A Mathematical Model for Cisplatin Cellular Pharmacodynamics

AbstractA simple theoretical model for the cellular pharmacodynamics of cisplatin is presented. The model, which takes into account the kinetics of cisplatin uptake by cells and the intracellular binding of the drug, can be used to predict the dependence of survival (relative to controls) on the time course of extracellular exposure. Cellular pharmacokinetic parameters are derived from uptake data for human ovarian and head and neck cancer cell lines. Survival relative to controls is assumed to depend on the peak concentration of DNA-bound intracellular platinum. Model predictions agree well with published data on cisplatin cytotoxicity for three different cancer cell lines, over a wide range of exposure times. In comparison with previously published mathematical models for anticancer drug pharmacodynamics, the present model provides a better fit to experimental data sets including long exposure times (∼100 hours). The model provides a possible explanation for the fact that cell kill correlates well with area under the extracellular concentration-time curve in some data sets, but not in others. The model may be useful for optimizing delivery schedules and for the dosing of cisplatin for cancer therapy

Two-Mechanism Peak Concentration Model for Cellular Pharmacodynamics of Doxorubicin

AbstractA mathematical model is presented for the cellular uptake and cytotoxicity of the anticancer drug doxorubicin. The model assumes sigmoidal, Hill-type dependence of cell survival on drug-induced damage. Experimental evidence indicates distinct intracellular and extracellular mechanisms of doxorubicin cytotoxicity. Drug-induced damage is therefore expressed as the sum of two terms, representing the peak values over time of concentrations of intracellular and extracellular drugs. Dependence of cell kill on peak values of concentration rather than on an integral over time is consistent with observations that dose-response curves for doxorubicin converge to a single curve as exposure time is increased. Drug uptake by cells is assumed to include both saturable and unsaturable components, consistent with experimental data. Overall, the model provides better fits to in vitro cytotoxicity data than previous models. It shows how saturation of cellular uptake or binding with concentration can result in plateaus in the dose-response curve at high concentrations and short exposure, as observed experimentally in some cases. The model provides a unified framework for analyzing doxorubicin cellular pharmacokinetic and pharmacodynamic data, can be applied in mathematical models for tumor response and treatment optimization

Origins of Metabolic Signals

Diameters of microvessels undergo continuous structural adaptation in response to hemodynamic and metabolic stimuli. To ensure adequate flow distribution, metabolic responses are needed to increase diameters of vessels feeding poorly perfused regions. Possible modes of metabolic control include release of signaling substances from vessel walls, from the supplied tissue and from red blood cells (RBC). Here, a theoretical model was used to compare the abilities of these metabolic control modes to provide adequate tissue oxygenation, and to generate blood flow velocities in agreement with experimental observations. Structural adaptation of vessel diameters was simulated for an observed mesenteric network structure in the rat with 576 vessel segments. For each mode of metabolic control, resulting distributions of oxygen and deviations between simulated and experimentally observed flow velocities were analyzed. It was found that wall-derived and tissue-derived growth signals released in response to low oxygen levels could ensure adequate oxygen supply, but RBC- derived signals caused inefficient oxygenation. Closest agreement between predicted and observed flow velocities was obtained with wall-derived growth signals proportional to vessel length. Adaptation in response to oxygen- independent release of a metabolic signal substance from vessel walls or the supplied tissue was also shown to be effective for ensuring tissue oxygenation due to a dilution effect if growth signal substances are released into the blood. The present results suggest that metabolic signals responsible for structural adaptation of microvessel diameters are derived from vessel walls or from perivascular tissue

Blood viscosity in microvessels: Experiment and theory

The apparent viscosity of blood flowing through narrow glass tubes decreases strongly with decreasing tube diameter over the range from about 300 μm to about 10 μm. This phenomenon, known as the Fåhraeus-Lindqvist effect, occurs because blood is a concentrated suspension of deformable red blood cells with a typical dimension of about 8 μm. Most of the resistance to blood flow through the circulatory system resides in microvessels with diameters in this range. Apparent viscosity of blood in microvessels in vivo has been found to be significantly higher than in glass tubes with corresponding diameters. Here we review experimental observations of blood’s apparent viscosity in vitro and in vivo, and progress towards a quantitative theoretical understanding of the mechanisms involved

The Viscoelastic Properties of Passive Eye Muscle in Primates. III: Force Elicited by Natural Elongations

