Pharmacokinetics of Anti-VEGF Agent Aflibercept in Cancer Predicted by Data-Driven, Molecular-Detailed Model.

Mathematical models can support the drug development process by predicting the pharmacokinetic (PK) properties of the drug and optimal dosing regimens. We have developed a pharmacokinetic model that includes a biochemical molecular interaction network linked to a whole-body compartment model. We applied the model to study the PK of the anti-vascular endothelial growth factor (VEGF) cancer therapeutic agent, aflibercept. Clinical data is used to infer model parameters using a Bayesian approach, enabling a quantitative estimation of the contributions of specific transport processes and molecular interactions of the drug that cannot be examined in other PK modeling, and insight into the mechanisms of aflibercept's antiangiogenic action. Additionally, we predict the plasma and tissue concentrations of unbound and VEGF-bound aflibercept. Thus, we present a computational framework that can serve as a valuable tool for drug development efforts.

Where is VEGF in the body? A meta-analysis of VEGF distribution in cancer.

Vascular endothelial growth factor (VEGF) is a major target for the inhibition of tumour vascularisation and the treatment of human cancer. Many tumours produce large quantities of VEGF, and as a result, diagnosis and prognosis of cancer may be predicted by measuring changes in VEGF concentrations in blood. In blood, the VEGF may be located in the plasma, or in the blood-borne cells and formed elements, in particular, platelets and leukocytes. In this study, we collate the measurements of VEGF in platelets, leukocytes, plasma and serum for breast, prostate, colorectal and other cancers. In addition, we analysed the concentration of VEGF in tumour tissue itself, as well as for other tissues in the human body. Although the concentration of VEGF in tumours is high, the size of tumours is small compared to other tissues, in particular, skeletal muscle. Thus, the total quantity of VEGF in tumours and in blood is small compared to the quantity in muscles. This large reservoir of VEGF may have important implications for the treatment of cancer.

Application of Chimera grid to modelling cell motion and aggregation in a narrow tube.

A computational scheme using the Chimera grid method is presented for simulation of three-dimensional motion and aggregation of two red blood cells (RBCs) in a narrow tube. The cells are modelled as rigid ellipsoidal particles; the computational scheme is applicable to deformable fluid-filled particles. Attractive energy between two RBCs is modelled by a depletion interaction theory and used for simulating aggregation of two cells. Through the simulation, we show that the Chimera grid method is applicable to the simulation of three-dimensional motion and aggregation of multiple RBCs in a microvessel and microvascular network.

Micro- and nanomechanics of the cochlear outer hair cell.

Outer hair cell electromotility is crucial for the amplification, sharp frequency selectivity, and nonlinearities of the mammalian cochlea. Current modeling efforts based on morphological, physiological, and biophysical observations reveal transmembrane potential gradients and membrane tension as key independent variables controlling the passive and active mechanics of the cell. The cell's mechanics has been modeled on the microscale using a continuum approach formulated in terms of effective (cellular level) mechanical and electric properties. Another modeling approach is nanostructural and is based on the molecular organization of the cell's membranes and cytoskeleton. It considers interactions between the components of the composite cell wall and the molecular elements within each of its components. The methods and techniques utilized to increase our understanding of the central role outer hair cell mechanics plays in hearing are also relevant to broader research questions in cell mechanics, cell motility, and cell transduction.

Effects of erythrocyte aggregation and venous network geometry on red blood cell axial migration.

Axial migration of red blood cells in small glass tubes can cause blood viscosity to be effectively independent of shear rate. However, this phase separation may not occur to the same degree in the venous network due to infusion of cells and aggregates at branch points. To investigate this hypothesis, we followed trajectories of fluorescently labeled red blood cells in the venular network of the rat spinotrapezius muscle at normal and reduced flow with and without red blood cell aggregation. Cells traveling near the wall of an unbranched venular segment migrated approximately 1% of the longitudinal path length without aggregation and migrated slightly more with aggregation. Venular segment length between branch points averaged three to five times the diameter. Cells in the main vessel were shifted centrally by up to 20% of diameter at branch points, reducing the migration rate of cells near the opposite wall to <1% even in the presence of aggregation. We conclude that formation of a cell-free marginal layer in the venular network is attenuated due to the time dependence of axial migration and the frequent branching of the network.

