A new approach for predicting the enhancement in the effective conductivity of perfused muscle tissue due to hyperthermia

Volumetric MRI-guided high-intensity focused ultrasound for noninvasive, in vivo determination of tissue thermal conductivity: initial experience in a pig model

PURPOSE

To estimate the local thermal conductivity of porcine thigh muscle at temperatures required for magnetic resonance imaging (MRI)-guided high-intensity focused ultrasound (MRgHIFU) surgery (60-90°C).

MATERIALS AND METHODS

Using MRgHIFU, we performed 40 volumetric ablations in the thigh muscles of four pigs. Thirty-five of the sonications were successful. We used MRI to monitor the resulting temperature increase. We then determined local thermal conductivity by analyzing the spatiotemporal spread of temperature during the cooling period.

RESULTS

The thermal conductivity of MRgHIFU-treated porcine thigh muscle fell within a narrow range (0.52 ± 0.05 W/[m*K]), which is within the range reported for porcine thigh muscle at temperatures of <40°C (0.52 to 0.62 W/[m*K]). Thus, there was little change in the thermal conductivity of porcine thigh muscle at temperatures required for MRgHIFU surgery compared to lower temperatures.

CONCLUSION

Our MRgHIFU-based approach allowed us to estimate, with good reproducibility, the local thermal conductivity of in vivo deep tissue in real time at temperatures of 60°C to 90°C. Therefore, our method provides a valuable tool for quantifying the influence of thermal conductivity on temperature distribution in tissues and for optimizing thermal dose delivery during thermal ablation with clinical MRgHIFU.

THERMAL MODELS OF BIOHEAT TRANSFER EQUATIONS IN LIVING TISSUE AND THERMAL DOSE EQUIVALENCE DUE TO HYPERTHERMIA

This review focuses both on the basic formulations of bioheat equation in the living tissue and on the determination of thermal dose during thermal therapy. The temperature distributions inside the heated tissues, generally controlled by heating modalities, are obtained by solving the bioheat transfer equation. However, the major criticism for the Pennes' model focused on the assumption that the heat transfer by blood flow occurs in a non-directional, heat sink- or source-like term. Several bioheat transfer models have been introduced to compare their convective and perfusive effects in vascular tissues. The present review also elucidates thermal dose equivalence that represents the extent of thermal damage or destruction of tissue in the clinical treatment of tumor with local hyperthermia. In addition, this study uses the porous medium concept to describe the heat transfer in the living tissue with the directional effect of blood flow, and the polynomial expression of thermal dose in terms of the curve fitting of the experimental isosurvival curve data by Dewey et al. Results show that the values of factor R is a function of the heating temperature instead of the two different constants suggested by Sapareto and Dewey.

Simultaneous measurements of local tissue temperature and blood perfusion rate in the canine prostate during radio frequency thermal therapy

Local tissue temperature and blood perfusion rate were measured simultaneously to study thermoregulation in the canine prostate during transurethral radio-frequency (RF) thermal therapy. Thermistor bead microprobes measured interstitial temperatures and a thermal clearance method measured the prostatic blood perfusion rate under both normal and hyperthermic conditions. Increase in local tissue temperature induced by the RF heating increased blood perfusion throughout the entirety of most prostates. The onset of the initial increase in blood perfusion was sometimes triggered by a temporal temperature gradient at low tissue temperatures. When tissue temperature was higher than 41 degrees C, however, the magnitude and the spatial gradient of temperature may play significant roles. It was found that the temperature elevation in response to the RF heating was closely coupled with local blood flow. The resulting decrease in or stabilization of tissue temperature suggested that blood flow might act as a negative feedback of tissue temperature in a closed control system. Results from this experiment provide insights into the regulation of local perfusion under hyperthermia. The information is important for accurate predictions of temperature during transurethral RF thermal therapy.

