Uncertainties in compartmental analysis studied by linear programming techniques.
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Biomedical subjects
Publications and source records attributed to K R Foster.
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The theoretical basis, practical design considerations, and prototype testing of a perfused model suitable for simulation studies of microwave heated tissue are presented. A parallel tube heat exchanger configuration is used to simulate the internal convection effects of blood flow. The global thermal response of the phantom, on a scale of several tube spacings, is shown theoretically to be nearly identical to that predicted by Pennes' bioheat equation, which is known to give a reasonable representation of tissue under many conditions. A parametric study is provided for the relationships between the tube size, spacing and material properties and the simulated perfusion rate. A prototype with a physiologically reasonable perfusion rate was tested using a typical hyperthermia applicator. The measured thermal response of the phantom compares favorably with the numerical solution of the bioheat equation under the same irradiation conditions. This similarity sheds light on the unexpected success of the bioheat equation for modeling the thermal response of real tissue.
We develop analytical expressions (scaling laws) for the local temperature fluctuations near isolated and countercurrent blood vessels during hyperthermia. These scaling laws relate the magnitude of such fluctuations to the size of the heated region and to the thermal equilibration length of the vessels. A new equilibration length is identified for countercurrent vessels. Significant temperature differences are predicted between the vessels and the immediately adjacent tissue when the equilibration length is comparable to or longer than the size of the heated tissue region. Countercurrent vessels are shown to have shorter equilibration lengths and produce smaller temperature fluctuations than isolated vessels of the same size.
We have conducted a parametric comparison of three different vascular models for describing heat transport in tissue. Analytical and numerical methods were used to predict the gross temperature distribution throughout the tissue and the small-scale temperature gradients associated with thermally significant blood vessels. The models are: an array of unidirectional vessels, an array of countercurrent vessels, and a set of large vessels feeding small vessels which then drain into large vessels. We show that three continuum formulations of bioheat transfer (directed perfusion, effective conductivity, and a temperature-dependent heat sink) are limiting cases of the vascular models with respect to the thermal equilibration length of the vessels. When this length is comparable to the width of the heated region of tissue, the local temperature changes near the vessels can be comparable to the gross temperature elevation. These results are important to the use of thermal techniques used to measure the blood perfusion rate and in the treatment of cancer with local hyperthermia.
The dielectric properties of two low-water-content tissues, bone marrow and adipose tissue, were measured from 1 kHz to 1 GHz. From 1 kHz to 13 MHz, the measurements were performed using a parallel-plate capacitor method. From 10 MHz to 1 GHz, a reflection coefficient technique using an open-ended coaxial transmission line was employed. The tissue water contents ranged from 1 to almost 70% by weight. The dielectric properties correlate well with the values predicted by mixture theory. Comparison with previous results from high-water-content tissues suggests that bone marrow and adipose tissues contain less motionally altered water per unit dry volume than do the previously studied tissues with lower lipid fractions. The high degree of structural heterogeneity of these tissues was reflected in the large scatter of the data, a source of uncertainty that should be considered in practical applications of the present data.
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A variety of transport properties have been measured for solutions of the water soluble polymer poly(ethylene oxide)(PEO) with molecular weights ranging from 200 to 14,000, and volume fractions ranging from 0-80%. The transport properties are thermal conductivity, electrical conductivity at audio frequencies (in solutions containing dilute electrolyte), and water self-diffusion. These data, together with dielectric relaxation data previously reported, are amenable to analysis by the same mixture theory. The ionic conductivity and water self-diffusion coefficient, but not the thermal conductivity, are substantially smaller than predicted by the Maxwell and Hanai mixture relations, calculated using the known transport properties of pure liquid water. A 25% (by volume) solution of PEO exhibits an average dielectric relaxation frequency of the suspending water of one half that of pure water, with clear evidence of a distribution of relaxation times present. The limits of the cumulative distribution of dielectric relaxation times that are consistent with the data are obtained using a linear programming technique. The application of simple mixture theory, under appropriate limiting conditions, yields hydration values for the more dilute polymer solutions that are somewhat larger than values obtained from thermodynamic measurements.
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We summarize the results of several of our recent studies on the dielectric properties of protein solutions, tissues, and nonionic microemulsions at microwave frequencies extending to 18 GHz. The data in all cases are analyzed using the Maxwell mixture theory to determine the dielectric properties of the suspending water and the amount and dielectric properties of the water hydration associated with the suspended phase. The dielectric data from the protein solutions and tissues are broadly consistent with the results of previous studies at UHF frequencies; they indicate hydration values in the range of 0.4-0.6 g water/g protein. There is evidence of a dielectric relaxation process occurring at low-GHz frequencies that can be attributed in part to dielectric relaxation of the "bound" water in the system. The remaining solvent water appears to have dielectric properties close to, if not precisely the same as, those of pure water. The average relaxation frequency of the suspending water in the microemulsions is reduced from that of pure water, evidently reflecting an average of that of the water of hydration (approximately 5-6 GHz) and that of pure water. This reduced average relaxation frequency implies an increased average viscosity of the water and (by Walden's rule) accounts for the unexpectedly low ionic conductivity of the preparations.
Dielectric permittivity and conductivity measurements are reported from various soft excised mammalian non-tumour tissues, at frequencies between 0.1 and 100 MHz, and at room and body temperatures. The data over this wide frequency range can be well represented by a Cole-Cole equation for either the complex conductivity or complex permittivity. A summary of fitted parameters for the tissue data is presented, which can be used to reconstruct the original data values. The data are compared to older data that are still frequently quoted. Finally, the contribution of cells and organelles to the dielectric permittivity of one tissue is estimated, to help elucidate the mechanisms that are responsible for the observed dielectric data.
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This study predicts the steady state temperature rise in a homogeneous tissue sphere exposed to plane wave electromagnetic energy. The differential equation for heat transfer is solved, assuming heat transfer mechanisms of convection (due to blood flow), conduction, and evapotranspiration from the surface. The tissue heating is described by the specific absorption rate (SAR), which is a known function of the size and dielectric properties of the sphere and the frequency of the incident electro-magnetic energy. We consider the limiting cases of irradiation at very low frequencies, very high distance in the SAR is effectively averaged to produce a smoothly varying temperature increase. The results of this study are used to predict the maximum temperature rise in the human head, produced by an incident electromagnetic plane wave.
Anesthetized rhesus monkeys and rabbits were exposed to pulsed ultrasound, from a 1.8 cm diameter transducer placed against the head. Each ultrasonic exposure lasted 4 min; it consisted of a series of 1-2 mu sec pulses, with a frequency spectrum broadly centered about the transducer resonant frequency of 1.5 MHz, repeated at a rate of 950 Hz. The time averaged ultrasonics power was 12.6 mW, with an estimated peak power of ca. 15 watts. No changes were observed in the EEG or its power spectrum during or immediately after the exposure. This contrasts to a previous report of significant changes in the EEG of squirrel monkeys during comparable exposures to pulsed ultrasound. Analysis of the earlier reported results suggests that some of the "effects" were due to aliasing artifacts.