Erythrocyte margination and sedimentation in skeletal muscle venules.

Previous studies in skeletal muscle of the dog and cat have shown that venous vascular resistance changes inversely with blood flow and may be due mainly to red blood cell aggregation, a phenomenon present in these species. To determine whether red blood cell axial migration and sedimentation contribute to this effect, we viewed either vertically or horizontally oriented venules of the rat spinotrapezius muscle with a horizontally oriented microscope during acute arterial pressure reduction. With normal (nonaggregating) rat blood, reduction of arterial pressure did not significantly change the relative diameter of the red blood cell column with respect to the venular wall. After induction of red blood cell aggregation in the rat by infusion of Dextran 500, red blood cell column diameter decreased up to 35% at low pseudoshear rates (below approximately 5 s(-1)); the magnitude was independent of venular orientation. In vertically oriented venules, the plasma layer was symmetrical, whereas in horizontally oriented venules, the plasma layer formed near the upper wall. We conclude that, although red blood cell axial migration and sedimentation develop in vivo, they occur only for larger flow reductions than are needed to elicit changes in venous resistance.

Simulation of motor-driven cochlear outer hair cell electromotility.

We propose a three-dimensional (3D) model to simulate outer hair cell electromotility. In our model, the major components of the composite cell wall are explicitly represented. We simulate the activity of the particles/motor complexes in the plasma membrane by generating active strains inside them and compute the overall response of the cell. We also consider the constrained wall and compute the generated active force. We estimate the parameters of our model by matching the predicted longitudinal and circumferential electromotile strains with those observed in the microchamber experiment. In addition, we match the earlier estimated values of the active force and cell wall stiffness. The computed electromotile strains in the plasma membrane and other components of the wall are in agreement with experimental observations in trypsinized cells and in nonmotile cells transfected with Prestin. We discover several features of the 3D mechanism of outer hair cell electromotilty. Because of the constraints under which the motors operate, the motor-related strains have to be 2-3 times larger than the observable strains. The motor density has a strong effect on the electromotile strain. Such effect on the active force is significantly lower because of the interplay between the active and passive properties of the cell wall.

A computational study of the effect of vasomotion on oxygen transport from capillary networks.

The objective of this study was to investigate the effect of arteriolar vasomotion on oxygen transport from capillary networks. A computational model was used to calculate blood flow and oxygen transport from a simulated network of striated muscle capillaries. For varying tissue oxygen consumption rates, the importance of the frequency and amplitude of vasomotion-induced blood flow oscillations was studied. The effect of myoglobin on oxygen delivery during vasomotion was also examined. In the absence of myoglobin, it was found that when consumption is high enough to produce regions of hypoxia under steady flow conditions, vasomotion-induced flow oscillations can significantly increase tissue oxygenation and decrease oxygen transport heterogeneity. The largest effect was seen for low-frequency, high-amplitude oscillations (1.5-3 cycles min(-1), 90% of steady-state velocity). By contrast, at physiological tissue myoglobin concentrations, vasomotion did not improve tissue oxygenation. This unexpected finding is due to the buffering effect of myoglobin, suggesting that in highly aerobic muscles short-term storage of oxygen is more important than the possibility of increasing transport through vasomotion.

Rheological effects of red blood cell aggregation in the venous network: a review of recent studies.

It has long been recognized that understanding the rheological properties of blood is essential to a full understanding of the function of the circulatory system. Given the difficulty of obtaining carefully controlled measurements in vivo, most of our current concepts of the flow behavior of blood in vivo are based on its properties in vitro. Studies of blood rheology in rotational and tube viscometers have defined the basic properties of blood and pointed to certain features that may be especially significant for understanding in vivo function. At the same time, differences between in vivo and in vitro systems combined with the complex rheological properties of blood make it difficult to predict in vivo blood rheology from in vitro studies. We have investigated certain flow properties of blood in vivo, using the venular network of skeletal muscle as our model system. In the presence of red blood cell aggregation, venous velocity profiles become blunted from the parabolic as in Poiseuille flow, as pseudo-shear rate (= mean fluid velocity/vessel diameter) is decreased from approximately 100 s(-1) to 5 s(-1). At control flow rates, the short distance between venular junctions does not appear to permit significant axial migration and red cell depletion of the peripheral fluid layer before additional red cells and aggregates are infused from a feeding tributary. Formation of a cell-free plasma layer at the vessel wall and sedimentation in vivo are evident only at very low pseudo-shear rates (<5 s(-1)). These findings may explain in large part observations in whole organs of increased venous resistance with reduction of blood flow.

