Showing papers in "Annals of Biomedical Engineering in 2001"

Nonlinear ligament viscoelasticity.

Abstract: Ligaments display time-dependent behavior, characteristic of a viscoelastic solid, and are nonlinear in their stress-strain response. Recent experiments (25) reveal that stress relaxation proceeds more rapidly than creep in medial collateral ligaments, a fact not explained by linear viscoelastic theory but shown by Lakes and Vanderby (17) to be consistent with nonlinear theory. This study tests the following hypothesis: nonlinear viscoelasticity of ligament requires a description more general than the separable quasilinear viscoelasticity (QLV) formulation commonly used. The experimental test for this hypothesis involves performing both creep and relaxation studies at various loads and deformations below the damage threshold. Freshly harvested, rat medial collateral ligaments (MCLs) were used as a model. Results consistently show a nonlinear behavior in which the rate of creep is dependent upon stress level and the rate of relaxation is dependent upon strain level. Furthermore, relaxation proceeds faster than creep; consistent with the experimental observations of Thornton et al. (25) The above results from rat MCLs are not consistent with a separable QLV theory. Inclusion of these nonlinearities would require a more general formulation.

Factors Influencing Blood Flow Patterns in the Human Right Coronary Artery

Abstract: Evidence suggests that atherogenesis is linked to local hemodynamic factors such as wall shear stress. We investigated the velocity and wall shear stress patterns within a human right coronary artery (RCA), an important site of atherosclerotic lesion development. Emphasis was placed on evaluating the effect of flow waveform and inlet flow velocity profile on the hemodynamics in the proximal, medial, and distal arterial regions. Using the finite-element method, velocity and wall shear stress patterns in a rigid, anatomically realistic model of a human RCA were computed. Steady flow simulations (ReD=500) were performed with three different inlet velocity profiles; pulsatile flow simulations utilized two different flow waveforms (both with Womersley parameter=1.82, mean ReD=233), as well as two of the three inlet profiles. Velocity profiles showed Dean-like secondary flow features that were remarkably sensitive to the local curvature of the RCA model. Particularly noteworthy was the "rotation" of these Dean-like profiles, which produced large local variations in wall shear stress along the sidewalls of the RCA model. Changes in the inlet velocity profiles did not produce significant changes in the arterial velocity and wall shear stress patterns. Pulsatile flow simulations exhibited remarkably similar cycle-average wall shear stress distributions regardless of waveform and inlet velocity profile. The oscillatory shear index was very small and was attributed to flow reversal in the waveform, rather than separation. Cumulatively, these results illustrate that geometric effects (particularly local three-dimensional curvature) dominate RCA hemodynamics, implying that studies attempting to link hemodynamics with atherogenesis should replicate the patient-specific RCA geometry.

Finite element analysis of the current-density and electric field generated by metal microelectrodes.

Abstract: Electrical stimulation via implanted microelectrodes permits excitation of small, highly localized populations of neurons, and allows access to features of neuronal organization that are not accessible with larger electrodes implanted on the surface of the brain or spinal cord. As a result there are a wide range of potential applications for the use of microelectrodes in neural engineering. However, little is known about the current-density and electric field generated by microelectrodes. The objectives of this project were to answer three fundamental questions regarding electrical stimulation with metal microelectrodes using geometrically and electrically accurate finite elements models. First, what is the spatial distribution of the current density over the surface of the electrode? Second, how do alterations in the electrode geometry effect neural excitation? Third, under what conditions can an electrode of finite size be modeled as a point source? Analysis of the models showed that the current density was concentrated at the tip of the microelectrode and at the electrode-insulation interface. Changing the surface area of the electrode, radius of curvature of the electrode tip, or applying a resistive coating to the electrode surface altered the current-density distribution on the surface of the electrode. Changes in the electrode geometry had little effect on neural excitation patterns, and modeling the electric field generated by sharply tipped microelectrodes using a theoretical point source was valid for distances > approximately 50 microm from the electrode tip. The results of this study suggest that a nearly uniform current-density distribution along the surface of the electrode can be achieved using a relatively large surface area electrode (500-1000 microm2), with a relatively blunt tip (3-6 microm radius of curvature), in combination with a thin (approximately 1 microm) moderately resistive coating (approximately 50 omega m).

Compartmental analysis of breathing in the supine and prone positions by optoelectronic plethysmography.

