Analysis of the Weinbaum-Jiji Model of Blood Flow in the Canine Kidney Cortex for Self-Heated Thermistors

1994 ◽  
Vol 116 (2) ◽  
pp. 201-207 ◽  
Author(s):  
Jonathan W. Valvano ◽  
Sungwoo Nho ◽  
Gary T. Anderson
Keyword(s):  
Heat Transfer ◽  
Blood Flow ◽  
Steady State ◽  
Dominant Role ◽  
Kidney Cortex ◽  
Transfer Model ◽  
Actual Length ◽  
Physical Measurements ◽  
Continuous Power ◽  
Canine Kidney

The Weinbaum-Jiji equation can be applied to situations where: 1) the vascular anatomy is known; 2) the blood velocities are known; 3) the effective modeling volume includes many vessels; and 4) the vessel equilibration length is small compared to the actual length of the vessel. These criteria are satisfied in the situation where steady-state heated thermistors are placed in the kidney cortex. In this paper, the Weinbaum-Jiji bioheat equation is used to analyze the steady state response of four different sized self-heated thermistors in the canine kidney. This heat transfer model is developed based on actual physical measurements of the vasculature of the canine kidney cortex. In this model, parallel-structured interlobular arterioles and venules with a 60 μm diameter play the dominant role in the heat transfer due to blood flow. Continuous power is applied to the thermistor, and the instrument measures the resulting steady state temperature rise. If an accurate thermal model is available, perfusion can be calculated from these steady-state measurements. The finite element simulations correlate well in shape and amplitude with experimental results in the canine kidney. In addition, this paper shows that the Weinbaum-Jiji equation can not be used to model the transient response of the thermistor because the modeling volume does not include enough vessels and the vessel equilibration length is not small compared to the actual length of the vessel.

scholarly journals A Small Artery Heat Transfer Model for Self-Heated Thermistor Measurements of Perfusion in the Kidney Cortex

1994 ◽  
Vol 116 (1) ◽  
pp. 71-78 ◽  
Author(s):  
G. T. Anderson ◽  
J. W. Valvano
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Blood Flow ◽  
Dominant Role ◽  
Kidney Cortex ◽  
Transfer Model ◽  
Small Artery ◽  
Tissue Conductivity ◽  
Arteries And Veins ◽  
Canine Kidney

A small artery model (SAM) for self-heated thermistor measurements of perfusion in the canine kidney is developed based on the anatomy of the cortex vasculature. In this model interlobular arteries and veins play a dominant role in the heat transfer due to blood flow. Effective thermal conductivity, kss, is calculated from steady state thermistor measurements of heat transfer in the kidney cortex. This small artery and vein model of perfusion correctly indicates the shape of the measured kss versus perfusion curve. It also correctly predicts that the sinusoidal response of the thermistor can be used to measure intrinsic tissue conductivity, km, in perfused tissue. Although this model is specific for the canine kidney cortex, the modeling approach is applicable for a wide variety of biologic tissues.

scholarly journals A Steady-State Mass Transfer Model of Removing CPAs From Cryopreserved Blood With Hollow Fiber Modules

2009 ◽  
Vol 132 (1) ◽  
Author(s):  
Weiping Ding ◽  
Xiaoming Zhou ◽  
Shelly Heimfeld ◽  
Jo-Anna Reems ◽  
Dayong Gao
Keyword(s):  
Blood Flow ◽  
Steady State ◽  
Hollow Fiber ◽  
State Model ◽  
Transfer Model ◽  
Unsteady State ◽  
Flow Rates ◽  
Dialysate Flow ◽  
Steady State Model ◽  
Mass Transfers

Hollow fiber modules are commonly used to conveniently and efficiently remove cryoprotective agents (CPAs) from cryopreserved cell suspensions. In this paper, a steady-state model coupling mass transfers across cell and hollow fiber membranes is theoretically developed to evaluate the removal of CPAs from cryopreserved blood using hollow fiber modules. This steady-state model complements the unsteady-state model, which was presented in our previous study. The steady-state model, unlike the unsteady-state model, can be used to evaluate the effect of ultrafiltration flow rates on the clearance of CPAs. The steady-state model is validated by experimental results, and then is compared with the unsteady-state model. Using the steady-state model, the effects of ultrafiltration flow rates, NaCl concentrations in dialysate, blood flow rates and dialysate flow rates on CPA concentration variation and cell volume response are investigated in detail. According to the simulative results, the osmotic damage of red blood cells can easily be reduced by increasing ultrafiltration flow rates, increasing NaCl concentrations in dialysate, increasing blood flow rates, or decreasing dialysate flow rates.

