electrophysiology of the rabbit atrial cell. Ionic current descriptions incorporate whole-cell voltage-clamp data from enzymatically isolated rabbit cardiomyocytes, and account for the reactivation timecourse of the largest ionic currents. Our model can simulate both the whole-cell voltage-clamp data upon which it is based and the steady-state AP wave-shapes observed over a range of stimulus rates. It also predicts the intracellular $\lbrack Ca\sp{2+}\rbrack\sb{i}$-transient that accompanies the AP, the "premature stimulus" response, and the effect of rapid stimulation on the AP. These responses provide insight into the electrophysiological mediators of atrial refractoriness and arrhythmia.Show more Item A new implementation of Super Resolution technique in PET imaging(2008) Chang, Guoping; Clark, John W., Jr.Show more A new implementation for Super-Resolution (SR) techniques has been proposed. This new SR implementation has multiple clinical advantages versus the original standard implementation. We tested and validated this new approach by comparing it to the original SR implementation in theoretical and experimental studies. Characterization and evaluation of this new SR processing are also conducted in experimental as well as patient studies. The results show that this new SR implementation can be used to replace the original standard SR implementation while exhibiting similar performance in image resolution and signal-to-noise ratio (SNR).Show more Item A Phantom Study of In-beam PET Imaging for Proton Beam Range Verification(2013-12-17) Lou, Kai; Clark, John W., Jr.; Kelly, Kevin F.; Jacot, Jeffrey G.; Shao, YipingShow more In-beam PET imaging is an advanced image-based method to verify the proton beam range for proton therapy by measuring proton-induced positron activity distribution and activity range. This study investigates the feasibility, accuracy and precision of the activity range measurement with a high-performance compact PET prototype system for in-beam PET imaging. An experiment with a homogeneous PMMA phantom and several Monte Carlo simulation studies are conducted. The results have shown that the prototype PET can provide reasonably good images for the activity range measurement even with low count statistics; the accuracy of activity range measurement reaches sub-millimeter; 11C is the most dominating positron emission isotope contributing to the overall positron activity; the image quality and the precision of activity range measurement depend on the count statistics, and high count statistics leads to improved image quality and precision. Although the study is preliminary with simple system set-ups, it does provide interesting and important results which should lay the basis leading to future clinically relevant investigations.Show more Item A phase sensitivity based method for prediction of modes of behavior in quadrupedal locomotion(1996) DeFranceschi, Anton Allan; Clark, John W., Jr.Show more The objective of this study is development of prediction methods for characterizing the electrical behavior of ring type central pattern generators (CPGs). A mathematical model of the prototypical bursting neuron R15 from the abdominal ganglion of Aplysia is used, along with a simple model of the inhibitory synapse, to form a four neuron ring model of a CPG. The basic mode of a four neuron ring CPG model is able to characterize the walk, trot and bound gaits associated with quadrupedal locomotion. The phase sensitivity of neuron R15 to an external input is investigated, and the results are expressed in terms of cophase curves that are used to formulate prediction algorithms for the behavior of ring type networks. These prediction algorithms are utilized in a Network Emulator that provides an accurate simulation of the behavior of the ring type networks at a considerable savings in computation time compared with numerical solutions of the ordinary differential equations associated with these networks. We further extend this work by examining the conditions for control of the modes of three and four neuron ring CPGs by external stimuli.Show more Item Adaptive regularization based on noise estimation and its application to the inverse problem in electrocardiography(1998) Zhang, Fulong; Clark, John W., Jr.Show more The inverse problem was solved to reconstruct endocardial electrograms from cavitary electrograms measured with a noncontact multielectrode probe. Noise levels were estimated at each time instant by extrapolating noise energy from high spatial frequency components of probe potentials. Based on estimated noise and energy distribution of probe potentials, a matrix of weighting factors was derived to inversely mimic the band shape of the energy spectrum. By incorporating those weighting factors into the inverse procedure, a set of regularization parameters was derived and applied in solving the inverse problem (i.e. adaptive regularization). Adaptive regularization was tested on an experimental canine model. Both traditional uniform regularization and adaptive regularization were applied to compute endocardial electrograms during normal as well as paced rhythms. Adaptive regularization demonstrated a great improvement over uniform regularization in terms of improved correlation coefficients, reduced relative error, better estimation of activation times and localization of pacing sites.Show more Item An adaptive model of left-heart function(1972) Heithecker, Ted. E; Clark, John W., Jr.Show more The methods of mathematical modeling and digital computer simulation can be beneficially applied to the development and testing of cardiac assist devices. Such methods, used in conjunction