We have recently shown that in monkey passive extraocular muscles the force induced by a stretch does not depend on the entire length history, but to a great extent is only a function of the last elongation applied. This led us to conclude that Fung's quasi-linear viscoelastic (QLV) model, and more general nonlinear models based on a single convolution integral, cannot faithfully mimic passive eye muscles. Here we present additional data about the mechanical properties of passive eye muscles in deeply anesthetized monkeys. We show that, in addition to the aforementioned failures, previous models also grossly overestimate the force exerted by passive eye muscles during smooth elongations similar to those experienced during normal eye movements. Importantly, we also show that the force exerted by a muscle following an elongation is largely independent of the elongation itself, and it is mostly determined by the final muscle length. These additional findings conclusively rule out the use of classical viscoelastic models to mimic the mechanical properties of passive eye muscles. We describe here a new model that extends previous ones using principles derived from research on thixotropic materials. This model is able to account reasonably well for our data, and could thus be incorporated into models of the eye plant

Effect of Hydrogen Peroxide and Superoxide Anions on Cytosolic Ca2+: Comparison of Endothelial Cells from Large-Sized and Small-Sized Arteries

We compared the Ca2+ responses to reactive oxygen species (ROS) between mouse endothelial cells derived from large-sized arteries, aortas (aortic ECs), and small-sized arteries, mesenteric arteries (MAECs). Application of hydrogen peroxide (H2O2) caused an increase in cytosolic Ca2+ levels ([Ca2+]i) in both cell types. The [Ca2+]i rises diminished in the presence of U73122, a phospholipase C inhibitor, or Xestospongin C (XeC), an inhibitor for inositol-1,4,5-trisphosphate (IP3) receptors. Removal of Ca2+ from the bath also decreased the [Ca2+]i rises in response to H2O2. In addition, treatment of endothelial cells with H2O2 reduced the [Ca2+]i responses to subsequent challenge of ATP. The decreased [Ca2+]i responses to ATP were resulted from a pre-depletion of intracellular Ca2+ stores by H2O2. Interestingly, we also found that Ca2+ store depletion was more sensitive to H2O2 treatment in endothelial cells of mesenteric arteries than those of aortas. Hypoxanthine-xanthine oxidase (HX-XO) was also found to induce [Ca2+]i rises in both types of endothelial cells, the effect of which was mediated by superoxide anions and H2O2 but not by hydroxyl radical. H2O2 contribution in HX-XO-induced [Ca2+]i rises were more significant in endothelial cells from mesenteric arteries than those from aortas. In summary, H2O2 could induce store Ca2+ release via phospholipase C-IP3 pathway in endothelial cells. Resultant emptying of intracellular Ca2+ stores contributed to the reduced [Ca2+]i responses to subsequent ATP challenge. The [Ca2+]i responses were more sensitive to H2O2 in endothelial cells of small-sized arteries than those of large-sized arteries

Model-based inference from microvascular measurements: Combining experimental measurements and model predictions using a Bayesian probabilistic approach

Objective: In vivo imaging of the microcirculation and network-oriented modeling have emerged as powerful means of studying microvascular function and understanding its physiological significance. Network-oriented modeling may provide the means of summarizing vast amounts of data produced by high-throughput imaging techniques in terms of key, physiological indices. To estimate such indices with sufficient certainty, however, network-oriented analysis must be robust to the inevitable presence of uncertainty due to measurement errors as well as model errors. Methods: We propose the Bayesian probabilistic data analysis framework as a means of integrating experimental measurements and network model simulations into a combined and statistically coherent analysis. The framework naturally handles noisy measurements and provides posterior distributions of model parameters as well as physiological indices associated with uncertainty. Results: We applied the analysis framework to experimental data from three rat mesentery networks and one mouse brain cortex network. We inferred distributions for more than 500 unknown pressure and hematocrit boundary conditions. Model predictions were consistent with previous analyses, and remained robust when measurements were omitted from model calibration. Conclusion: Our Bayesian probabilistic approach may be suitable for optimizing data acquisition and for analyzing and reporting large data sets acquired as part of microvascular imaging studies

Permanent Occlusion of Feeding Arteries and Draining Veins in Solid Mouse Tumors by Vascular Targeted Photodynamic Therapy (VTP) with Tookad

