1995 Whitaker lecture: Delivery of molecules,particles, and cells to solid tumors

To reach cancer cells in a tumor, a blood-borne therapeutic agent must make its way into the blood vessels of the tumor and across the vessel wall into the interstitium, and finally migrate through the interstitium. Unfortunately, tumors often develop in ways that hinder each of these steps. Our research goals are to analyze each of these steps experimentally and theoretically, and then to integrate the resulting information in a unified theoretical framework. This paradigm of analysis and synthesis has allowed us to obtain a better understanding of physiological barriers in solid tumors, and to develop novel strategies to exploit and/or to overcome these barriers for improved cancer detection and treatment.     

Estimating transit time for capillary blood in selected muscles of exercising animals

The mean minimal capillary transit time was estimated in muscles of various animals using a combination of physiological and morphometric methods. Radioactive microspheres were injected intravascularly in various animals running on a treadmill at maximum oxygen consumption rate (VO_2,max) to label blood flow to individual muscles. The muscles were then removed and preserved by standard methods for electron microscopy. The volume density of mitochondria was measured to assess muscle oxidative capacity. Capillary densities in muscle cross-sections, capillary diameters and tortuosities were incorporated into an estimate of capillary volume per unit muscle mass. Mean capillary transit time (t _c) in the exercising muscles was estimated by dividing mass-specific capillary volume by mass-specific blood flow. Estimates of t _c ranged from values near 1 s in horse heart and thigh muscles to 0.2 s in duck gastrocnemius. The relationship between muscle blood flow and t _c was hyperbolic. The experimental data indicate a limiting value of 0.2 s for transit times at very high blood flows. There was no correlation between t _c and body-mass-specific VO_2,max.     

A mathematical model of thrombin production in blood coagulation,Part I: The sparsely covered membrane case

This paper presents the first attempt to model the blood coagulation reactions in flowing blood. The model focuses on the common pathway and includes activation of factor X and prothrombin, including feedback activation of cofactors VIII and V by thrombin, and plasma inhibition of factor Xa and thrombin. In this paper, the first of two, the sparsely covered membrane (SCM) case is presented. This considers the limiting situation where platelet membrane binding sites are in excess, such that no membrane saturation or binding competition occurs. Under these conditions, the model predicts that the two positive feedback loops lead to multiple steady-state behavior in the range of intermediate mass transfer rates. It will be shown that this results in three parameter regions exhibiting very different thrombin production patterns. The model predicts the effect of flow on steady-state and dynamic thrombin production and attempts to explain the difference between venous and arterial thrombi. The reliance of thrombin production on precursor procoagulant protein concentrations is also assessed.     

A numerical coupling model to analyze the blood flow, temperature, and oxygen transport in human breast tumor under laser irradiation

The aim of this study is to investigate the variation of the blood perfusion rate and distribution of oxygen partial pressure (PO2) in human tumors by a coupling numerical model when laser irradiation is used as an adjuvant method in the treatment of cancer. A two-dimensional finite element (FE) thermal model of a human breast with a tumor was developed. The blood circulation inside the breast was modeled using one-dimensional non-linear equations of pulsatile fluid flow. The distribution of PO2 inside the capillaries, tumor vessels, and surrounding tissue was obtained by the Krogh analysis model. Finally, the variations of the average tumor temperature, blood perfusion, and PO2 during laser heating were computed by coupling the blood circulation, FE thermal, and oxygen transport models.     

Effects of different patterns of long-term stimulation on blood flow,fuel uptake and enzyme activities in rabbit fast skeletal muscles

Long-term electrical stimulation (14–28 days) of rabbit fast muscles (tibialis anterior, TA and extensor digitorum longus, EDL) using intermittent high frequency (3 trains per min of 5 s duration at 40 Hz, for 8 h per day) produced changes in enzyme activities similar to those found with continuous stimulaton at a frequency occuring in nerves to slow muscles (10 Hz). The activity of citrate synthetase, 3-hydroxyacyl-CoA dehydrogenase and succinate dehydrogenase increased two to 3-fold within 28 days. There was a 4-fold increase in hexokinase whereas phosphofructokinase, pyruvate kinase, lactate dehydrogenase and fructose-1,6-diphosphatase decreased to about 60% of the activity levels in the contralateral unstimulated muscles. Blood flow and oxygen consumption at rest were not changed even after 28 days of stimulation, but were increased during contractions in muscles stimulated at either frequency, the level being twice as high as in control muscles. Glucose uptake was similar to that in control muscles both at rest and during contractions and the output of lactate was similar to that found in control muscles in muscles stimulated at 40 Hz. Muscles stimulated at 10 Hz had smaller lactate output. Thus intermittent stimulation at high frequency (40 Hz) and continuous low frequency (10 Hz) produced similar changes in aerobic metabolism and fuel uptake provided that the total number of stimuli was comparable and that the stimulation was carried out for sufficiently long period.This work was supported by MRC of Great Britain and by Deutsche Forschungsgemeinschaft     

Through the microcirculatory maze with machete,molecule, and minicomputer (1986 Alza lecture)

This is a personal historical essay on meanderings through the jungle of the microcirculatory swamp. Because one pretends that the wandering was purposefully exploratory, a few guideposts are placed at positions where one could discern blazemarks from earlier wanderers, and the path cut a little wider along some of the routes that may be enjoyed by investigators wanting to put their blazes along more distant paths. Naturally, one starts by coming up the broad rivers, the branching into the little streams. Each of us chooses to seek a different “mother lode,” up a different stream. Supported by grants HL19135, HL19139, RR1243 from the National Institutes of Health.     

Blood Flow in Compliant Arteries: An Effective Viscoelastic Reduced Model, Numerics, and Experimental Validation

The focus of this work is on modeling blood flow in medium-to-large systemic arteries assuming cylindrical geometry, axially symmetric flow, and viscoelasticity of arterial walls. The aim was to develop a reduced model that would capture certain physical phenomena that have been neglected in the derivation of the standard axially symmetric one-dimensional models, while at the same time keeping the numerical simulations fast and simple, utilizing one-dimensional algorithms. The viscous Navier–Stokes equations were used to describe the flow and the linearly viscoelastic membrane equations to model the mechanical properties of arterial walls. Using asymptotic and homogenization theory, a novel closed, “one-and-a-half dimensional” model was obtained. In contrast with the standard one-dimensional model, the new model captures: (1) the viscous dissipation of the fluid, (2) the viscoelastic nature of the blood flow – vessel wall interaction, (3) the hysteresis loop in the viscoelastic arterial walls dynamics, and (4) two-dimensional flow effects to the leading-order accuracy. A numerical solver based on the 1D-Finite Element Method was developed and the numerical simulations were compared with the ultrasound imaging and Doppler flow loop measurements. Less than 3% of difference in the velocity and less than 1% of difference in the maximum diameter was detected, showing excellent agreement between the model and the experiment.