Lumped parameter thermal model for the study of vascular reactivity in the fingertip

Vascular reactivity (VR) denotes changes in volumetric blood flow in response to arterial occlusion. Current techniques to study VR rely on monitoring blood flow parameters and serve to predict the risk of future cardiovascular complications. Because tissue temperature is directly impacted by blood flow, a simplified thermal model was developed to study the alterations in fingertip temperature during arterial occlusion and subsequent reperfusion (hyperemia). This work shows that fingertip temperature variation during VR test can be used as a cost-effective alternative to blood perfusion monitoring. The model developed introduces a function to approximate the temporal alterations in blood volume during VR tests. Parametric studies are performed to analyze the effects of blood perfusion alterations, as well as any environmental contribution to fingertip temperature. Experiments were performed on eight healthy volunteers to study the thermal effect of 3 min of arterial occlusion and subsequent reperfusion (hyperemia). Fingertip temperature and heat flux were measured at the occluded and control fingers, and the finger blood perfusion was determined using venous occlusion plethysmography (VOP). The model was able to phenomenologically reproduce the experimental measurements. Significant variability was observed in the starting fingertip temperature and heat flux measurements among subjects. Difficulty in achieving thermal equilibration was observed, which indicates the important effect of initial temperature and thermal trend (i.e., vasoconstriction, vasodilatation, and oscillations).     

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.     

Inducing occlusion effect in Y-shaped vessels using high-intensity focused ultrasound: finite element analysis and phantom validation

High-intensity focused ultrasound (HIFU) surgery offers a truly non-invasive treatment method with no skin incision, but precise targeting of tumour tissues for thermotherapy. Clinical experience reveals that the efficacy of tumour destruction not only involves in coagulating necrosis, but also involves in damaging the tumour vessels, which play an important role in tumour progression. These vessels take the elevated temperature away by perfusion, resulting in uncertainty of the occlusion effect during HIFU treatment. In this study, a Y-shaped vessel model comprising common and tumour vessels and an indirect fabrication method are proposed. The physical properties of the fabricated vessel phantom are measured and compared with human tissue. Simulation is performed using finite element modelling according to the tissue parameter, perfusion rate of the tumour vessel and treatment parameters including power intensity and exposure duration. The phantom experiments are carried out with perfusion of egg white to validate the threshold time prediction obtained from the simulation results. Our findings reveal that the threshold time obtained from experiments is consistent with the simulated one.     

Anisotropic adaptive finite element method for modelling blood flow

In this study, we present an adaptive anisotropic finite element method (FEM) and demonstrate how computational efficiency can be increased when applying the method to the simulation of blood flow in the cardiovascular system. We use the SUPG formulation for the transient 3D incompressible Navier-Stokes equations which are discretised by linear finite elements for both the pressure and the velocity field. Given the pulsatile nature of the flow in blood vessels we have pursued adaptivity based on the average flow over a cardiac cycle. Error indicators are derived to define an anisotropic mesh metric field. Mesh modification algorithms are used to anisotropically adapt the mesh according to the desired size field. We demonstrate the efficiency of the method by first applying it to pulsatile flow in a straight cylindrical vessel and then to a porcine aorta with a stenosis bypassed by a graft. We demonstrate that the use of an anisotropic adaptive FEM can result in an order of magnitude reduction in computing time with no loss of accuracy compared to analyses obtained with uniform meshes.     

Anisotropic adaptive finite element method for modelling blood flow

In this study, we present an adaptive anisotropic finite element method (FEM) and demonstrate how computational efficiency can be increased when applying the method to the simulation of blood flow in the cardiovascular system. We use the SUPG formulation for the transient 3D incompressible Navier–Stokes equations which are discretised by linear finite elements for both the pressure and the velocity field.

Given the pulsatile nature of the flow in blood vessels we have pursued adaptivity based on the average flow over a cardiac cycle. Error indicators are derived to define an anisotropic mesh metric field. Mesh modification algorithms are used to anisotropically adapt the mesh according to the desired size field. We demonstrate the efficiency of the method by first applying it to pulsatile flow in a straight cylindrical vessel and then to a porcine aorta with a stenosis bypassed by a graft. We demonstrate that the use of an anisotropic adaptive FEM can result in an order of magnitude reduction in computing time with no loss of accuracy compared to analyses obtained with uniform meshes.     