Abstract: Optoelectronic plethysmography (OEP) has been shown to be a reliable method for the analysis of chest wall kinematics partitioned into pulmonary rib cage, abdominal rib cage, abdomen, and right and left side in the seated and erect positions. In this paper, we extended the applicability of this method to the supine and prone positions, typically adopted in critically ill patients. For this purpose we have first developed proper geometrical and mathematical models of the chest wall which are able to provide consistent and reliable estimations of total and compartmental volume variations in these positions suitable for clinical settings. Then we compared chest wall (CW) volume changes computed from OEP(deltaVCW) with lung volume changes measured with a water seal spirometer (SP) (deltaVSP) in 10 normal subjects during quiet (QB) and deep (DB) breathing on rigid and soft supports. We found that on a rigid support the average differences between deltaVSP and deltaVCW were -4.2% +/- 6.2%, -3.0% +/- 6.1%, -1.7% +/- 7.0%, and -4.5% +/- 9.8%, respectively, during supine/QB, supine/DB, prone/QB, and prone/DB. On the soft surface we obtained -0.1% +/- 6.0%, -1.8% +/- 7.8%, 18.0% +/- 11.7%, and 10.2% +/- 9.6%, respectively. On rigid support and QB, the abdominal compartment contributed most of the deltaVCW in the supine (63.1% +/- 11.4%) and prone (53.5% +/- 13.1%) positions. deltaVCW was equally distributed between right and left sides. In the prone position we found a different chest wall volume distribution between pulmonary and abdominal rib cage (22.1% +/- 8.6% and 24.4% +/- 6.8%, respectively) compared with the supine position (23.3% +/- 9.3% and 13.6% +/- 13.0%).

Real-Time linux dynamic clamp: a fast and flexible way to construct virtual ion channels in living cells.

Abstract: We describe a system for real-time control of biological and other experiments. This device, based around the Real-Time Linux operating system, was tested specifically in the context of dynamic clamping, a demanding real-time task in which a computational system mimics the effects of nonlinear membrane conductances in living cells. The system is fast enough to represent dozens of nonlinear conductances in real time at clock rates well above 10 kHz. Conductances can be represented in deterministic form, or more accurately as discrete collections of stochastically gating ion channels. Tests were performed using a variety of complex models of nonlinear membrane mechanisms in excitable cells, including simulations of spatially extended excitable structures, and multiple interacting cells. Only in extreme cases does the computational load interfere with high-speed "hard" real-time processing (i.e., real-time processing that never falters). Freely available on the worldwide web, this experimental control system combines good performance. immense flexibility, low cost, and reasonable ease of use. It is easily adapted to any task involving real-time control, and excels in particular for applications requiring complex control algorithms that must operate at speeds over 1 kHz.

The role of matrix metalloproteinase-2 in the remodeling of cell-seeded vascular constructs subjected to cyclic strain.

Abstract: Tissue engineering offers the opportunity to develop vascular substitutes that mimic the responsive nature of native arteries. A good blood vessel substitute should be able to remodel its matrix in response to mechanical stimulation, as imposed by the hemodynamic environment. We have developed a novel method of studying the influence of mechanical strain on the remodeling of cell-seeded collagen gel blood vessel analogs. We assessed the remodeling capacity by examining the effect of mechanical conditioning upon the expression of enzymes which remodel the extracellular matrix, called matrix metalloproteinases (MMPs), and upon the mechanical properties of the constructs. We found that subjecting collagen constructs to a 10% cyclic radial distention, over a course of 4 days, resulted in an overall increase in the production of MMP-2. Cyclic mechanical strain also stimulated enzymatic activation of latent MMP-2. We found that cyclic strain also significantly increased the mechanical strength and material modulus, as indicated by an increase in circumferential tensile properties of the constructs. These observations suggested that MMP-2-dependent remodeling affects the material properties of vascular tissue analogs. To further investigate this possible connection we examined the effects of dynamic conditioning in the presence of two nonspecific inhibitors of MMP activity. Interestingly, we found that nonspecific inhibition of MMP ablated the benefits of mechanical conditioning upon mechanical properties. Our observations suggest that a better understanding of the complex relation between mechanical stimulation and construct remodeling is key for the proper design of tissue-engineered blood vessel substitutes.

Chondrocyte differentiation is modulated by frequency and duration of cyclic compressive loading.

Abstract: As part of a program of research aimed at determining the role of mechanical forces in connective tissue differentiation, we have developed a model for investigating the effects of dynamic compressive loading on chondrocyte differentiation in vitro. In the current study, we examined the influence of cyclic compressive loading of chick limb bud mesenchymal cells to a constant peak stress of 9.25 kPa during each of the first 3 days in culture. Cells embedded in agarose gel were subjected to uniaxial, cyclic compression at 0.03, 0.15, or 0.33 Hz for 2 h. In addition, load durations of 12, 54, or 120 min were evaluated while holding frequency constant at 0.33 Hz. For a 2 h duration, there was no response to loading at 0.03 Hz. A significant increase in chondrocyte differentiation was associated with loading at 0.15 Hz, and an even greater increase with loading at 0.33 Hz. Holding frequency constant at 0.33 Hz, a loading duration of 12 min elicited no response, whereas chondrocyte differentiation was enhanced by loading for either 54 or 120 min. Although not statistically significant from the 120 min response, average cartilage nodule density and glycosaminoglycan synthesis rate were highest in the 54 min duration group. This result suggests that cells may be sensitive to the level of cumulative (nonrecoverable) compressive strain, as well as to the dynamic strain history.

Evaluation of a deformable musculoskeletal model for estimating muscle-tendon lengths during crouch gait.