Effect of erythrocyte aggregation on velocity profiles in venules.

A recent whole organ study in cat skeletal muscle showed that the increase in venous resistance seen at reduced arterial pressures is nearly abolished when the muscle is perfused with a nonaggregating red blood cell suspension. To explore a possible underlying mechanism, we tested the hypothesis that red blood cell aggregation alters flow patterns in vivo and leads to blunted red blood cell velocity profiles at reduced shear rates. With the use of fluorescently labeled red blood cells in tracer quantities and a video system equipped with a gated image intensifier, we obtained velocity profiles in venous microvessels (45-75 microm) of rat spinotrapezius muscle at centerline velocities between 0.3 and 14 mm/s (pseudoshear rates 3-120 s(-1)) under normal (nonaggregating) conditions and after induction of red blood cell aggregation with Dextran 500. Profiles are nearly parabolic (Poiseuille flow) over this flow rate range in the absence of aggregation. When aggregation is present, profiles are parabolic at high shear rates and become significantly blunted at pseudoshear rates of 40 s(-1) and below. These results indicate a possible mechanism for increased venous resistance at reduced flows.

A two-phase model for flow of blood in narrow tubes with increased effective viscosity near the wall.

A two-phase model for the flow of blood in narrow tubes is described. The model consists of a central core of suspended erythrocytes and a cell-free layer surrounding the core. It is assumed that the viscosity in the cell-free layer differs from that of plasma as a result of additional dissipation of energy near the wall caused by the red blood cell motion near the cell-free layer. A consistent system of nonlinear equations is solved numerically to estimate: (i) the effective dimensionless viscosity in the cell-free layer (beta), (ii) thickness of the cell-free layer (1-lambda) and (iii) core hematocrit (H(c)). We have taken the variation of apparent viscosity (mu(app)) and tube hematocrit with the tube diameter (D) and the discharge hematocrit (H(D)) from in vitro experimental studies [16]. The thickness of the cell-free layer computed from the model is found to be in agreement with the observations [3,21]. Sensitivity analysis has been carried out to study the behavior of the parameters 1-lambda, beta, H(c), B (bluntness of the velocity profile) and mu(app) with the variation of D and H(D).

Computational fluid dynamic studies of leukocyte adhesion effects on non-Newtonian blood flow through microvessels.

The study of the effect of leukocyte adhesion on blood flow in small vessels is of primary interest to understand the resistance changes in venular microcirculation. Available computational fluid dynamic studies provide information on the effect of leukocyte adhesion when blood is considered as a homogeneous Newtonian fluid. In the present work we aim to understand the effect of leukocyte adhesion on the non-Newtonian Casson fluid flow of blood in small venules; the Casson model represents the effect of red blood cell aggregation. In our model the blood vessel is considered as a circular cylinder and the leukocyte is considered as a truncated spherical protrusion in the inner side of the blood vessel. The cases of single leukocyte adhesion and leukocyte pairs in positions aligned along the same side, and opposite sides of the vessel wall are considered. The Casson fluid parameters are chosen for cat blood and human blood and comparisons are made for the effects of leukocyte adhesion in both species. Numerical simulations demonstrated that for a Casson fluid with hematocrit of 0.4 and flow rate Q = 0.072 nl/s, a single leukocyte increases flow resistance by 5% in a 32 microns diameter and 100 microns long vessel. For a smaller vessel of 18 microns, the flow resistance increases by 15%.

Calculations of intracapillary oxygen tension distributions in muscle.