Frequency response characteristics of cerebral blood flow autoregulation in rats

Transfer function analysis of blood pressure and cerebral blood flow in humans demonstrated that cerebrovascular autoregulation operates most effectively for slow fluctuations in perfusion pressure, not exceeding a frequency of approximately 0.15 Hz. No information on the dynamic properties of cerebrovascular autoregulation is available in rats. Therefore, we tested the hypothesis that cerebrovascular autoregulation in rats is also most effective for slow fluctuations in perfusion pressure below 0.15 Hz. Normotensive Wistar-Kyoto rats (n = 10) were instrumented with catheters in the left common carotid artery and jugular vein and flow probes around the right internal carotid artery. During isoflurane anesthesia, fluctuations in cerebral perfusion pressure were elicited by periodically occluding the abdominal aorta at eight frequencies ranging from 0.008 Hz to 0.5 Hz. The protocol was repeated during inhibition of myogenic vascular function (nifedipine, 0.25 mg/kg body wt iv). Increases in cerebral perfusion pressure elicited initial increases in cerebrovascular conductance and decreases in resistance. At low occlusion frequencies (<0.1 Hz), these initial responses were followed by decreases in conductance and increases in resistance that were abolished by nifedipine. At occlusion frequencies of 0.1 Hz and above, the gains of the transfer functions between pressure and blood flow and between pressure and resistance were equally high in the control and nifedipine trial. At occlusion frequencies below 0.1 Hz, the gains of the transfer functions decreased twice as much under control conditions than during nifedipine application. We conclude that dynamic autoregulation of cerebral blood flow is restricted to very low frequencies (<0.1 Hz) in rats.     

Investigation of the influence of blood flow rate on large vessel cooling in hepatic radiofrequency ablation.

Radiofrequency (RF) ablation using high-frequency current has become an important treatment method for patients with non-resectable liver tumors. Tumor recurrence is associated with tissue cooling in the proximity of large blood vessels. This study investigated the influence of blood flow rate on tissue temperature and lesion size during monopolar RF ablation at a distance of 10 mm from single 4- and 6-mm vessels using two different approaches: 1) an ex vivo blood perfusion circuit including an artificial vessel inserted into porcine liver tissue was developed; and 2) a finite element method (FEM) model was created using a novel simplified modeling technique for large blood vessels. Blood temperatures at the inflow/outflow of the vessel and tissue temperatures at 10 and 20 mm from the electrode tip were measured in the ex vivo set-up. Tissue temperature, blood temperature and lesion size were analyzed under physiological, increased and reduced blood-flow conditions. The results show that changes in blood flow rate in large vessels do not significantly affect tissue temperature and lesion size far away from the vessel. Monopolar ablation could not produce lesions surrounding the vessel due to the strong heat-sink effect. Simulated tissue temperatures correlated well with ex vivo measurements, supporting the FEM model.     

The effect of perfusion on soft tissue mechanical properties: a computational model

Some simple finite element models were constructed to investigate the magnitude and character of changes in mechanical properties of very soft tissues due to the loss of perfusion. Changes in the apparent stress-strain curve were used to characterise the effect of simulated blood perfusion pressure on the engineering stress-strain curve. The results indicated that the blood to tissue volume ratio and the perfusion pressure have the strongest effect on the effective stress-strain response of a representative tissue cell. Tissue viscoelasticity increased the sensitivity of the system to perfusion pressure changes.     

Galerkin's finite element-Laplace transform technique to transient heat migration in human skin and subcutaneous tissues

Galerkin's finite element-Laplace transform technique (GAFELTTE) has been used to study transient temperature distribution in human skin and subcutaneous tissues. This study incorporates heat conduction, heat carried by perfusion of blood in the capillary beds and metabolic heat generation in the tissues. Different values of various quantities have been considered in all three parts, namely epidermis, dermis and subcutaneous tissues, depending on physiological considerations. The GAFELTTE provides interface temperatures for a wide range of the values of skin surface temperatures. These values have been used to obtain temperature profiles in the region considered. Steady-state temperature distribution has been deduced from the solution obtained by GAFELTTE and has been compared with the results obtained by using different methods.     