Abstract: The hamstrings and psoas muscles are often length- ened surgically in an attempt to correct crouch gait in persons with cerebral palsy. The purpose of this study was to determine if, and under what conditions, medial hamstrings and psoas lengths estimated with a ''deformable'' musculoskeletal model accurately characterize the lengths of the muscles during walk- ing in individuals with crouch gait. Computer models of four subjects with crouch gait were developed from magnetic reso- nance ~MR! images. These models were used in conjunction with the subjects' measured gait kinematics to calculate the muscle-tendon lengths at the body positions corresponding to walking. The lengths calculated with the MR-based models were normalized and were compared to the lengths estimated using a deformable generic model. The deformable model was either left undeformed and unscaled, or was deformed or scaled to more closely approximate the femoral geometry or bone dimensions of each subject. In most cases, differences between the normalized lengths of the medial hamstrings computed with the deformable and MR-based models were less than 5 mm. Differences in the psoas lengths computed with the deformable and MR-based models were also small ~, 3m m! when the deformable model was adjusted to represent the femoral geom- etry of each subject. This work demonstrates that a deformable musculoskeletal model, in combination with a few subject- specific parameters and simple normalization techniques, can provide rapid and accurate estimates of medial hamstrings and psoas lengths in persons with neuromuscular disorders. © 2001 Biomedical Engineering Society. @DOI: 10.1114/1.1355277#

Separable least squares identification of nonlinear Hammerstein models: application to stretch reflex dynamics.

Abstract: The Hammerstein cascade, consisting of a zero-memory nonlinearity followed by a linear filter, is often used to model nonlinear biological systems. This structure can represent some high-order nonlinear systems accurately with relatively few parameters. However, it is not possible, in general, to estimate the parameters of a Hammerstein cascade in closed form. The most effective method available to date uses an iterative approach, which alternates between estimating the linear element from a crosscorrelation, and then fitting a polynomial to the nonlinearity via linear regression. This paper proposes the use of separable least squares optimization methods to estimate the linear and nonlinear elements simultaneously in a least squares framework. A separable least squares algorithm for the identification of Hammerstein cascades is developed and used to analyze stretch reflex electromyogram data from two experimental subjects. The results show that in each case the proposed algorithm produced a better model, in that it predicted the system’s response to novel inputs more accurately, than did models estimated using the traditional iterative algorithm. Monte-Carlo simulations demonstrated that when the input is a non-Gaussian, nonwhite signal, as is often the case experimentally, the traditional iterative identification approach produces biased models, whereas the separable least squares approach proposed in this paper does not. © 2001 Biomedical Engineering Society.

Compressive deformation and damage of muscle cell subpopulations in a model system.

Abstract: To study the effects of compressive straining on muscle cell deformation and damage an in vitro model system was developed. Myoblasts were seeded in agarose constructs and cultured in growth medium for 4 days. Subsequently, the cells were allowed to fuse into multinucleated myotubes for 8 days in differentiation medium, resulting in a population of spherical myoblasts (50%), spherical myotubes (35%), and elongated myotubes (15%) with an overall viability of 90%. To evaluate cell deformation upon construct compression half-core shaped constructs were compressed up to 40% strain and the resulting cell shape was assessed from confocal scans through the central plane of spherical cells. The ratio of cell diameters measured parallel and perpendicular to the axis of compression was used as an index of deformation (DI). The average DI of myoblasts decreased with strain level (0.99±0.03, 0.70±0.04, and 0.56±0.10 at 0%, 20%, and 40% strain), whereas for myotubes DI decreased up to 20% strain and then remained fairly constant (0.99±0.06, 0.55±0.06, 0.50±0.11). The discrepancy in DI between spherical myoblasts and myotubes at 20% strain was explained by the relative sensitivity of the cell membrane to buckling, which is more pronounced in the myotubes. Sustained compression up to 24 h at 20% strain resulted in a significant increase in cell damage with time as compared to unstrained controls. Despite differences in membrane buckling no difference in damage between myoblasts and spherical myotubes was observed over time, whereas the elongated myotubes were more susceptible to damage. © 2001 Biomedical Engineering Society.

An experimentalist's approach to accurate localization of phase singularities during reentry.

Abstract: A phase variable that uniquely represents the time course of the action potential has been used to study the mechanisms of cardiac fibrillation. A spatial phase singularity (PS) occurs during reentrant wave propagation and represents the organizing center of the rotating wave. Here, we present an error analysis to investigate how well PSs can be localized. Computer simulations of rotating spiral waves scaled appropriately for cardiac tissue were studied with various levels of noise added. The accuracy in identifying and localizing singularities depended on three factors: (i) the point chosen as the origin in state space used to calculate the phase variable; (ii) signal to noise ratio; and (iii) discretization (number of levels used to represent data). We found that for both simulation as well as experimental data, there existed a wide range for the choice of origin for which PSs could be identified. Discretization coupled with noise affected this range adversely. However, there always existed a range for choice of the origin that was 20% or more of the action potential amplitude within which the accuracy of localizing PSs was better than 2 mm. Thus, a precise determination of origin was not necessary for accurately identifying PSs. © 2001 Biomedical Engineering Society. PAC01: 8719Nn, 8710+e, 8719Hh

Modeling advection and diffusion of oxygen in complex vascular networks.

