The effect of a cylindrical baffle on heat transfer to an immersed heat exchanger is investigated in initially thermally stratified tanks. The heat exchanger is located in the annular region created by the baffle and the tank wall. Three different cases of initial thermal stratification are explored, and in each case experiments are conducted with and without the baffle in the stratified tank and in a comparable isothermal tank with the same initial energy, enabling exploration of the role of the baffle in a stratified tank and the role of stratification in tanks with or without the baffle. The baffle maintains the high initial temperature of the upper zone of the stratified tank for 10–16 minutes, as cool plumes that form on the heat exchanger are confined to the annular baffle region until they exit at the bottom of the tank. Regardless of stratification, the baffle always improves heat transfer to the immersed heat exchanger. In the isothermal tanks, the baffle increases total energy extracted in the first 30 minutes of discharge by over 20%. In stratified tanks, the baffle increases total energy extracted in 30 minutes of discharge by 9% to 16%. Initially, the improvement in heat transfer is due to the higher driving temperature differences around the heat exchanger. After all the water from the hot zone has entered and flowed through the baffle, the tank is basically isothermal, and velocity increases as the fluid temperature drops, maintaining rates of heat transfer higher than that in the tank without the baffle. Stratification improves heat transfer in tanks without a baffle because, by design, the driving temperature difference between the heat exchanger wall and the surrounding fluid is considerably higher. However, in tanks with the baffle, stratification has only a modest effect on heat transfer to the immersed heat exchanger.

The efficacy of convection-enhanced delivery as a technique to treat disorders of the central nervous system is limited by backflow, in which the infused fluid flows backward along surface of the catheter rather than toward the targeted area. In order to improve treatment protocols, finite element models of backflow have been developed to understand the underlying physics. García et al. (2013, "Description and Validation of a Finite Element Model of Backflow During Infusion Into a Brain Tissue Phantom," ASME J. Comput. Nonlinear Dyn., 8(1), p. 011017) presented a finite element model that accounted for the flow in the annular gap that develops between the tissue and the outer surface of the catheter by using a layer of biphasic elements with a formula for the axial hydraulic conductivity to represent annular Poiseuille flow. In this study, we present a generalization of that model using fluid-FSI and biphasic-FSI elements that are recently available in febio. We demonstrate that our model of a 0.98 mm radius catheter is able to reproduce experimental backflow lengths and maximum fluid pressures for infusions into a brain tissue surrogate and that it agrees well with the previous model by García et al. (2013, "Description and Validation of a Finite Element Model of Backflow During Infusion Into a Brain Tissue Phantom," ASME J. Comput. Nonlinear Dyn., 8(1), p. 011017). The model predicts that the backflow length and the total amount of flow into the hemispherical region forward of the catheter tip is comparable for two different catheter sizes, albeit at a higher fluid pressure for the smaller catheter. This biphasic-FSI model has the potential to be extended to a stepped catheter geometry, which has been shown in experiments to be successful in controlling backflow.

The effect of the pitch of a copper coil heat exchanger immersed in a hot water storage tank on heat transfer from the storage tank to the heat exchanger working fluid is investigated. The storage tank is initially quiescent and full of hot water. The heat exchanger located at the top of the tank has a coil diameter just under the tank diameter and has a pitch of 2, 3, 4, 6, or 12 times the heat exchanger diameter, D. The effect of the pitch is explored both with and without a cylindrical baffle, which creates an annular region with the tank wall that has a width of 1.5D and within which the heat exchanger is located. In experiments without the baffle, increasing the heat exchanger pitch improves the rate of heat transfer to the working fluid. The improved heat transfer is attributed to the increased thermal stratification generated by the larger pitches. In experiments with the baffle, the results for experiments with pitches of 2D, 3D, 4D, and 6D are all very similar, with 3D slightly outperforming the others. Heat transfer to the heat exchanger with a 12D pitch was significantly lower than the others. In experiments both with and without the baffle, the larger pitches resulted in more variation in experimental results, despite strict standards for initial and operating conditions. As in the prior work, the presence of the baffle resulted in significantly higher heat transfer rates compared to respective experiments without the baffle.