Analytical Prediction of the Heat Transfer From a Blood Vessel Near the Skin Surface Cooled by a Symmetrical Strip

1975 ◽  
Vol 97 (1) ◽  
pp. 61-65 ◽  
Author(s):  
J. C. Chato ◽  
A. Shitzer
Keyword(s):  
Heat Transfer ◽  
Blood Flow ◽  
Steady State ◽  
Carotid Artery ◽  
Blood Vessel ◽  
Analytical Method ◽  
Skin Surface ◽  
Analytical Prediction ◽  
Flow Through ◽  
Optimum Width

A steady-state analytical method has been developed to estimate the amount of heat extracted from a blood vessel running close to the skin surface which is cooled in a symmetrical fashion by a cooling strip. The results indicate that the optimum width of a cooling strip is approximately three times the depth to the centerline of the blood vessel. The heat extracted from a blood vessel similar to the carotid artery by such a strip is about 0.9 w/m-deg C, which is too small to affect significantly the temperature of the blood flow through a main blood vessel, such as the carotid artery.

scholarly journals Thermal Analysis of Heat Transfer from Catheters and Implantable Devices to the Blood Flow

Micromachines ◽  
2021 ◽  
Vol 12 (3) ◽  
pp. 230
Author(s):  
Hossein Zangooei ◽  
Seyed Ali Mirbozorgi ◽  
Seyedabdollah Mirbozorgi
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Blood Flow ◽  
Temperature Rise ◽  
Implantable Devices ◽  
The Body ◽  
Transfer Model ◽  
Governing Equations ◽  
Blood Flow Velocities ◽  
Flow Velocities

Implantable devices, ultrasound imaging catheters, and ablation catheters (such as renal denervation catheters) are biomedical instruments that generate heat in the body. The generated heat can be harmful if the body temperature exceeds the limit of almost 315 K. This paper presents a heat-transfer model and analysis, to evaluate the temperature rise in human blood due to the power loss of medical catheters and implantable devices. The dynamic of the heat transfer is modeled for the blood vessel, at different blood flow velocities. The physics and governing equations of the heat transfer from the implanted energy source to the blood and temperature rise are expressed by developing a Non-Newtonian Carreau–Yasuda fluid model. We used a Finite Element method to solve the governing equations of the established model, considering the boundary conditions and average blood flow velocities of 0–1.4 m/s for the flow of the blood passing over the implanted power source. The results revealed a maximum allowable heat flux of 7500 and 15,000 W/m2 for the blood flow velocities of 0 and 1.4 m/s, respectively. The rise of temperature around the implant or tip of the catheter is slower and disappeared gradually with the blood flow, which allows a higher level of heat flux to be generated. The results of this analysis are concluded in the equation/correlation T=310+H3000(1+e−7V), to estimate and predict the temperature changes as a function of heat flux, H, and the blood flow velocity, V, at the implant/catheter location.

Numerical Model Study of the Field of View and Temporal Response of the Infrared Sense Organ in Crotaline Pit Vipers

2001 ◽  
Author(s):  
John A. Pearce ◽  
Anke Schmitz
Keyword(s):  
Heat Transfer ◽  
Blood Flow ◽  
Steady State ◽  
Temperature Rise ◽  
Sense Organ ◽  
Field Of View ◽  
Infrared Source ◽  
Steady State Condition ◽  
Pit Organ ◽  
Thermal Steady State

Abstract The IR sensitive membrane of the Crotaline pit organ was modeled numerically to help interpret electrophysiologic measurements of the pit organ response to a calibrated infrared source simulating a biological target. The model results are compared to electrophysiologic measurements for an on-axis exposure (target normal to the pit organ axis, oriented for maximum response). Additional model studies were conducted to: 1) estimate the field of view of the pit organ and 2) estimate the expected temperature rise in the membrane from the target at varying distances. The pit organ model was based on detailed measurements of its geometry. The membrane illumination irradiance difference from background thermal radiation (in W/mm2) was calculated from a quasi-analytical solution for the radiation coupling factor, Fjj. The illumination function was used to estimate temperature rise neglecting infrared heat transfer between the membrane and surrounding pit organ tissues. That is, the membrane was assumed in thermal steady state with the snake body and the environment outside of the target. The mammalian target is thus assumed to represent a small perturbation to the thermal steady state condition. This matches the electrophysiologic data, and is reasonable since the snake is cold blooded and snake body temperature is very close to its surroundings. The membrane includes blood flow effects, but it turns out that the membrane blood flow is strictly capillary in nature and changes the effective lateral thermal conductivity rather than providing significant heat transfer. The membrane is “optically thin”, being only about 5 wavelengths in thickness, and the specific optical properties of the interior layers were estimated from relative water content.

Boundary Design of Reflection Properties of a Steady-State Complex Heat Transfer Model

2016 ◽  
Vol 685 ◽  
pp. 90-93
Author(s):  
Alexander Yu. Chebotarev ◽  
Andrey E. Kovtanyuk
Keyword(s):  
Heat Transfer ◽  
Steady State ◽  
Control Problem ◽  
Radiation Effects ◽  
Heat Transfer Model ◽  
Heat Radiation ◽  
Transfer Model ◽  
Multiplicative Control ◽  
Steady State Heat ◽  
Steady State Heat Transfer

A boundary multiplicative control problem for a nonlinear steady-state heat transfer model accounting for heat radiation effects is considered. The aim of control consists in obtaining a prescribed temperature or radiative intensity distributions in a part of the model domain by controlling the boundary reflectivity. The solvability of this control problem is proved, and optimality conditions are derived.

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