Characterizing the resistances to O(2) transport from the erythrocyte to the mitochondrion is important to understanding potential transport limitations. A mathematical model is developed to accurately determine the effects of erythrocyte spacing (hematocrit), velocity, and capillary radius on the mass transfer coefficient. Parameters of the hamster cheek pouch retractor muscle are used in the calculations, since significant amounts of experimental physiological data and mathematical modeling are available for this muscle. Capillary hematocrit was found to have a large effect on the PO(2) distribution and the intracapillary mass transfer coefficient per unit capillary area, k(cap), increased by a factor of 3.7 from the lowest (H=0.25) to the highest (H=0.55) capillary hematocrits considered. Erythrocyte velocity had a relatively minor effect, with only a 2.7% increase in the mass transfer coefficient as the velocity was increased from 5 to 25 times the observed velocity in resting muscle. The capillary radius is varied by up to two standard deviations of the experimental measurements, resulting in variations in k(cap) that are <15% at the reference case. The magnitude of these changes increases with hematocrit. An equation to approximate the dependence of the mass transfer coefficient on hematocrit is developed for use in simulations of O(2) transport from a capillary network.

A computational study of the effect of capillary network anastomoses and tortuosity on oxygen transport.

The objective of this study was to investigate the effects of capillary network anastomoses and tortuosity on oxygen transport in skeletal muscle, as well as the importance of muscle fibers in determining the arrangement of parallel capillaries. Countercurrent flow and random capillary blockage (e.g. by white blood cells) were also studied. A general computational model was constructed to simulate oxygen transport from a network of blood vessels within a rectangular volume of tissue. A geometric model of the capillary network structure, based on hexagonally packed muscle fibers, was constructed to produce networks of straight unbranched capillaries, capillaries with anastomoses, and capillaries with tortuosity, in order to examine the effects of these geometric properties. Quantities examined included the tissue oxygen tension and the capillary oxyhemoglobin saturation. The computational model included a two-phase simulation of blood flow. Appropriate parameters were chosen for working hamster cheek-pouch retractor muscle. Our calculations showed that the muscle-fiber geometry was important in reducing oxygen transport heterogeneity, as was countercurrent flow. Tortuosity was found to increase tissue oxygenation, especially when combined with anastomoses. In the absence of tortuosity, anastomoses had little effect on oxygen transport under normal conditions, but significantly improved transport when vessel blockages were present.

Estimating oxygen transport resistance of the microvascular wall.

The problem of diffusion of O(2) across the endothelial surface in precapillary vessels and its utilization in the vascular wall remains unresolved. To establish a relationship between precapillary release of O(2) and vascular wall consumption, we estimated the intravascular flux of O(2) on the basis of published in vivo measurements. To interpret the data, we utilized a diffusion model of the vascular wall and computed possible physiological ranges for O(2) consumption. We found that many flux values were not consistent with the diffusion model. We estimated the mitochondrial-based maximum O(2) consumption of the vascular wall (M(mt)) and a possible contribution to O(2) consumption of nitric oxide production by endothelial cells (M(NO)). Many values of O(2) consumption predicted from the diffusion model exceeded M(mt) + M(NO). In contrast, reported values of O(2) consumption for endothelial and smooth muscle cell suspensions and vascular strips in vitro do not exceed M(mt). We conjecture that most of the reported values of intravascular O(2) flux are overestimated, and the likely source is in the experimental estimates of convective O(2) transport at upstream and downstream points of unbranched vascular segments.

Diameter changes in skeletal muscle venules during arterial pressure reduction.

Previous studies in skeletal muscle have shown a substantial (>100%) increase in venous vascular resistance with arterial pressure reduction to 40 mmHg, but a microcirculatory study showed no significant venular diameter changes in the horizontal direction during this procedure. To examine the possibility of venular collapse in the vertical direction, a microscope was placed horizontally to view a vertically mounted rat spinotrapezius muscle preparation. We monitored the diameters of venules (mean diameter 73. 8 +/- 37.0 microm, range 13-185 microm) oriented horizontally and vertically with a video system during acute arterial pressure reduction by hemorrhage. Our analysis showed small but significant (P < 0.0001) diameter reductions of 1.0 +/- 2.5 microm and 1.8 +/- 3. 1 microm in horizontally and vertically oriented venules, respectively, upon reduction of arterial pressure from 115.0 +/- 26. 3 to 39.8 +/- 12.3 mmHg. The venular responses were not different after red blood cell aggregation was induced by Dextran 500 infusion. We conclude that diameter changes in venules over this range of arterial pressure reduction are isotropic and would likely increase venous resistance by <10%.