with other investigative techniques, provide the researcher with a powerful tool for approaching the many difficult problems associated with operation and control of assist devices. Of utmost priority in this modeling application is the availability of a left-heart model which is responsive to variations in left-heart operating conditions. A left-heart model capable of realistically adapting to variations in operating conditions is necessary for evaluation of the effects which an assist device may have on the left-heart. For this purpose a left-heart model is formulated which is responsive to variations in heart rate, left-atrial filling pressure, left-ventricular end-diastolic volume, left-ventricular end-systolic volume and aortic load. The operation of this left-heart model is demonstrated by use of a simple aortic model in computer simulations. The potential of the modeling technique in general (and of the adaptive left-heart model in particular) for use as a research tool is exhibited by the development and use in simulations of a model for an intra-aortic balloon pump assist device. Suggested enhancements to the models for research application are presented.Show more Item An electrodiffusion model of conduction in nerve fibers(1995) McMahon, Michael George; Clark, John W., Jr.Show more A new membrane model for mammalian nerve fibers has been developed. The membrane model utilizes new characterizations for delayed-rectifier currents, and adds an inwardly-rectifying potassium channel as well as a sodium-potassium pump current. Fits are shown to action potential and I-V data at two different temperatures. The Nernst-Planck electrodiffusion equation was then utilized to derive a linked compartmental model of the unmyelinated mammalian nerve fiber with lumped parameter values. The results from this unmyelinated fiber model were presented and compared to data in the literature. A myelinated nerve axon model is also developed and issues of numerical implementation are discussed.Show more Item An ionic current model for neurons in the rat medial nucleus tractus solitarius receiving sensory afferent input(1992) Khushalani, Samir; Clark, John W., Jr.Show more An ionic current model has been developed for the rat medial nucleus tractus solitarius (mNTS) neuron that provides a quantitative description of the ionic macrocurrents present in the soma of the cell, and their interaction in the genesis of patterned electrical activity. It consists of two parts, a model of the somatic membrane, and a fluid compartment model of the intra- and extracellular media. The somatic membrane model is of Hodgkin-Huxley form, and includes mathematical descriptions of time- and voltage-dependent ion selective channels, as well as pump, exchanger and other background currents present in the generic mNTS neuron. The lumped fluid compartment model accounts for intracellular changes in the $Ca\sp{2+}$ concentration. The model is able to successfully mimic the response of the neuron to different sequences of depolarizing and hyperpolarizing pulses, and has provided useful insights into the biophysical interactions underlying the phenomena of delayed excitation (DE) and spike frequency adaptation (SFA).Show more Item Analysis and reduction of a modeled bursting neuron(1996) Butera, Robert John, Jr; Clark, John W., Jr.Show more A modeled bursting neuron was analyzed using methods based upon geometric singular perturbation theory. The mathematical mechanism of bursting in the model consisted of two slow variables traversing the state-space across a saddle-node bifurcation that defined an interface between quiescence and periodic spiking of the subsystem of fast variables. The parabolic nature of the burst was due to the homoclinicity of the saddle-node bifurcation. The response to the model to perturbatory current pulses was analyzed in the state-space of the slow variables. To aid in the analysis nullclines were calculated, including "average" nullclines, which are the nullclines of the slow-variables averaged over one period of the oscillation of the fast subsystem. The averaged nullclines predicted the existence of beating solutions. The relative stability of beating solutions at different parameter sets was related to specific biophysical mechanisms within the model. In addition, the manner in which the equilibrium and average nullclines for a given variable approached each other provided an indication as to which slow variables' dynamics were significantly perturbed by the firing of action potentials. The results of the numerical analysis were applied to develop a reduced model of the underlying subthreshold oscillations (slow-wave) in membrane potential. Two different low-order models were developed: a 3-variable model, which mimicked the slow-wave of the full model in the absence of action potentials and a second 4-variable model, which included expressions accounting for the perturbatory effects of action potentials on the slow-wave. The 4-variable model more accurately predicted the activity mode (bursting, beating, or silence) in response to application of extrinsic stimulus current or modulatory agents. The 4-variable model also possessed a phase-response curve that was very similar to that of the original 11-variable model. The results suggest that low-order models of bursting cells which do not consider the effects of action potentials may erroneously predict modes of activity and transient responses of the full model upon which the reductions are based. These results also show that it is possible to develop low-order models that retain many of the characteristics of the activity of the higher-order system.Show more