Pulsatile blood flow effects on temperature distribution and heat transfer in rigid vessels

The effect of blood velocity pulsations on bioheat transfer is studied. A simple model of a straight rigid blood vessel with unsteady periodic flow is considered. A numerical solution that considers the fully coupled Navier-Stokes and energy equations is used for the simulations. The influence of the pulsation rate on the temperature distribution and energy transport is studied for four typical vessel sizes: aorta, large arteries, terminal arterial branches, and arterioles. The results show that: the pulsating axial velocity produces a pulsating temperature distribution; reversal of flow occurs in the aorta and in large vessels, which produces significant time variation in the temperature profile. Change of the pulsation rate yields a change of the energy transport between the vessel wall and fluid for the large vessels. For the thermally important terminal arteries (0.04-1 mm), velocity pulsations have a small influence on temperature distribution and on the energy transport out of the vessels (8 percent for the Womersley number corresponding to a normal heart rate). Given that there is a small difference between the time-averaged unsteady heat flux due to a pulsating blood velocity and an assumed nonpulsating blood velocity, it is reasonable to assume a nonpulsating blood velocity for the purposes of estimating bioheat transfer.     

Stable,metastable, and supercritical phases in solutions of globular proteins between upper and lower denaturation temperatures

The temperature trends of the standard thermodynamic functions of the native and denatured protein in solution are considered within the concept of excess mixing functions. It is assumed that some protein molecules adopt an intermediate state between native and denatured forms within the temperature range between cold and thermal denaturation and form metastable microphases as a result of a specific interaction with water. A phase diagram in the temperature–standard entropy coordinate plane representing an isobar family is proposed. Two limiting isobars are characterized by an entropy jump, which reflects the first-order phase transition between the native and denatured states. The isobars in the intermediate temperature range are represented as van der Waals curves, which reflect the equilibrium between the main phase of the molecules in native state and microphases. The difference between the phases disappears at critical points. It is assumed that the supercritical range is a macroscopically homogeneous single phase zone of reduced stability, which is represented by a dynamic system of monomers and oligomers of the native protein, monomers and clusters of the protein with partially unfolded structure. The phase diagram is collated with the elliptic phase diagram in the temperature–osmotic pressure plane.     

Temperature evolution in tissues embedded with large blood vessels during photo-thermal heating

During laser-assisted photo-thermal therapy, the temperature of the heated tissue region must rise to the therapeutic value (e.g., 43 °C) for complete ablation of the target cells. Large blood vessels (larger than 500 micron in diameter) at or near the irradiated tissues have a considerable impact on the transient temperature distribution in the tissue. In this study, the cooling effects of large blood vessels on temperature distribution in tissues during laser irradiation are predicted using finite element based simulation. A uniform flow is assumed at the entrance and three-dimensional conjugate heat transfer equations in the tissue region and the blood region are simultaneously solved for different vascular models. A volumetric heat source term based on Beer–Lambert law is introduced into the energy equation to account for laser heating. The heating pattern is taken to depend on the absorption and scattering coefficients of the tissue medium. Experiments are also conducted on tissue mimics in the presence and absence of simulated blood vessels to validate the numerical model. The coupled heat transfer between thermally significant blood vessels and their surrounding tissue for three different tissue-vascular networks are analyzed keeping the laser irradiation constant. A surface temperature map is obtained for different vascular models and for the bare tissue (without blood vessels). The transient temperature distribution is seen to differ according to the nature of the vascular network, blood vessel size, flow rate, laser spot size, laser power and tissue blood perfusion rate. The simulations suggest that the blood flow through large blood vessels in the vicinity of the photothermally heated tissue can lead to inefficient heating of the target.     