Abstract: A realistic geometric model for the three-dimensional capillary network geometry is used as a framework for studying the transport and consumption of oxygen in cardiac tissue. The nontree-like capillary network conforms to the available morphometric statistics and is supplied by a single arterial source and drains into a pair of venular sinks. We explore steady-state oxygen transport and consumption in the tissue using a mathematical model which accounts for advection in the vascular network, nonlinear binding of dissolved oxygen to hemoglobin and myoglobin, passive diffusion of freely dissolved and protein-bound oxygen, and Michaelis–Menten consumption in the parenchymal tissue. The advection velocity field is found by solving the hemodynamic problem for flow throughout the network. The resulting system is described by a set of coupled nonlinear elliptic equations, which are solved using a finite-difference numerical approximation. We find that coupled advection and diffusion in the three-dimensional system enhance the dispersion of oxygen in the tissue compared to the predictions of simplified axially distributed models, and that no “lethal corner,” or oxygen-deprived region occurs for physiologically reasonable values for flow and consumption. Concentrations of 0.5–1.0 mM myoglobin facilitate the transport of oxygen and thereby protect the tissue from hypoxia at levels near its p50 that is, when local oxygen consumption rates are close to those of delivery by flow and myoglobin-facilitated diffusion, a fairly narrow range. © 2001 Biomedical Engineering Society.

Computational flow modeling of the left ventricle based on in vivo MRI data: initial experience.

Abstract: A combined computational fluid dynamics (CFD) and magnetic resonance imaging (MRI) methodology has been developed to simulate blood flow in heart chambers, with specific application in the present study to the human left ventricle. The proposed framework employs MRI scans of a human heart to obtain geometric data, which are then used for the CFD simulations. These latter are accomplished by geometrical modeling of the ventricle using time-resolved anatomical slices of the ventricular geometry and imposition of inflow/outflow conditions at orifices notionally representing the mitral and aortic valves. The predicted flow structure evolution and physiologically relevant flow characteristics were examined and compared to existing information. The CFD model convincingly captures the three-dimensional contraction and expansion phases of endocardial motion in the left ventricle, allowing simulation of dominant flow features, such as the vortices and swirling structures. These results were qualitatively consistent with previous physiological and clinical experiments on in vivo ventricular chambers, but the accuracy of the simulated velocities was limited largely by the anatomical shortcomings in the valve region. The study also indicated areas in which the methodology requires improvement and extension.

A mechanistic model of acute platelet accumulation in thrombogenic stenoses.

Abstract: Thrombosis on an atherosclerotic lesion can cause heart attack or stroke. Thrombosis may be triggered by plaque rupture or erosion, creating a thrombogenic stenosis. To measure and model this situation, collagen-coated stenoses have been exposed to nonanticoagulated blood in a baboon ex vivo shunt. The maximum rate of platelet accumulation, measured using a gamma camera, was highest in the throat region of moderate and severe stenoses, and increased with increasing stenosis severity. A species transport model of platelet accumulation was developed, which included mechanisms of convection, shear-enhanced diffusion, near-wall platelet concentration, and a kinetic model of platelet activation and aggregation. The model accurately reproduced the average spatial pattern and time rate of platelet accumulation in the upstream and throat regions of the stenosis, where shear-enhanced diffusivity increased platelet transport in the stenosis throat. Downstream of the throat where flow is complicated by recirculation, the model computed a transport-limited region with lower than measured platelet accumulation, suggesting that fluid-phase platelet activation may significantly affect both transport and adhesion rates in the poststenotic region. This model may provide an initial quantitative estimate of the likelihood of occlusive thrombus in individual patients due to plaque erosion, artery spasm, incomplete angioplasty, or plaque rupture. © 2001 Biomedical Engineering Society.

Noninvasive electrical imaging of the heart: theory and model development.

Abstract: The aim of this work is to begin quantifying the performance of a recently developed activation imaging algorithm of Huiskamp and Greensite [IEEE Trans. Biomed. Eng. 44:433–446]. We present here the modeling and computational issues associated with this process. First, we present a practical construction of the appropriate transfer matrix relating an activation sequence to body surface potentials from a general boundary value problem point of view. This approach makes explicit the role of different Green's functions and elucidates features (such as the anisotropic versus isotropic distinction) not readily apparent from alternative formulations. A new analytic solution is then developed to test the numerical implementation associated with the transfer matrix formulation presented here and convergence results for both potentials and normal currents are given. Next, details of the construction of a generic porcine model using a nontraditional data-fitting procedure are presented. The computational performance of this model is carefully examined to obtain a mesh of an appropriate resolution to use in inverse calculations. Finally, as a test of the entire approach, we illustrate the activation inverse procedure by reconstructing a known activation sequence from simulated data. For the example presented, which involved two ectopic focii with large amounts of Gaussian noise (100 μV rms) present in the torso signals, the reconstructed activation sequence had a similarity index of 0.880 when compared to the input source. © 2001 Biomedical Engineering Society.

Biosynthetic activity in heart valve leaflets in response to in vitro flow environments.