Experimental measurements of the temperature variation along artery-vein pairs from 200 to 1000 microns diameter in rat hind limb

Theoretical studies have indicated that a significant fraction of all blood-tissue heat transfer occurs in artery-vein pairs whose arterial diameter varies between 200 and 1000 microns. In this study, we have developed a new in vivo technique in which it is possible to make the first direct measurements of the countercurrent thermal equilibration that occurs along thermally significant vessels of this size. Fine wire thermocouples were attached by superglue to the femoral arteries and veins and their subsequent branches in rats and the axial temperature variation in each vessel was measured under different physiological conditions. Unlike the blood vessels < 200 microns in diameter, where the blood rapidly equilibrates with the surrounding tissue, we found that the thermal equilibration length of blood vessels between 200 microns and 1000 microns in diameter is longer than or at least equivalent to the vessel length. It is shown that the axial arterial temperature decays from 44% to 76% of the total core-skin temperature difference along blood vessels of this size, and this decay depends strongly on the local blood perfusion rate and the vascular geometry. Our experimental measurements also showed that the SAV venous blood recaptured up to 41% of the total heat released from its countercurrent artery under normal conditions. The contribution of countercurrent heat exchange is significantly reduced in these larger thermally significant vessels for hyperemic conditions as predicted by previous theoretical analyses. Results from this study, when combined with previous analyses of vessel pairs less than 200 microns diameter, enable one estimate the arterial supply temperature and the correction coefficient in the modified perfusion source term developed by the authors.

Temperature and angiogenesis: the possible role of mechanical factors in capillary growth

This review examines the effect of prolonged cold exposure on muscle capillary supply in mammals and fishes. In rats and hamsters, the response to a simulated onset of winter is to conserve the microcirculation and maintain a constant capillary to fibre ratio (C:F), implying either an unaltered vacular bed or angiogenesis matched by muscle hyperplasia, while chronic acclimation to low environmental temperature induces a variable degree of muscle atrophy, which in turn increases capillary density (CD). In striped bass and rainbow trout, cold-induced angiogenesis results in an increase in C:F, but also a cold-induced fibre hypertrophy that is accompanied by a powerful angiogenic response such that CD is much less sensitive to changes in fibre size. Endothelial cells can act as mechanotransducers such that angiogenesis may be initiated by changes in their physical environment. It is hypothesised that in mammals, the metabolic consequences of cold exposure increases the luminal shear stress, while in fishes the stimulus for angiogenesis is abluminal stretch following an increase in fibre size.

Analysis of temperature measurement for monitoring radio-frequency brain lesioning

During ablative neurosurgery of movement disorders, for instance therapy of Parkinson's disease, temperature monitoring is crucial. This study aims at a quantitative comparison of measurement deviations between the maximum temperature located outside the lesioning electrode and two possible thermocouple locations inside the electrode. In order to obtain the detailed temperature field necessary for the analysis, four finite element models associated with different surroundings and with different power supplies are studied. The results from the simulations show that both the power level and the power density as well as the surrounding medium affect the temperature measurement and the temperature field in general. Since the maximum temperature is located outside the electrode there will always be a deviation in time and level between the measured and the maximum temperature. The deviation is usually 2-7 s and 3-12 degrees C, depending on, for example, the thermocouple location and surrounding medium. Therefore, not only the measured temperature but also the relation between measured and maximum temperature must be accounted for during therapy and device design.

Dose uniformity of ferromagnetic seed implants in tissue with discrete vasculature: a numerical study on the impact of seed characteristics and implantation techniques

The results from simulations with a new three-dimensional treatment planning system for interstitial hyperthermia with ferromagnetic seeds are presented in this study. The thermal model incorporates discrete vessel structures as well as a heat sink and enhanced thermal conductivity. Both the discrete vessels and the ferroseeds are described parametrically in separate calculation spaces. This parametric description has the advantage of an arbitrary orientation of the structures within the tissue grid, easy manipulation of the structures and independence from the resolution of the tissue voxels (tissue calculation space). The power absorption of the self-regulating seeds is according to empirical data. The thermal effects of an unlimited number of thin layers surrounding the seed (coatings, catheters) can be modelled. The initial calculations have been performed for an array of 12 identical ferromagnetic seeds in a tissue volume with a computer generated artificial vessel network spanning four vessel generations in both the arterial and venous tree. The heterogeneously distributed large isolated vessels impair the temperature distribution significantly, indicating the limited accuracy of continuum models. Simulations with different types of ferromagnetic seeds have confirmed that the efforts of previous studies to optimize the self-regulating temperature control and the implantation techniques of the ferroseeds will improve the homogeneity of the temperature distribution in the target volume. Multifilament seeds implanted in brachytherapy needles and tubular seeds appear to be the most favourable configurations. The division of long seeds into shorter segments with the appropriate Curie temperature will further improve the homogeneity of the temperature distribution without increasing the average temperature in the volume of interest. Given the proper thermal tissue data, the model presented in this study will prove to be a useful tool in making choices for the implant geometry, seed spacing and Curie temperature.