Thermal stability of the helical structure of type IV collagen within basement membranes in situ: determination with a conformation-dependent monoclonal antibody

To examine the thermal stability of the helical structure of type IV collagen within basement membranes in situ, we have employed indirect immunofluorescence histochemistry performed at progressively higher temperatures using a conformation-dependent antibody, IV-IA8. We previously observed by competition enzyme-linked immunosorbent assay that, in neutral solution, the helical epitope to which this antibody binds undergoes thermal denaturation over the range of 37-40 degrees C. In the present study, we have reacted unfixed cryostat tissue sections with this antibody at successively higher temperatures. We have operationally defined denaturation as the point at which type IV- specific fluorescence is no longer detectable. Under these conditions, the in situ denaturation temperature of this epitope in most basement membranes is 50-55 degrees C. In capillaries and some other small blood vessels the fluorescent signal is still clearly detectable at 60 degrees C, the highest temperature at which we can confidently use this technique. We conclude that the stability of the helical structure of type IV collagen within a basement membrane is considerably greater than it is in solution, and that conformation-dependent monoclonal antibodies can be useful probes for investigations of molecular structure in situ.     

Network thermodynamic analysis of vasomotion in a microvascular network.

The modulation of microvascular blood flow by vasomotion in the individual vessels of a simple vascular network was simulated by means of a network thermodynamic model. The flow is driven under a pulsating pressure through two arcades of branching vasoactive arterioles into a passive resistance representing the capillary and venular beds. Each vessel was assumed to have the capability of decreasing rhythmically the local diameter over a short section by a specified fraction of the maximum value and to change the average diameter along its total length in response to alterations in intraluminal pressure. Blood was assumed to exhibit a simple linear viscous flow resistance. Alterations in flow rate and distribution through the network were determined as a function of the magnitude and frequency of vasomotion within the individual arterioles supplying blood to the microvascular bed. Specific cases are shown to illustrate how blood flow can be influenced by the patterns of vasomotion within the network.     

A laboratory exercise using a physical model for demonstrating countercurrent heat exchange

A physical model was used in a laboratory exercise to teach students about countercurrent exchange mechanisms. Countercurrent exchange is the transport of heat or chemicals between fluids moving in opposite directions separated by a permeable barrier (such as blood within adjacent blood vessels flowing in opposite directions). Greater exchange of heat or chemicals between the fluids occurs when the flows are in opposite directions (countercurrent) than in the same direction (concurrent). When a vessel loops back on itself, countercurrent exchange can occur between the two arms of the loop, minimizing loss or uptake at the bend of the loop. Comprehension of the physical principles underlying countercurrent exchange helps students to understand how kidneys work and how modifications of a circulatory system can influence the movement of heat or chemicals to promote or minimize exchange and reinforces the concept that heat and chemicals move down their temperature or concentration gradients, respectively. One example of a well-documented countercurrent exchanger is the close arrangement of veins and arteries inside bird legs; therefore, the setup was arranged to mimic blood vessels inside a bird leg, using water flowing inside tubing as a physical proxy for blood flow within blood vessels.     

Analytical solutions for the specific activities of a traced substance within the component parts of a simulated kidney-ureter system

Two models for a kidney-ureter system are considered: one model of one vessel in which a traced substance, undergoing exchange between the vessel and an external compartment, is emptying into the ureter; the second model of two approximately parallel, identical vessels in which a traced substance, undergoing exchange between each vessel and an external compartment, is emptying into the ureter. A single impulsive input of label into a vessel is assumed. For mathematical simplicity, the major conditions imposed on each system are: (1) rapid mixing transverse to a vessel axis and no mixing longitudinal to a vessel axis within the plasma; (2) small variation of the specific activity within the plasma in the longitudinal direction to a vessel axis; (3) constant flow rate of urine into the ureter and (4) constant exchange coefficients, tubule flow velocity and traced substance concentrations within individual compartments.     