Abstract: The development of bioreactors for tissue engineered heart valves would be aided by a thorough understanding of how mechanical forces impact cells within valve leaflets. The hypothesis of the present study is that flow may influence the biosynthetic activity of aortic valve leaflet cells. Porcine leaflets were exposed to one of several conditions for 48 h, including steady or pulsatile flow in a tubular flow system at 10 or 20 l/min, and steady shear stress in a parallel plate flow system at 1, 6, or 22 dyne/cm2. Protein, glycosaminoglycan, and DNA synthesis increased during static incubation but remained at basal levels after exposure to flow. The modulation of synthetic activity was attributed to the presence of a shear stress on the leaflet surface, which may be transmitted to cells within the leaflet matrix through tensile forces. The alpha-smooth muscle (alpha-SM) actin distribution observed in fresh leaflets was proportionately decreased after exposure to antibiotics and not recovered by either static incubation or exposure to flow. These results indicate that exposure to flow maintains leaflet synthetic activity near normal levels, but that the inclusion of another force, such as bending or backpressure, may be necessary to preserve alpha-SM actin immunoreactive cells.

Dynamic in vitro quantification of bioprosthetic heart valve leaflet motion using structured light projection.

Abstract: Quantification of heart valve leaflet deformation during the cardiac cycle is essential in understanding normal and pathological valvular function, as well as in the design of replacement heart valves. Due to the technical complexities involved, little work to date has been performed on dynamic valve leaflet motion. We have developed a novel experimental method utilizing a noncontacting structured laser-light projection technique to investigate dynamic leaflet motion. Using a simulated circulatory loop, a matrix of 150–200 laser light points were projected over the entire leaflet surface. To obtain unobstructed views of the leaflet surface, a stereo system of high-resolution boroscopes was used to track the light points at discrete temporal points during the cardiac cycle. The leaflet surface at each temporal point was reconstructed in three dimensions, and fit using our biquintic hermite finite element approach (Smith et al., Ann. Biomed. Eng. 26:598–611, 2001). To demonstrate our approach, we utilized a bovine pericardial bioprosthetic heart valve, which revealed regions of complex flexural deformation and substantially different shapes during the opening and closing phases. In conclusion, the current method has high spatial and temporal resolution and can reconstruct the entire surface of the cusp simultaneously. Because it is completely noncontacting, this approach is applicable to studies of fatigue and bioreactor technology for tissue engineered heart valves. © 2001 Biomedical Engineering Society. PAC01: 8719Hh, 8780-y, 4262Be, 8719St

Electrical impedance of cultured endothelium under fluid flow

Abstract: The morphological and functional status of organs, tissues, and cells can be assessed by evaluating their electrical impedance. Fluid shear stress regulates the morphology and function of endothelial cells in vitro. In this study, an electrical biosensor was used to investigate the dynamics of flow-induced alterations in endothelial cell morphology in vitro. Quantitative, real-time changes in the electrical impedance of endothelial monolayers were evaluated using a modified electric cell-substrate impedance sensing (ECIS) system. This ECIS/Flow system allows for a continuous evaluation of the cell monolayer impedance upon exposure to physiological fluid shear stress forces. Bovine aortic endothelial cells grown to confluence on thin film gold electrodes were exposed to fluid shear stress of 10 dynes/cm2 for a single uninterrupted 5 h time period or for two consecutive 30 min time periods separated by a 2 h no-flow interval. At the onset of flow, the monolayer electrical resistance sharply increased reaching 1.2 to 1.3 times the baseline in about 15 min followed by a sustained decrease in resistance to 1.1 and 0.85 times the baseline value after 30 min and 5 h of flow, respectively. The capacitance decreased at the onset of flow, started to recover after 15 min and after slightly overshooting the baseline values, decreased again with a prolonged exposure to flow. Measured changes in capacitance were in the order of 5% of the baseline values. The observed changes in endothelial impedance were reversible upon flow removal with a recovery rate that varied with the duration of the preceding flow exposure. These results demonstrate that the impedance of endothelial monolayers changes dynamically with flow indicating morphological and/or functional changes in the cell layer. This in vitro model system (ECIS/Flow) may be a very useful tool in the quantitative evaluation of flow-induced dynamic changes in cultured cells when used in conjunction with biological or biochemical assays able to determine the nature and mechanisms of the observed changes. © 2001 Biomedical Engineering Society. PAC01: 8719Nn, 8719Uv, 8717-d

A mathematical model for chemoattractant gradient sensing based on receptor-regulated membrane phospholipid signaling dynamics.

Abstract: The crawling movement of cells in response to a chemoattractant gradient is a complex process requiring the coordination of various subcellular activities. Although a complete description of the mechanisms underlying cell movement remains elusive, the very first step of directional sensing, enabling the cell to perceive the imposed gradient, is becoming more transparent. A fundamental problem of directional sensing is its exquisite sensitivity. Even in the presence of relatively shallow chemoattractant gradients, cell projections are extended precisely in the region exposed to the highest chemoattractant concentration. This reflects the existence of a mechanism for amplifying the external signal. Recent experiments have identified a potential candidate for the seat of this amplification-membrane phosphoinositides such as PI4,5P2 and PI3,4,5P3 appear to be the first components of the signal transduction pathway to be amplified. Perturbing the cell with various chemoattractant gradients reveals a rich spectrum of phosphoinositide dynamics (Parent, C. A., and P. N. Devreotes. Science 284:765, 1999). The goal of this work is to develop a mathematical model of these phosphoinositide dynamics. Specifically, we address the following questions: (a) Which signaling pathway could lead to the localized accumulation of membrane phosphoinositides? (b) Why is this accumulation independent of the slope and mean value of the chemoattractant gradient? The model is based on the phosphoinositide cycle that transfers phosphoinositides between the plasma membrane and endoplasmic reticulum. We show that a mathematical model taking due account of receptor desensitization and the reaction-diffusion processes of the phosphoinositide cycle captures many of the experimentally observed dynamics. Having shown the plausibility of the model with respect to directional sensing, we discuss its implications for lamellipod extension, the process that follows directional sensing.