Antiangiogenic and anti-vascular therapies present intriguing alternatives to cancer therapy. However, despite promising preclinical results and significant delays in tumor progression, none have demonstrated long-term curative features to date. Here, we show that a single treatment session of Tookad-based vascular targeted photodynamic therapy (VTP) promotes permanent arrest of tumor blood supply by rapid occlusion of the tumor feeding arteries (FA) and draining veins (DV), leading to tumor necrosis and eradication within 24–48 h.A mouse earlobe MADB106 tumor model was subjected to Tookad-VTP and monitored by three complementary, non-invasive online imaging techniques: Fluorescent intravital microscopy, Dynamic Light Scattering Imaging and photosensitized MRI. Tookad-VTP led to prompt tumor FA vasodilatation (a mean volume increase of 70%) with a transient increase (60%) in blood-flow rate. Rapid vasoconstriction, simultaneous blood clotting, vessel permeabilization and a sharp decline in the flow rates then followed, culminating in FA occlusion at 63.2 sec±1.5SEM. This blockage was deemed irreversible after 10 minutes of VTP treatment. A decrease in DV blood flow was demonstrated, with a slight lag from FA response, accompanied by frequent changes in flow direction before reaching a complete standstill. In contrast, neighboring, healthy tissue vessels of similar sizes remained intact and functional after Tookad-VTP.Tookad-VTP selectively targets the tumor feeding and draining vessels. To the best of our knowledge, this is the first mono-therapeutic modality that primarily aims at the larger tumor vessels and leads to high cure rates, both in the preclinical and clinical arenas

Coalescent angiogenesis—evidence for a novel concept of vascular network maturation

Angiogenesis describes the formation of new blood vessels from pre-existing vascular structures. While the most studied mode of angiogenesis is vascular sprouting, specific conditions or organs favor intussusception, i.e., the division or splitting of an existing vessel, as preferential mode of new vessel formation. In the present study, sustained (33-h) intravital microscopy of the vasculature in the chick chorioallantoic membrane (CAM) led to the hypothesis of a novel non-sprouting mode for vessel generation, which we termed "coalescent angiogenesis." In this process, preferential flow pathways evolve from isotropic capillary meshes enclosing tissue islands. These preferential flow pathways progressively enlarge by coalescence of capillaries and elimination of internal tissue pillars, in a process that is the reverse of intussusception. Concomitantly, less perfused segments regress. In this way, an initially mesh-like capillary network is remodeled into a tree structure, while conserving vascular wall components and maintaining blood flow. Coalescent angiogenesis, thus, describes the remodeling of an initial, hemodynamically inefficient mesh structure, into a hierarchical tree structure that provides efficient convective transport, allowing for the rapid expansion of the vasculature with maintained blood supply and function during development

Structural Adaptation and Heterogeneity of Normal and Tumor Microvascular Networks

Relative to normal tissues, tumor microcirculation exhibits high structural and functional heterogeneity leading to hypoxic regions and impairing treatment efficacy. Here, computational simulations of blood vessel structural adaptation are used to explore the hypothesis that abnormal adaptive responses to local hemodynamic and metabolic stimuli contribute to aberrant morphological and hemodynamic characteristics of tumor microcirculation. Topology, vascular diameter, length, and red blood cell velocity of normal mesenteric and tumor vascular networks were recorded by intravital microscopy. Computational models were used to estimate hemodynamics and oxygen distribution and to simulate vascular diameter adaptation in response to hemodynamic, metabolic and conducted stimuli. The assumed sensitivity to hemodynamic and conducted signals, the vascular growth tendency, and the random variability of vascular responses were altered to simulate ‘normal’ and ‘tumor’ adaptation modes. The heterogeneous properties of vascular networks were characterized by diameter mismatch at vascular branch points (d3var) and deficit of oxygen delivery relative to demand (O2def). In the tumor, d3var and O2def were higher (0.404 and 0.182) than in normal networks (0.278 and 0.099). Simulated remodeling of the tumor network with ‘normal’ parameters gave low values (0.288 and 0.099). Conversely, normal networks attained tumor-like characteristics (0.41 and 0.179) upon adaptation with ‘tumor’ parameters, including low conducted sensitivity, increased growth tendency, and elevated random biological variability. It is concluded that the deviant properties of tumor microcirculation may result largely from defective structural adaptation, including strongly reduced responses to conducted stimuli