Influence of carbon dioxide on the impregnation of the nervous tissue by silver

It has been shown that 4% carbon dioxide (CO₂) in the air above reaction mixture inhibits the initiation of the formation of silver nanoparticles from complexes with biogenic amines (noradrenaline and serotonin). At the same concentration of CO₂ in the air above solution of AgNO₃, which is used for staining nerve tissues by the method of Golgi, neurons are preferentially stained, whereas at a concentration of 0.06%, vessels are stained. It is suggested that the entry of free silver ions to neurons is due to the inhibition of sites of initiation of silver nanoparticles in vessels at high CO₂ concentrations, while the lack of inhibition leads to silver precipitation in vessels at low CO₂ concentrations. It can be assumed that, for stable silver impregnation, the concentration of CO₂ must be controlled.     

Three-dimensional organization of the developing vasculature of the kidney

Kidney function depends on a well-developed vascular system. Any impairment of the blood supply disturbs the integrity and function of the organ. The differentiation of renal vessels has been investigation for many years, but little is known about the relationship between nephrogenesis and vessel development. In the present work the spatial organization of the differentiating vessels was analyzed in precisely oriented tissue sections and in optical sections acquired by laser scan microscopy. Developing vessels as well as small capillaries were visualized with two endothelium-detecting antibodies. Small vessels running in parallel towards the organ capsule were detected in numerous cortico-medullary-oriented tissue sections. Cross-sections of the nephrogenic zone showed a regularly arranged network, which was composed of cells detected by both monoclonal antibodies. Parts of this network were localized in regions of the nephrogenic zone which have been assumed to be free of vessels or vessel-like structures for a long time. These results were confirmed by the laser-scan-microscopic analysis of complete cortex explants. The extraordinarily regular arrangement of the endothelial network in the nephrogenic zone allowed us to reconstruct the developing vascular system. The results presented here underline the close relationship between nephrogenesis and vessel development. Received: 20 May 1996 / Accepted: 11 July 1996     

Common-intersection hypothesis of development rate lines of ectotherms within a taxon revisited

The relationship between development rate of an ectotherm and temperature in experiments where insects or mites are reared under several constant temperatures, while non-linear over the entire range, can be approximately described by a line in the mid-temperature range. It was hypothesized that the development rate lines of ectotherms within a taxon such as a family would have a common intersection. Thus for a given temperature, the development time should be the same for all the species within any specified taxon. In the current study, the data on temperature-dependent development rates of species of the Aphididae and Tetranychidae families were used to test the validity of the common-intersection hypothesis. The hypothesis was supported with either dataset used. In addition, the current study tested the common-intersection hypothesis through mathematical analysis on the basis of two linear relationships (i.e., the linear relationship between temperature and development rate and that between the lower developmental threshold and the sum of effective temperatures). An attempt was made to combine the rate isomorphy hypothesis that all the lower developmental thresholds of different stages were assumed to be equal for a single species with the common-intersection hypothesis for related species within a taxon and hypothesize that if these two hypotheses hold, then for any developmental stages a common temperature of all stages should exist.     

Modeling of Bacterial Growth with Shifts in Temperature

The temperature of chilled foods is an important variable for the shelf life of a product in a production and distribution chain. To predict the number of organisms as a function of temperature and time, it is essential to model the growth as a function of temperature. The temperature is often not constant in various stages of distribution. The objective of this research was to determine the effect of shifts in temperature. The suitability and usefulness of several models to describe the growth of Lactobacillus plantarum with fluctuating temperatures was evaluated. It can be assumed that temperature shifts within the lag phase can be handled by adding relative parts of the lag time to be completed and that temperature shifts within the exponential phase result in no lag phase. With these assumptions, the kinetic behavior of temperature shift experiments was reasonably well predicted, and this hypothesis was accepted statistically in 73% of the cases. Only shifts of temperature around the minimum temperature for growth showed very large deviations from the model prediction. The best results were obtained with the assumption that a temperature shift (within the lag phase as well as within the exponential phase) results in an additional lag phase. This hypothesis was accepted statistically in 93% of the cases. The length of the additional lag phase is one-fourth of the lag time normally found at the temperature after the shift.     