Why is the subendocardium more vulnerable to ischemia? A new paradigm

Myocardial ischemia is transmurally heterogeneous where the subendocardium is at higher risk. Stenosis induces reduced perfusion pressure, blood flow redistribution away from the subendocardium, and consequent subendocardial vulnerability. We propose that the flow redistribution stems from the higher compliance of the subendocardial vasculature. This new paradigm was tested using network flow simulation based on measured coronary anatomy, vessel flow and mechanics, and myocardium-vessel interactions. Flow redistribution was quantified by the relative change in the subendocardial-to-subepicardial perfusion ratio under a 60-mmHg perfusion pressure reduction. Myocardial contraction was found to induce the following: 1) more compressive loading and subsequent lower transvascular pressure in deeper vessels, 2) consequent higher compliance of the subendocardial vasculature, and 3) substantial flow redistribution, i.e., a 20% drop in the subendocardial-to-subepicardial flow ratio under the prescribed reduction in perfusion pressure. This flow redistribution was found to occur primarily because the vessel compliance is nonlinear (pressure dependent). The observed thinner subendocardial vessel walls were predicted to induce a higher compliance of the subendocardial vasculature and greater flow redistribution. Subendocardial perfusion was predicted to improve with a reduction of either heart rate or left ventricular pressure under low perfusion pressure. In conclusion, subendocardial vulnerability to a acute reduction in perfusion pressure stems primarily from differences in vascular compliance induced by transmural differences in both extravascular loading and vessel wall thickness. Subendocardial ischemia can be improved by a reduction of heart rate and left ventricular pressure.     

Determination of the 3D temperature distribution during ferromagnetic hyperthermia under the influence of blood flow

A numerical simulation of tissue heating during thermo-seed ferromagnetic hyperthermia was performed to determine the temperature distribution of treated tumor tissues under the influence of three large blood vessels at different locations. The effects of the blood velocity waveform, blood vessel size, Curie point of the thermo-seeds and the thermo-seed number on temperature distributions were analyzed. The results indicate that the existence of a blood vessel inside the tumor has a significant cooling effect on the temperature distribution in a treated tumor tissue, which is enhanced with an increase in blood velocity. However, the pulsatile blood flow does not have apparently different effects on the outcomes of uniformly heating target tissues in comparison with the steady blood flow during the hyperthermia process. It is also concluded that a higher Curie point temperature and an increase in the number of thermo-seeds can result in profound increases in the temperature variations of the tumor tissue. In addition, tissue-equivalent phantom experiments were conducted to confirm the cooling effects of the blood vessels, and to validate the effectiveness and accuracy of the proposed heat transfer model for the ferromagnetic hyperthermia.     

Direct numerical simulation of a 2D-stented aortic heart valve at physiological flow rates

We study the nonlinear interaction of an aortic heart valve, composed of hyperelastic corrugated leaflets of finite density attached to a stented vessel under physiological flow conditions. In our numerical simulations, we use a 2D idealised representation of this arrangement. Blood flow is caused by a time-varying pressure gradient that mimics that of the aortic valve and corresponds to a peak Reynolds number equal to 4050. Here, we fully account for the shear-thinning behaviour of the blood and large deformations and contact between the leaflets by solving the momentum and mass balances for blood and leaflets. The mixed finite element/Galerkin method along with linear discontinuous Lagrange multipliers for coupling the fluid and elastic domains is adopted. Moreover, a series of challenging numerical issues such as the finite length of the computational domain and the conditions that should be imposed on its inflow/outflow boundaries, the accurate time integration of the parabolic and hyperbolic momentum equations, the contact between the leaflets and the non-conforming mesh refinement in part of the domain are successfully resolved. Calculations for the velocity and the shear stress fields of the blood reveal that boundary layers appear on both sides of a leaflet. The one along the ventricular side transfers blood with high momentum from the core region of the vessel to the annulus or the sinusoidal expansion, causing the continuous development of flow instabilities. At peak systole, vortices are convected in the flow direction along the annulus of the vessel, whereas during the closure stage of the valve, an extremely large vortex develops in each half of the flow domain.     

The Effect of Perfusion on Soft Tissue Mechanical Properties: A Computational Model

Some simple finite element models were constructed to investigate the magnitude and character of changes in mechanical properties of very soft tissues due to the loss of perfusion. Changes in the apparent stress-strain curve were used to characterise the effect of simulated blood perfusion pressure on the engineering stress-strain curve. The results indicated that the blood to tissue volume ratio and the perfusion pressure have the strongest effect on the effective stress-strain response of a representative tissue cell. Tissue viscoelasticity increased the sensitivity of the system to perfusion pressure changes.     