Convection-enhanced delivery is a technique to bypass the blood–brain barrier and deliver therapeutic drugs into the brain tissue. However, animal investigations and preliminary clinical trials have reported reduced efficacy to transport the infused drug in specific zones, attributed mainly to backflow, in which an annular gap is formed outside the catheter and the fluid preferentially flows toward the surface of the brain rather than through the tissue in front of the cannula tip. In this study, a three-dimensional human brain finite element model of backflow was developed to study the influence of anatomical structures during flow-controlled infusions. Predictions of backflow length were compared under the influence of ventricular pressure and the distance between the cannula and the ventricles. Simulations with zero relative ventricle pressure displayed similar backflow length predictions for larger cannula-ventricle distances. In addition, infusions near the ventricles revealed smaller backflow length and the liquid was observed to escape to the longitudinal fissure and ventricular cavities. Simulations with larger cannula-ventricle distances and nonzero relative ventricular pressure showed an increase of fluid flow through the tissue and away from the ventricles. These results reveal the importance of considering both the subject-specific anatomical details and the nonlinear effects in models focused on analyzing current and potential treatment options associated with convection-enhanced delivery optimization for future clinical trials.

Heat exchangers immersed in solar thermal storage tanks to charge and/or discharge energy from the tank provide several benefits over conventional systems that rely on pressurized tanks or pumps. The present study builds on a recent experimental study of heat transfer to an immersed heat exchanger with different baffle and shroud geometries (Nicodemus et al., Solar Energy, 157:911-919, 2017). A simple straight geometry was found to provide more benefit than a more complex geometry, in which the baffle underneath the heat exchanger narrows relative to the shroud around the heat exchanger. In this study, we propose an axi-symmetric model of a two-loop heat exchanger in order to investigate the mechanisms by which the straight baffle-shroud improves the heat transfer relative to the complex baffle-shroud. Further, we compare results of the two-loop model to a one-loop representation of the heat exchanger in order to determine whether or not a model with more fidelity to realistic storage systems better predicts experimental performance. Both the two-loop and one-loop models yield higher heat transfer with the straight baffle-shroud and confirm that the improved heat transfer in the straight baffle-shroud geometries is due to higher velocities around the heat exchanger relative to those in the complex baffle-shroud geometries, consistent with the experiments. However, the one-loop model significantly underestimates the differences between the baffle-shrouds relative to the experimental results. Since the two-loop model more accurately captures the fluid dynamics in the tank and better predicts the heat transfer and rate of energy discharge, it is an appropriate tool for future studies of immersed heat exchanger performance.

In this work, we investigate the effects of the width of an annular baffle region on natural convection heat transfer to an immersed, coiled heat exchanger in an otherwise quiescent sensible hot water storage tank. In the experiments, the coiled heat exchanger sits in an annular region created by the tank wall and a straight, cylindrical baffle. The width of this baffle region is 1.5, 2, 3, or 4 times the heat exchanger diameter. These experiments are compared to each other and to corresponding control experiments with no baffle. In general, all baffles create considerable benefits over their respective control experiments, consistent with past studies. The considered metrics of heat transfer rate, fraction of energy discharged from the tank, heat exchanger outlet temperature, and heat exchanger effectiveness show that heat transfer is improved slightly by narrowing the baffle region. For example, relative to their respective controls, the energy extracted from the tank after 30 min of discharge in the 1.5D, 2D, 3D, and 4D experiments is 23.3%, 20.8%, 18.1%, and 14.6% higher, respectively. This improvement in natural convection heat transfer as the baffle region narrows is attributed to the increasing thermal stratification observed with increasingly narrow baffle regions.

─ Convection-enhanced delivery as a means to deliver therapeutic drugs directly to the brain has shown limited clinical efficacy, primarily attributed to the phenomena of backflow, in which the infused fluid flows preferentially along the shaft catheter rather than forward into the tissue. We have previously developed a finite element model of backflow that includes both material and geometric nonlinearities and the free boundary conditions associated with the displacement of the tissue away from the external surface of the catheter. However, that study was limited to predictions of the tissue deformation and resulting convective fluid velocity in the interstitial space. In this study, we use results from that model to solve for the distribution of the infused therapeutic agent. We demonstrate that a significant percentage of the infused drug is not transported into the region of tissue located forward from the catheter tip, but instead is transported into the region along the lateral sides of the catheter. For lower flow rates, this study suggests that the use of a catheter with a larger radius may be preferable since it will provide the higher amount of drug to be transported to the tissue in front of the catheter. In contrast, for higher flow rates consistent with clinical infusions, the radius of the infusion catheter had minimal effect on the distribution of the infused drug, with most being transported into the tissue around the shaft of the catheter. Resumen ─ Convection-enhanced delivery es una tecnica que permite transportar drogas directamente en el cerebro para el tratamiento de enfermedades del sistema nervioso central. Este metodo ha mostrado una eficacia limitada debido principalmente al fenomeno de reflujo (backflow), segun el cual, el fluido inyectado fluye preferiblemente a lo largo del cateter y no hacia el tejido delante de la punta. Previamente desarrollamos un modelo de elementos finitos para representar el reflujo, el cual incluye las no linealidades geometricas y del material y las condiciones de borde libre asociadas con el desplazamiento del tejido en la superficie externa del cateter. Sin embargo, ese modelo solo predice la deformacion del tejido y el campo de velocidades en el espacio intersticial. En este estudio, hemos utilizado los resultados provenientes del mencionado modelo bifasico para resolver la ecuacion de transporte de masa y predecir la distribucion de droga suministrada. Se pudo demostrar que un porcentaje significativo de droga no penetra en el tejido ubicado delante de la punta del cateter, sino que es transportado hacia el tejido ubicado alrededor del cateter. Para bajo caudales, este estudio sugiere que el uso de un cateter con un radio mayor permitiria transportar una mayor cantidad de droga hacia el tejido al frente de la punta. Por otro lado, para los mayores caudales usados en la practica clinica, el radio del cateter tiene un efecto marginal en la distribucion del farmaco, y la mayor cantidad de droga se transporta hacia el tejido ubicado alrededor del cateter