Thermoregulation in the canine prostate during transurethral microwave hyperthermia, Part I: Temperature response

In this research, experiments were performed to study thermoregulation in the canine prostate during microwave hyperthermia. The transurethral thermal therapy (T3) system provided by Urologix, Inc. was used to impose microwave heating in the canine prostate. Five types of temperature responses to different microwave power levels as time varies, including both damped and sustained oscillatory temperature responses, have been observed. Decreases in prostatic tissue temperature during the microwave heating are believed to be caused by the increase in local blood flow stimulated by tissue temperature elevations. In this study, the characteristic temperatures and time associated with each response. This work will help to provide a better understanding of how tissue temperature is regulated within the canine prostate during transurethral microwave hyperthermia. Results of the present study offer an experimental foundation for a more detailed theoretical analysis on the temperature distribution based on the power input and local blood perfusion.

Enhancement in the effective thermal conductivity in rat spinotrapezius due to vasoregulation

This study was undertaken to gain a better understanding of the countercurrent heat exchange of thermally significant blood vessels in skeletal muscle by measuring the vascular structure and flow in an exteriorized rat spinotrapezius muscle and estimating the enhancement in the effective thermal conductivity of the muscle. Detailed anatomic measurements of the number density and length of countercurrent vessel pairs between 45 and 165 microns diameter were obtained. Moreover, diameter and blood flow in the 1A to 3A vessels were measured for muscles in which pharmacological vasoactive agents were introduced, allowing one to vary the local blood flow Peclet number from 1 to 18 in the major feeding arteries. These combined measurements have been used to estimate the range of possible enhancement in the effective thermal conductivity of the tissue. The newly derived conduction shape factor in Zhu et al. for countercurrent vessels in two-dimensional tissue preparations was used in this analysis. Our experimental data indicated that the value of this conduction shape factor was about one-third to two-thirds the value for two countercurrent vessels of the same size and spacing in an infinite medium. The experiment also revealed that the Weinbaum-Jiji expression for keff was valid for the spinotrapezius muscle when the largest vessels were less than 195 microns diameter. A fivefold increase in keff was predicted for 195 microns diameter vessels. Vasoregulation was also shown to have a dramatic effect on keff. A tissue that exhibits only small increases in keff due to countercurrent convection in its vasoconstricted state can exhibit a more than fivefold increase in keff in its vasodilated state.

A new fundamental bioheat equation for muscle tissue: Part I--Blood perfusion term

A new model for muscle tissue heat transfer has been developed using Myrhage and Eriksson's [23] description of a muscle tissue cylinder surrounding secondary (s) vessels as the basic heat transfer unit. This model provides a rational theory for the venous return temperature for the perfusion source term in a modified Pennes bioheat equation, and greatly simplifies the anatomical description of the microvascular architecture required in the Weinbaum-Jiji bioheat equation. An easy-to-use closed-from analytic expression has been derived for the difference between the inlet artery and venous return temperatures using a model for the countercurrent heat exchange in the individual muscle tissue cylinders. The perfusion source term calculated from this model is found to be similar in form to the Pennes's source term except that there is a correction factor or efficiency coefficient multiplying the Pennes term, which rigorously accounts for the thermal equilibration of the returning vein. This coefficient is a function of the vascular cross-sectional geometry of the muscle tissue cylinder, but independent of the Peclet number in contrast to the recent results in Brinck and Werner [8]. The value of this coefficient varies between 0.6 and 0.7 for most muscle tissues. In part II of this study a theory will be presented for determining the local arterial supply temperature at the inlet to the muscle tissue cylinder.