An analysis of the hydraulic conductivity of the extracisternal space of the cochlear outer hair cell.

The cylindrically shaped cochlear outer hair cell (OHC) plays an important role in the transduction of acoustic energy into electrical energy in the cochlea. The extracisternal space (ECiS) of the lateral wall of the OHC is the fluid-filled space between the plasma membrane (PM) and the intracellular subsurface cisterna (SSC). In the ECiS, an array of cylindrical micropillars extends from the SSC to the PM. We obtain equations for the pressure, osmotic concentration and fluid velocity in the ECiS from the Brinkman-Stokes equations for steady incompressible flow in a plane channel that encloses an array of cylinders and whose upper wall, i.e. the plasma membrane, has a hydraulic conductivity of P(PM). From these equations we obtain an estimate for the hydraulic conductivity of the ECiS, P(ECiS). We show that the ECiS geometry accounts for P(ECiS) being several orders of magnitude larger than P(PM) and that P(ECiS) increases with the width of the ECiS and decreases with the length of the ECiS.

A membrane bending model of outer hair cell electromotility.

We propose a new mechanism for outer hair cell electromotility based on electrically induced localized changes in the curvature of the plasma membrane (flexoelectricity). Electromechanical coupling in the cell's lateral wall is modeled in terms of linear constitutive equations for a flexoelectric membrane and then extended to nonlinear coupling based on the Langevin function. The Langevin function, which describes the fraction of dipoles aligned with an applied electric field, is shown to be capable of predicting the electromotility voltage displacement function. We calculate the electrical and mechanical contributions to the force balance and show that the model is consistent with experimentally measured values for electromechanical properties. The model rationalizes several experimental observations associated with outer hair cell electromotility and provides for constant surface area of the plasma membrane. The model accounts for the isometric force generated by the cell and explains the observation that the disruption of spectrin by diamide reduces force generation in the cell. We discuss the relation of this mechanism to other proposed models of outer hair cell electromotility. Our analysis suggests that rotation of membrane dipoles and the accompanying mechanical deformation may be the molecular mechanism of electromotility.

Mechanical and electromotile characteristics of auditory outer hair cells.

The passive and active properties of the cochlear outer hair cell are studied. The outer hair cell is currently considered the major candidate for the active component of mammalian hearing. Understanding of its properties may explain the amplification and sharp frequency selectivity of the ear. To analyse the cell behaviour, a model of a nonlinear anisotropic electro-elastic shell is used. Using the data from three independent experiments, where the mechanical strains of the cell are measured, estimates of the cell wall in-plane Young's moduli and Poisson's ratios are given, as well as estimates of three modes of bending stiffness. Based on these estimates and data from the microchamber experiment, where the cell is under the action of transmembrane potential changes, the characteristics of the outer hair cell active behaviour are found. These characteristics include the coefficients of the active force production per unit of the transmembrane potential change and limiting parameters of the electromotile response for extreme hyperpolarisation and depolarisation of the cell. The obtained estimates provide important information for the modelling of organ-level cochlear mechanics.

Canine sternal force-displacement relationship during cardiopulmonary resuscitation.

A viscoelastic model developed to model human sternal response to the cyclic loading of manual cardiopulmonary resuscitation (CPR) [8] was used to evaluate the properties of canine chests during CPR. Sternal compressions with ventilations after every fifth compression were applied to supine canines (n = 7) with a mechanical resuscitation device. The compressions were applied at a nominal rate of 90/min with a peak force near 400 N. From measurements of sternal force, sternal displacement, and tracheal airflow, model parameters were estimated and their dependence on time and lung volume evaluated. The position to which the chest recoiled between compressions changed with time at a mean rate of 1.0 mm/min. Within each ventilation cycle (five compressions) the sternal recoil position decreased by 2.0 cm for each liter of decrease in lung volume. The elastic force and damping decreased with time and decreasing lung volume. Canine and human [8] model parameters were found to be similar despite the notable differences in thoracic anatomy between the species, supporting the continued use of canines as models for human CPR. These parameters may be useful in the development of a model relating sternal compression forces to blood flow during CPR.