Mass Transport in an Anatomically Realistic Human Right Coronary Artery

Abstract: The coronary arteries are a common site of athero- sclerotic plaque formation, which has been putatively linked to hemodynamic and mass transport patterns. The purpose of this paper was to study mass transport patterns in a human right coronary artery ~RCA! model, focusing on the effects of local geometric features on mass transfer from blood to artery walls. Using a previously developed characteristic/finite element scheme for solving advection-dominated transport problems, mass transfer calculations were performed in a rigid, anatomi- cally realistic model of a human RCA. A qualitative and quan- titative examination of the RCA geometry was also carried out. The concentration field within the RCA was seen to closely follow primary and secondary flow features. Local variations in mass transfer patterns due to geometric features were signifi- cant and much larger in magnitude than local variations in wall shear stress. We conclude that the complex secondary flows in a realistic arterial model can produce very substantial local variations in blood-wall mass transfer rates, and may be im- portant in atherogenesis. Further, RCA mass transfer patterns are more sensitive to local geometric features than are wall shear stress patterns. © 2001 Biomedical Engineering Society. @DOI: 10.1114/1.1349704#

Parameters of postocclusive reactive hyperemia measured by near infrared spectroscopy in patients with peripheral vascular disease and in healthy volunteers

Abstract: The main purpose of our study was to determine the parameters of the postocclusive reactive hyperemia test that could help and provide the clinician with information about the tissue oxygenation, the severity of the disease, and the results of the applied therapies. Near infrared spectroscopy (NIRS) proved to be a valid noninvasive trend monitor useful for investigating the physiology of oxygen transport to tissue. Important advantages of NIRS over transcutaneous oximetry (TcpO2) are: (a) a more dynamic nature of the NIRS signals which reflects more closely the actual response of the peripheral vasculature to the occlusive provocation; (b) larger sampling volume; and (c) the ability of assessing tissue oxygenation at deeper tissue levels. We demonstrated that the time parameters of reactive hyperemia, the rate of reactive hyperemia, and the maximal change during reactive hyperemia, all calculated from the oxyhemoglobin (HbO2) signal of the NIRS, clearly distinguish between healthy volunteers and patients with vascular disorder. The time parameters of reactive hyperemia were significantly longer (p < 0.01), and the rate of reactive hyperemia (p = 0.01) as well as the maximal change during reactive hyperemia (p = 0.02) were significantly lower in patient group compared to healthy volunteers. These parameters were also in good correlation with the values of ankle brachial index (ABI) and the resting values of oxygen partial pressure (TcpO2). Values of the chosen parameters obtained from the HbO2 signal were further compared between groups of diabetic and nondiabetic patients with peripheral vascular disease. Although longer time parameters of reactive hyperemia and lower rates of hyperemic response were detected, the difference between both groups was not statistically significant. © 2001 Biomedical Engineering Society.

Effect of Muscle Biomechanics on the Quantification of Spasticity

Abstract: The impact of muscle biomechanics on spasticity was assessed by comparison of the reflex responses of the elbow and metacarpophalangeal (MCP) flexor muscles in individuals with chronic spastic hemiplegia following stroke. Specifically, methods were developed to quantify reflex responses and to normalize these responses for comparison across different muscle groups. Stretch reflexes were elicited in the muscles of interest by constant velocity ramp-and-hold stretches at the corresponding joint. The muscles were initially passive, with the joint placed in a midrange position. Estimates of biomechanical parameters were used to convert measured reflex joint torque and joint angle into composite flexor muscle stress and stretch. We found that the stretch reflex response for the MCP muscle group had a 74% greater mean stiffness modulus than that for the elbow muscle group, and that the reflex threshold was initiated at an 80% shorter mean muscle stretch. However, we determined that initial normalized fiber length was significantly greater for the experiments involving the MCP muscles than for those involving the elbow muscles. Increasing the initial composite fiber length of the elbow flexors produced significant reduction of the reflex threshold (p < 0.001), while decreasing the initial length of the MCP flexors significantly reduced their measured reflex stiffness (p < 0.001). Thus, biomechanical parameters of muscle do appear to have an important effect on the stretch reflex in individuals with impairment following stroke, and this effect should be accounted for when attempting to quantify spasticity. © 2001 Biomedical Engineering Society.

Analysis of oxygen transport to hepatocytes in a flat-plate microchannel bioreactor.