Tests of the geometrical description of blood vessels in a thermal model using counter-current geometries

We have developed a thermal model, for use in hyperthermia treatment planning, in which blood vessels are described as geometrical objects; 3D curves with associated diameters. For the calculation of the heat exchange with the tissue an analytic result is used. To arrive at this result some assumptions were made. One of these assumptions is a cylindrically symmetric temperature distribution. In this paper the behaviour of the model is examined for counter-current vessel geometries for which this assumption is not valid. Counter-current vessel pairs intersecting a circular tissue slice are tested. For these 2D geometries vessel spacing, tissue radius and resolution are varied, as well as the position of the vessel pair with respect to the discretized tissue grid. The simulation results are evaluated by comparison of the different heat flow rates with analytical predictions. The tests show that for a fixed vessel configuration the accuracy is not a simple decreasing function of the voxel dimensions, but is also sensitive to the position of the configuration with respect to the discretized tissue grid.

On the Nusselt number in heat transfer between multiple parallel blood vessels

Arrays of two or more parallel blood vessels in a tissue matrix have been studied extensively in the context of bioheat transfer. The average vessel Nusselt number (based on the difference between the mixed-mean blood temperature and the average vessel surface temperature) is a crucial parameter in such studies. Various workers have noted tht in particular cases the average Nusselt number is identical to that for fully developed flow in a single vessel in an infinite medium. In other words, the Nusselt number is unaffected by the presence of other vessels. It is proven here that this surprising result holds true for arbitrary number, size, flow direction, and velocity profile in the blood vessels, and for very general boundary conditions on the outer tissue boundary. A useful corollary is that the average wall temperature in a particular vessel may be found by evaluating the temperature fields due to the other vessels and the tissue boundaries at a single point, the center of the vessels in question.

Microvascular thermal equilibration in rat cremaster muscle

A new experimental approach was developed to obtain the first direct measurements of the axial countercurrent thermal equilibration in a microvascular tissue preparation using high resolution infrared thermography. Detailed surface temperature measurements were obtained for an exteriorized rat cremaster muscle in which pharmacological vasoactive agents were used to change the local blood flow Peclet number from 1 to 14 in the feeding artery. Under normal conditions, only the 1A arteries (> 70 microns diameter) showed thermal nonequilibration with the surrounding tissue. The theoretical model developed by Zhu and Weinbaum (28) for a two-dimensional tissue preparation with arbitrarily embedded countercurrent vessels was modified to include axial conduction and the presence of the supporting glass slide. This modified model was used to interpret the experimental results and to relate the surface temperature profiles to the bulk temperature profiles in the countercurrent artery and vein and the local average tissue temperature in the cross-sectional plane. Surface temperature profiles transverse to the vessel axis are shown to depend significantly on the tissue inlet temperature. The eigenfunction for the axial thermal equilibration depends primarily on the blood flow Peclet number and the environmental convective coefficient. The theoretical results predict that when rho(ar)*Pe is less than 1 mm (the range in our experiments), axial conduction is the dominant mode of axial thermal equilibration. For 1 < rho(ar)*PE < 3 mm, countercurrent blood flow becomes comparable to axial conduction, whereas, when rho(ar)*Pe > 3 mm, countercurrent blood flow is the dominant mode of axial thermal equilibration. Therefore, for rho(ar)*Pe > 3 mm the axial equilibration length is proportional to the blood flow Peclet number, as predicted previously by Zhu and Weinbaum in a study in which axial conduction was neglected. It also is shown that the axial decay of the tissue temperature at low perfusion rates can be described by a simple one-dimensional Weinbaum-Jiji equation with a newly derived conduction shape factor.

A model for heat transfer from embedded blood vessels in two-dimensional tissue preparations

Two-dimensional microvascular tissue preparations have been extensively used to study blood flow in the microcirculation, and, most recently, the mechanism of thermal equilibration between thermally significant countercurrent artery-vein pairs. In this paper, an approximate three-dimensional solution for the heat transfer from a periodic array of blood vessels in a tissue preparation of uniform thickness with surface convection is constructed using a newly derived fundamental solution for a Green's function for this flow geometry. This approximate solution is exact when the ratio K' of the blood to tissue conductivity is unity and a highly accurate approximation when K' not equal to 1. This basic solution is applied to develop a model for the heat transfer from a countercurrent artery-vein pair in an exteriorized rat cremaster muscle preparation. The numerical results provide important new insight into the design of microvascular experiments in which the axial variation of the thermal equilibration in microvessels can be measured for the first time. The solutions also provide new insight into the design of fluted fins and microchips that are convectively cooled by internal pores.