Porcine coronary collateral formation in the absence of a pressure gradient remote of the ischemic border zone

In the current paradigm on coronary collateral development, it is assumed that these vessels develop consequentially from increased fluid shear stress (FSS) through preexisting collateral arteries. The increased FSS follows from an increase in pressure gradient between the region at risk and well-perfused surroundings. The objective of this study was to test the hypothesis that, in the heart, collateral connections can form in the absence of an increased FFS and consequentially at any depth and region within the ventricular wall. In Yorkshire pigs, gradual left circumflex coronary artery occlusion was obtained over 6 wk by an ameroid constrictor, whereas the control group underwent a sham operation. Hearts were harvested and subsequently processed in an imaging cryomicrotome, resulting in 40-μm voxel resolution three-dimensional reconstructions of the intramural vascular vessels. Dedicated software segmented the intramural vessels and all continuous vascular pathways containing a collateral connection. In the ameroid group, 192 collaterals, 22-1,049 μm in diameter, were detected with 62% within the subendocardium. Sixty percent of collaterals bridged from the left anterior descending artery to left circumflex coronary artery. A novel result is that 25% (n = 48) of smaller-radius collaterals (P = 0.047) connected with both origin and terminus in the nontarget area where perfusion was assumed uncompromised. In the porcine heart, collateral vessels develop not only in ischemic border zones with increased FSS but also away from such border zones where increased FSS is unlikely. The majority of collaterals were located at the subendocardium, corresponding to the region with highest prevalence for ischemia.     

A kinetic theory of enzymatic oxidation-reduction reactions based on a postulate of electron conduction in a macromolecular enzyme with an application to active transport of small ions across biological membranes

Experimental evidence of electron conduction within a protein has recently been given by Rosenberg. This paper gives a quantitative kinetic treatment of a hypothetical enzyme reaction that is rate-limited by electron conduction within the enzyme molecule. In particular, a kinetic theory of enzymatic oxidation-reduction has been built considering the enzyme to consist of a large protein molecule catalyzing oxidation-reduction of two different substrates at two different enzymatic sites on the same macromolecule. The electrons on each substrate are assumed in free and rapid equilibrium with the substrate's enzymatic site on the protein molecule. The rate-limiting process is assumed to be electron conduction in the protein molecule between the two sites. The resulting substrate concentrationvs. time curves appear to be zero order in some cases, and appear first order in other cases within narrow substrate concentration limits. Quantitative criteria are given for testing whether experimental data fit this type of kinetics. Oxidation-reduction reactions by this mechanism seem likely to be coupled to countercurrents of small charged ions in the surrounding solution, which suggests that a similar process could produce active transport of small ions across biological membranes. Opinions and conclusions contained in this report are those of the author. They are not to be construed as necessarily reflecting the views or the endorsement of the Navy Department.     

Xylem occlusions in the stems of common lilac during postharvest life

Flowering stems of lilac wilt within a few days of cutting and placing in water, probably as a consequence of xylem blockage. The aim of this study was to identify the types of occlusions blocking xylem vessels during the postharvest life of common lilac stems cut between March and May, and the possible associations of these occlusions with the holding solution used. Scanning electron microscope observations of the basal parts of cut lilac stems (1–5 cm) revealed that the blockage of xylem vessels was caused primarily by tyloses and less so by microorganisms. The number of tyloses depended on the holding solution used during the postharvest life. The biggest number of tyloses was observed in stems kept in water in all harvesting periods. In this solution, in ca 40% of observed vessels, tyloses were visible. The highest number of tyloses according to harvesting period was observed in May.     

Controlled freezing of nonideal solutions with application to cryosurgical processes.