Two-photon imaging of cortical surface microvessels reveals a robust redistribution in blood flow after vascular occlusion

A highly interconnected network of arterioles overlies mammalian cortex to route blood to the cortical mantle. Here we test if this angioarchitecture can ensure that the supply of blood is redistributed after vascular occlusion. We use rodent parietal cortex as a model system and image the flow of red blood cells in individual microvessels. Changes in flow are quantified in response to photothrombotic occlusions to individual pial arterioles as well as to physical occlusions of the middle cerebral artery (MCA), the primary source of blood to this network. We observe that perfusion is rapidly reestablished at the first branch downstream from a photothrombotic occlusion through a reversal in flow in one vessel. More distal downstream arterioles also show reversals in flow. Further, occlusion of the MCA leads to reversals in flow through approximately half of the downstream but distant arterioles. Thus the cortical arteriolar network supports collateral flow that may mitigate the effects of vessel obstruction, as may occur secondary to neurovascular pathology.     

Procedure for Human Saphenous Veins Ex Vivo Perfusion and External Reinforcement

The mainstay of contemporary therapies for extensive occlusive arterial disease is venous bypass graft. However, its durability is threatened by intimal hyperplasia (IH) that eventually leads to vessel occlusion and graft failure. Mechanical forces, particularly low shear stress and high wall tension, are thought to initiate and to sustain these cellular and molecular changes, but their exact contribution remains to be unraveled. To selectively evaluate the role of pressure and shear stress on the biology of IH, an ex vivo perfusion system (EVPS) was created to perfuse segments of human saphenous veins under arterial regimen (high shear stress and high pressure). Further technical innovations allowed the simultaneous perfusion of two segments from the same vein, one reinforced with an external mesh. Veins were harvested using a no-touch technique and immediately transferred to the laboratory for assembly in the EVPS. One segment of the freshly isolated vein was not perfused (control, day 0). The two others segments were perfused for up to 7 days, one being completely sheltered with a 4 mm (diameter) external mesh. The pressure, flow velocity, and pulse rate were continuously monitored and adjusted to mimic the hemodynamic conditions prevailing in the femoral artery. Upon completion of the perfusion, veins were dismounted and used for histological and molecular analysis. Under ex vivo conditions, high pressure perfusion (arterial, mean = 100 mm Hg) is sufficient to generate IH and remodeling of human veins. These alterations are reduced in the presence of an external polyester mesh.     

A comparative study of thermal effects of 3 types of laser in eye: 3D simulation with bioheat equation

The application of laser in ophthalmology and eye surgery is so widespread that hardly can anyone deny its importance. On the other hand, since the human eye is an organ susceptible to external factors such as heat waves, laser radiation rapidly increases the temperature of the eye and therefore the study of temperature distribution inside the eye under laser irradiation is crucial; but the use of experimental and invasive methods for measuring the temperature inside the eye is typically high-risk and hazardous. In this paper, using the three-dimensional finite element method, the distribution of heat transfer inside the eye under transient condition was studied through three different lasers named Nd:Yag, Nd:Yap and ArF. Considering the metabolic heat and blood perfusion rate in various regions of the eye, numerical solution of space–time dependant Pennes bioheat transfer equation has been applied in this study. Lambert–Beer's law has been used to model the absorption of laser energy inside the eye tissues. It should also be mentioned that the effect of the ambient temperature, tear evaporation rate, laser power and the pupil diameter on the temperature distribution have been studied. Also, temperature distribution inside the eye after applying each laser and temperature variations of six optional regions as functions of time have been investigated. The results show that these radiations cause temperature rise in various regions, which will in turn causes serious damages to the eye tissues. Investigating the temperature distribution inside the eye under the laser irradiation can be a useful tool to study and predict the thermal effects of laser radiation on the human eye and evaluate the risk involved in performing laser surgery.     

Theoretical temperature distributions produced by an annular phased array-type system in CT-based patient models

Theoretical calculations for the specific absorption rate (SAR) and the resulting temperature distributions produced by an annular phased array (APA)-type system are made. The finite element numerical method is used in the formulation of both the electromagnetic (EM) and thermal boundary value problems. A number of detailed two-dimensional patient models based on CT-scan data from the pelvic, visceral, and thoracic regions are generated to simulate a variety of tumor locations and surrounding normal tissues. The SAR values from the EM solution are put into the bioheat transfer equation, and steady-state temperature distributions are calculated for a wide range of blood flow rates. Based on our theoretical modeling, the APA shows no preferential heating of superficial over deep-seated tumors. However, in most cases for all three regions of the human trunk only fair thermal profiles (therapeutic area near 60%) are obtained in tumors with little or no blood flow and poor temperature patterns (therapeutic area less than 50%) are found in tumors with moderate to high perfusion rates. These theoretical calculations should aid the clinician in the evaluation of the effectiveness of APA-type devices in heating tumors located in the trunk region.     