Abstract: Oxygen transfer to cultured hepatocytes in microchannel parallel-plate bioreactors with and without an internal membrane oxygenator was investigated with a mathematical model and the results were corroborated with fluorescence imaging experiments. The consumption of oxygen by hepatocytes was assumed to follow Michaelis-Menten kinetics. Our simulations indicate that under conditions of low Peclet (Pe) number (<80) and fixed Damlkohler number (= 0.14, corresponding to rat hepatocytes) the cells are hypoxic in the bioreactor without an internal membrane oxygenator. Under the same conditions, the bioreactor with an internal membrane oxygenator can avoid cell hypoxia by appropriate selection of membrane Sherwood number and/or the gas phase oxygen partial pressure, thus providing greater control of cell oxygenation. At high Pe, both bioreactors are well oxygenated. Experimentally determined oxygen concentrations within the bioreactors were in good qualitative agreement with model predictions. At low Pe, cell surface oxygen depletion was predicted from analytically derived criteria. Hepatocytes with oxygen dependent functional heterogeneity may exhibit optimal function in the bioreactor with the internal membrane oxygenator.

Importance of accurate geometry in the study of the total cavopulmonary connection: computational simulations and in vitro experiments.

Abstract: Previous in vitro studies have shown that total cavopulmonary connection (TCPC) models incorporating offset between the vena cavae are energetically more efficient than those without offsets. In this study, the impact of reducing simplifying assumptions, thereby producing more physiologic models, was investigated by computational fluid dynamics (CFD) and particle flow visualization experiments. Two models were constructed based on angiography measurements. The first model retained planar arrangement of all vessels involved in the TCPC but incorporated physiologic vessel diameters. The second model consisted of constant-diameter vessels with nonplanar vascular features. CFD and in vitro experiments were used to study flow patterns and energy losses within each model. Energy losses were determined using three methods: theoretical control volume, simplified control volume, and velocity gradient based dissipation. Results were compared to a simplified model control. Energy loss in the model with physiologically more accurate vessel diameters was 150% greater than the simplified model. The model with nonplanar features produced an asymmetric flow field with energy losses approximately 10% higher than simplified model losses. With the velocity gradient based dissipation technique, the map of energy dissipation was plotted revealing that most of the energy was dissipated near the pulmonary artery walls. © 2001 Biomedical Engineering Society.

Effects of Strain Level and Proteoglycan Depletion on Preconditioning and Viscoelastic Responses of Rat Dorsal Skin

Abstract: The mechanical response of rat dorsal skin was experimentally studied under cyclic uniaxial ramp stretches to various strain levels. Special emphasis was paid to the effects of the preconditioning protocol on the stress-strain relationship, and to the effects of ramp strain level and proteoglycan (PG) depletion, on viscoelasticity and preconditioning responses. The results show that preconditioning significantly reduced both the slope of the low strain stress-strain relationship, and the stress levels at consecutive stretch cycles. Following a short rest there was a significant partial recovery. Stress decay due to preconditioning was significant at all strain levels, and increased with strain. Stress relaxation was significant at all strain levels, but varied little with strain. Recovery following a 10 min rest was minor at all strain levels and varied little with strain. PG-depleted samples manifested similar response patterns. These results are consistent with the following notion: (1) skin consists of three mechanical components: elastin and proteoglycan which dominate the low strain response and are effected by preconditioning and (PG) depletion, and collagen which dominates the high strain response and is unaffected by preconditioning and PG depletion; (2) that the viscoelasticity of elastin and PG vs that of collagen are similar, so that rat dorsal skin can be regarded quasilinear viscoelastic.

A self-coherence enhancement algorithm and its application to enhancing three-dimensional source estimation from EEGs.

Abstract: In this paper a new algorithm is proposed to enhance the spatial resolution of solutions of the underdetermined EEG inverse problem. Termed the self-coherence enhancement algorithm (SCEA), the present algorithm provides a self-coherence solution, which is a function of the high order self-coherence estimate of an unbiased smooth estimate of the underdetermined EEG inverse solution. The order of the high order self-coherence function is determined by the blurring level of the actual source distribution as represented by a normalized blurring index. The proposed SCEA algorithm may be used to enhance the spatial resolution of an inverse solution obtained by any inverse reconstruction algorithm. Computer simulation studies have been conducted to evaluate the performance of the SCEA and to compare its performance to that of the LORETA and the FOCUSS algorithms.

Modulation of ATP/ADP concentration at the endothelial surface by shear stress: effect of flow-induced ATP release.

Abstract: The adenine nucleotides ATP and ADP induce the production of vasoactive compounds in vascular endothelial cells (ECs). Therefore, knowledge of how flow affects the concentration of ATP and ADP at the EC surface may be important for understanding shear stress-mediated vasoregulation. The concentration of ATP and ADP is determined by convective and diffusive transport as well as by hydrolysis of these nucleotides by ectonucleotidases at the EC surface. Previous mathematical modeling has demonstrated that for steady flow in a parallel plate flow chamber, the combined ATP+ADP concentration does not change considerably over a wide range of shear stress. This finding has been used to argue that the effect of flow on adenine nucleotide transport could not account for the dependence of endothelial responses to ATP on the magnitude of applied shear stress. The present study extends the previous modeling to include pulsatile flow as well as flow-induced endothelial ATP release. Our results demonstrate that flow-induced ATP release has a pronounced effect on nucleotide concentration under both steady and pulsatile flow conditions. While the combined ATP+ADP concentration at the EC surface in the absence of flow-induced ATP release changes by only approximately 10% over the wall shear stress range 0.1-10 dyne cm(-2), inclusion of this release leads to a concentration change of approximately 34%-106% over the same shear stress range, depending on how ATP release is modeled. These results suggest that the dependence of various endothelial responses to shear stress on the magnitude of the applied shear stress may be partially attributable to flow-induced changes in cell-surface adenine nucleotide concentration.