Success of a cryosurgical procedure, i.e., maximal cell destruction, requires that the cooling rate be controlled during the freezing process. Standard cryosurgical devices are not usually designed to perform the required controlled process. In this study, a new cryosurgical device was developed which facilitates the achievement of a specified cooling rate during freezing by accurately controlling the probe temperature variation with time. The new device has been experimentally tested by applying it to an aqueous solution of mashed potatoes. The temperature field in the freezing medium, whose thermal properties are similar to those of biological tissue, was measured. The cryoprobe temperature was controlled according to a desired time varying profile which was assumed to maximize necrosis. The tracking accuracy and the stability of the closed loop control system were investigated. It was found that for most of the time the tracking accuracy was excellent and the error between the measured probe temperature and the desired set point is within +/- 0.4 degrees C. However, noticeable deviations from the set point occurred due to the supercooling phenomenon or due to the instability of the liquid nitrogen boiling regime in the cryoprobe. The experimental results were compared to those obtained by a finite elements program and very good agreement was obtained. The deviation between the two data sets seems to be mainly due to errors in positioning of the thermocouple junctions in the medium.     

On the generalization of the Weinbaum-Jiji bioheat equation to microvessels of unequal size; the relation between the near field and local average tissue temperatures

The extensive series of experiments reported in Lemons et al. [1] show that measureable local tissue temperature fluctuations are observed primarily in the vicinity of the 100-500 micron countercurrent vessels of the microcirculation and thus strongly support the basic hypothesis in the new bioheat equation of Weinbaum and Jiji [2] that these countercurrent microvessels are the principal determinants of local blood-tissue heat transfer. However, the detailed temperature profiles in the vicinity of these vessels indicate that large asymmetries in the local temperature field can result from the significant differences in size between the countercurrent artery and vein. Using the superposition techniques of Baish et al. [9], the paper first presents a solution to the classic problem of an unequal countercurrent heat exchanger with heat loss to the far field. This solution is then used to generalize the Weinbaum-Jiji bioheat equation and the conductivity tensor that appears in this equation to vessels of unequal size. An asymptotic analysis has also been developed to elucidate the relationship between the near field temperature of the artery-vein pair and the local average tissue temperature. This analysis is used to rigorously prove the closure approximation relating the local arterial-venous temperature difference and the mean tissue temperature gradient which had been derived in [2] using a more heuristic approach.     

Finite volume analysis of temperature effects induced by active MRI implants: 2. Defects on active MRI implants causing hot spots

Background

Active magnetic resonance imaging implants, for example stents, stent grafts or vena cava filters, are constructed as wireless inductively coupled transmit and receive coils. They are built as a resonator tuned to the Larmor frequency of a magnetic resonance system. The resonator can be added to or incorporated within the implant. This technology can counteract the shielding caused by eddy currents inside the metallic implant structure. This may allow getting diagnostic information of the implant lumen (in stent stenosis or thrombosis for example). The electro magnetic rf-pulses during magnetic resonance imaging induce a current in the circuit path of the resonator. A by material fatigue provoked partial rupture of the circuit path or a broken wire with touching surfaces can set up a relatively high resistance on a very short distance, which may behave as a point-like power source, a hot spot, inside the body part the resonator is implanted to. This local power loss inside a small volume can reach ¼ of the total power loss of the intact resonating circuit, which itself is proportional to the product of the resonator volume and the quality factor and depends as well from the orientation of the resonator with respect to the main magnetic field and the imaging sequence the resonator is exposed to.

Methods

First an analytical solution of a hot spot for thermal equilibrium is described. This analytical solution with a definite hot spot power loss represents the worst case scenario for thermal equilibrium inside a homogeneous medium without cooling effects. Starting with this worst case assumptions additional conditions are considered in a numerical simulation, which are more realistic and may make the results less critical. The analytical solution as well as the numerical simulations use the experimental experience of the maximum hot spot power loss of implanted resonators with a definite volume during magnetic resonance imaging investigations. The finite volume analysis calculates the time developing temperature maps for the model of a broken linear metallic wire embedded in tissue. Half of the total hot spot power loss is assumed to diffuse into both wire parts at the location of a defect. The energy is distributed from there by heat conduction. Additionally the effect of blood perfusion and blood flow is respected in some simulations because the simultaneous appearance of all worst case conditions, especially the absence of blood perfusion and blood flow near the hot spot, is very unlikely for vessel implants.