A 3D thermal model to analyze the temperature changes of digits during cold stress and predict the danger of frostbite in human fingers

The existing computational models of frostbite injury are limited to one and two dimensional schemes. In this study, a coupled thermo-fluid model is applied to simulate a finger exposed to cold weather. The spatial variability of finger-tip temperature is compared to experimental ones to validate the model. A semi-realistic 3D model for tissue and blood vessels is used to analyze the transient heat transfer through the finger. The effect of heat conduction, metabolic heat generation, heat transport by blood perfusion, heat exchange between tissues and large vessels are considered in energy balance equations. The current model was then tested in different temperatures and air speeds to predict the danger of frostbite in humans for different gloves. Two prevalent gloves which are commonly used in cold climate are considered for investigation. The endurance time and the fraction of necrotic tissues are two main factors suggested for obtaining the response of digit tissues to different environmental conditions.     

Differences in finger skin contact cooling response between an arterial occlusion and a vasodilated condition.

To assess the presence and magnitude of the effect of skin blood flow on finger skin cooling on contact with cold objects against the background of circulatory disorder risks in occupational exposures, this study investigates the effect of zero vs. close-to-maximal hand blood flow on short-term (< or =180 s) skin contact cooling response at a contact pressure that allows capillary perfusion of the distal pulp of the fingertip. Six male volunteers touched a block of aluminium with a finger contact force of 0.5 N at a temperature of -2 degrees C under a vasodilated and an occluded condition. Before both conditions, participants were required to exercise in a hot room for > or = 30 min for cutaneous vasodilation to occur (increase in rectal temperature of 1 degrees C). Under the vasodilated condition, forearm blood flow rate rose as high as 16.8 ml.100 ml(-1).min(-1). Under the occluded condition, the arm was exsanguinated, after which a blood pressure cuff was secured on the wrist inducing arterial occlusion. Contact temperature of the finger pad during the subsequent cold contact exposure was measured. No significant difference was found between the starting skin temperatures for the two blood flow conditions, but a distinct difference in shape of the contact cooling curve was apparent between the two blood flow conditions, with Newtonian cooling observed under the occluded condition, whereas a rewarming of the finger skin toward the end of the exposure occurred for the vasodilated condition. Blood flow was found to significantly increase contact temperature from 40 s onward (P < 0.01). It is concluded that, at a finger contact force compatible with capillary perfusion of the finger pad ( approximately 0.5 N), circulating blood provides a heat input source that significantly affects finger skin contact cooling during a vasodilated state.     

Use of a modified oxygen microelectrode and laser-Doppler flowmetry to monitor changes in oxygen tension and microcirculation in a flap

Flap failure is a clinical problem in free tissue transfer, and there is no reliable device for monitoring the tissue. Differentiating between an arterial occlusion and venous congestion is also a problem. A study was undertaken to monitor viability in a pedicled groin flap and to compare two different monitoring methods. The oxygen tension in the flap, measured with a modified Clark-type microelectrode (tip diameter = 3 to 8 microm; 90 percent response within 2.6 +/- 0.5 seconds), was compared with changes in blood flow in the flap, measured with a laser-Doppler probe. In 11 Sprague-Dawley rats, the changes in oxygen tension and blood flow in the pedicled groin flap were studied after clamping and subsequent reperfusion of the artery or vein. After occlusion of the artery to the flap, oxygen tension decreased to a stable value (i.e., the recording level remained unchanged for 30 seconds), from 19.7 +/- 1.8 to 0.3 +/- 0.1 mmHg, after 193 +/-25 seconds; blood flow decreased to a stable value, from 117 +/- 21 to 54 +/- 18 perfusion units, after 26 +/- 6 seconds. Clamping of the vein resulted in a decrease in oxygen tension, from 17.1 +/- 1.8 to 1.4 +/- 0.7 mmHg, after 416 +/- 67 seconds, and blood flow decreased to a stable value, from 90 +/- 14 to 35 +/- 6 perfusion units, after 107 +/- 27 seconds. The results of this study show that there is a difference in oxygen tension and blood flow responses between arterial and venous occlusion and that it may be possible with both methods to distinguish arterial from venous occlusion. However, although oxygen tension measurements are slightly slower in response than laser-Doppler measurements, the values are more reliable as a diagnostic tool for interpretation of a vessel occlusion.