Stimulus induced pH changes in cochlear implants: an in vitro and in vivo study.

Abstract: Large pH changes have been shown to be potentially harmful to tissue. The present study was designed to examine stimulus induced changes in pH for a variety of stimulus parameters both in vitro and in vivo, in order to ensure that stimulation strategies for neural prostheses result in minimal pH change. Stimulation using charge balanced biphasic pulses at intensities both within and well above maximum clinical levels for cochlear implants (0.025-0.68 microC per phase), were delivered to platinum electrodes in vitro [saline, phosphate buffered saline (PBS), or saline with human serum albumin (HSA)], and in vivo (scala tympani). Stimulus rates were typically varied from 62.5 to 1000 pulses per second (pps), although rates of up to 14,500 pps were used in some experiments. The pH level was recorded using a pH indicator (Phenol red) or pH microelectrodes. While electrical stimulation at intensities and rates used clinically showed no evidence of a pH shift, intensities significantly above these levels induced pH changes both in vitro and in vivo. The extent of pH change was related to stimulus rate and intensity. In addition, pH change was closely associated with the residual direct current (dc) level. As expected, stimulation with capacitive coupling induced little dc and a minimal pH shift. Moreover, no pH shift was observed using alternating leading phase pulse trains at intensities up to 0.68 microC per phase and 1000 pps. Saline with HSA or buffered solutions dramatically reduced the extent of pH shift observed following stimulation in unbuffered inorganic saline. Reduced pH shift was also observed following in vivo stimulation. These findings provide an insight into mechanisms of safe change injection in neural prostheses.

Short-Term biomechanical adaptation of the rat carotid to acute hypertension: contribution of smooth muscle.

Abstract: The biomechanical adaptation of the arterial wall to hypertension has been studied extensively in recent years; however, the exact biomechanical contribution of vascular smooth muscle cells (VSMCs) during the adaptation process in conduit vessels is not known. We induced hypertension in 8 wk old Wistar rats by total ligation of the aorta between the two kidneys. Mean blood pressure increased from 92 +/- 2 (mean +/- SE) mm Hg to approximately 150 mmHg. Rats were sacrificed 2, 4, and 8 d after surgery and the left common carotid artery was excised for analysis. Wall thickness increased by 18% in 8 d and the opening angle by 32% in 4 d. The elastic properties were measured under normal VSMC tone (i.e., the amount of VSMC tone under normal conditions also called basal VSMC tone or normal resting VSMC tone), under maximally contracted VSMC (NE, 5 x 10(-7) mol/L) and under totally relaxed VSMC conditions (papaverine, 10(-4) mol/L). The most pronounced modifications were the changes in elastic properties related to normal VSMC tone. The functional contraction ratio at 100 mm Hg, defined as the relative contraction under normal conditions (normal VSMC tone), increased by 439% 4 d after the induction of hypertension. The total contraction capacity of the VSMC increased by 38% within 8 d. The changes in normal VSMC tone led to important changes in the mechanical properties of the arterial wall. Under normal VSMC conditions, compliance at mean pressure (148 mm Hg) increased by 159% within 8 d, whereas in the absence of VSMC tone, compliance did not increase significantly. We conclude that in conduit vessels, the VSMC, which is the sensing and effecting element of the adaptation process, is subjected to large-scale changes during the early phase of arterial adaptation to acute hypertension.

Ligand coated nanosphere adhesion to E- and P-selectin under static and flow conditions.

Abstract: The heterogeneous distribution of endothelial cell adhesion molecules (ECAMs) on the lumenal surface of vascular endothelium provides an opportunity to deliver drugs to select tissues. The targeting could be achieved by using carriers whose outer surface has a ligand for a selectively expressed ECAM. The carriers would interact with the endothelium in a fluid dynamic environment and in many of these schemes nanoparticles would be used. It is unclear what role various parameters (e.g., ligand-ECAM chemistry, fluid shear) will have on the adhesion of the nanoparticles to the endothelium. To facilitate studies in this area, we have developed a prototypical in vitro model that allows investigation of nanoparticle adhesion. We coated polystyrene nanospheres with a humanized mAb (HuEP5C7.g2) that recognizes the ECAMs E- and P-selectin. Adhesion assays revealed that HuEP5C7.g2 nanospheres exhibit augmented, specific adhesion to selectin presenting cellular monolayers and that the adhesion can be affected by the fluid shear. These results; (i) strongly suggest that HuEP5C7.g2 could be used to target nanoparticles to selectin presenting endothelium; (ii) demonstrate that fluid shear can affect nanoparticle adhesion; and (iii) define a system which can be used to study the effects of various system parameters on nanoparticle adhesion.