Results

The analytical solution as worst case scenario as well as the finite volume analysis for near worst case situations show not negligible volumes with critical temperature increases for part of the modeled hot spot situations. MR investigations with a high rf-pulse density lasting below a minute can establish volumes of several cubic millimeters with temperature increases high enough to start cell destruction. Longer exposure times can involve volumes larger than 100 mm³. Even temperature increases in the range of thermal ablation are reached for substantial volumes. MR sequence exposure time and hot spot power loss are the primary factors influencing the volume with critical temperature increases. Wire radius, wire material as well as the physiological parameters blood perfusion and blood flow inside larger vessels reduce the volume with critical temperature increases, but do not exclude a volume with critical tissue heating for resonators with a large product of resonator volume and quality factor.

Conclusion

The worst case scenario assumes thermal equilibrium for a hot spot embedded in homogeneous tissue without any cooling due to blood perfusion or flow. The finite volume analysis can calculate the results for near and not close to worst case conditions. For both cases a substantial volume can reach a critical temperature increase in a short time. The analytical solution, as absolute worst case, points out that resonators with a small product of inductance volume and quality factor (Q V_ind < 2 cm³) are definitely save. Stents for coronary vessels or resonators used as tracking devices for interventional procedures therefore have no risk of high temperature increases. The finite volume analysis shows for sure that also conditions not close to the worst case reach physiologically critical temperature increases for implants with a large product of inductance volume and quality factor (Q V_ind > 10 cm³). Such resonators exclude patients from exactly the MRI investigation these devices are made for.     

Refilling of a hydraulically isolated embolized xylem vessel: model calculations

When they are hydraulically isolated, embolized xylem vessels can be refilled, while adjacent vessels remain under tension. This implies that the pressure of water in the refilling vessel must be equal to the bubble gas pressure, which sets physical constraints for recovery. A model of water exudation into the cylindrical vessel and of bubble dissolution based on the assumption of hydraulic isolation is developed. Refilling is made possible by the turgor of the living cells adjacent to the refilling vessel, and by a reflection coefficient below 1 for the exchange of solutes across the interface between the vessel and the adjacent cells. No active transport of solutes is assumed. Living cells are also capable of importing water from the water-conducting vessels. The most limiting factors were found to be the osmotic potential of living cells and the ratio of the volume of the adjacent living cells to that of the embolized vessel. With values for these of 1.5 MPa and 1, respectively, refilling times were in the order of hours for a broad range of possible values of water conductivity coefficients and effective diffusion distances for dissolved air, when the xylem water tension was below 0.6 MPa and constant. Inclusion of the daily pattern for xylem tension improved the simulations. The simulated gas pressure within the refilling vessel was in accordance with recent experimental results. The study shows that the refilling process is physically possible under hydraulic isolation, while water in surrounding vessels is under negative pressure. However, the osmotic potentials in the refilling vessel tend to be large (in the order of 1 MPa). Only if the xylem water tension is, at most, twice atmospheric pressure, the reflection coefficient remains close to 1 (0.95) and the ratio of the volume of the adjacent living cells to that of the embolized vessel is about 2, does the osmotic potential stay below 0.4 MPa.     

Reason for externalization of the testis of mammals

Testes externalized in a scrotum are found only in those mammals whose present lifestyle (or that of their ancestors) involves jumping, leaping or galloping, thereby creating concussive hydrostatic rises in peritoneal pressure. This would be expected to expel the contents of the reproductive tract since it does not possess a sphincter. The lower temperature of the externalized testes is then seen as a secondary adjuvant adaptation to a cooler location than within the body cavity. The theory also explains the close phylogenetic relationship between the Proboscidea, Hyracoidea, and Sirenia, if it is assumed that their common ancestor was not endowed with the genes necessary for externalization.