A previously proposed finite element model that considers geometric and material nonlinearities and the free boundary problems that occur at the catheter tip and in the annular zone around the lateral surface of the catheter was revised and was used to fit a power-law formula to predict backflow length during infusions into brain tissue. Compared to a closed-form solution based on linear elasticity, the power-law formula for compliant materials predicted a substantial lower influence of the shear modulus and catheter radius on the backflow length, whereas the corresponding influence for stiffer materials was more consistent with the closed-form solution. The finite element model predicted decreases of the backflow length for reduction of the shear modulus for highly compliant materials (shear modulus less than 500 Pa) due to the increased area of infusion and the high fluid fraction near the infusion cavity that greatly increased the surface area available for fluid transfer and reduced the hydraulic resistance toward the tissue. These results show the importance of taking into account the material and geometrical nonlinearities that arise near the infusion surface as well as the change of hydraulic conductivity with strain for a proper characterization of backflow length during flow-controlled infusions into the brain.

Cerebrospinal fluid (CSF) is produced at a constant rate in the choroid plexuses of the lateral and third ventricles, and it predominately drains through the Sylvius aqueduct to the fourth ventricle. If the Sylvius aqueduct becomes obstructed, such as caused by a growing tumor adjacent to it, CSF accumulates in the ventricles and the ventricles expand significantly, leading to a medical condition known as noncommunicating, hydrocephalus.

Convection enhanced delivery is a protocol to deliver large volumes of drugs over localized zones of the brain for the treatment of diseases and tumors. Brain infusion experiments at higher flow rates showed backflow, in which an annular zone is formed outside the catheter and the infused drug preferentially flows toward the surface of the brain rather than through the tissue in the direction of the area targeted for delivery. The foundational model of Morrison et al. [1] considered the deformation of the tissue around the external boundary of the catheter, the axial flow in the annular gap formed around the cannula, and the radial flow from this annular region into the porous tissue in the development of an exponential correlation for backflow length L: (1)L∝Q0.6R0.8rc0.8G-0.6μ-0.2, where Q is the infusion flow rate, R is a tissue hydraulic resistance, rc is the catheter radius, G is the tissue shear modulus, and μ is the fluid viscosity. However, this formula was derived under some limiting assumptions, such as considering the solid phase of the infused tissue as a linearly elastic material under infinitesimal deformations, whereas mechanical testing has shown large deformations under physiological loadings [2, 3].

The mechanical properties of human brain tissue are the subject of interest because of their use in understanding brain trauma and in developing therapeutic treatments and procedures. To represent the behavior of the tissue, we have developed hyperelastic mechanical models whose parameters are fitted in accordance with experimental test results. However, most studies available in the literature have fitted parameters with data of a single type of loading, such as tension, compression, or shear. Recently, Jin et al. (Journal of Biomechanics 46:2795-2801, 2013) reported data from ex vivo tests of human brain tissue under tension, compression, and shear loading using four strain rates and four different brain regions. However, they do not report parameters of energy functions that can be readily used in finite element simulations. To represent the tissue behavior for the quasi-static loading conditions, we aimed to determine the best fit of the hyperelastic parameters of the hyperfoam, Ogden, and polynomial strain energy functions available in ABAQUS for the low strain rate data, while simultaneously considering all three loading modes. We used an optimization process conducted in MATLAB, calling iteratively three finite element models developed in ABAQUS that represent the three loadings. Results showed a relatively good fit to experimental data in all loading modes using two terms in the energy functions. Values for the shear modulus obtained in this analysis (897-1653Pa) are in the range of those presented in other studies. These energy-function parameters can be used in brain tissue simulations using finite element models.

A biphasic model for noncommunicating hydrocephalus in patient-specific geometry is proposed. The model can take into account the nonlinear behavior of brain tissue under large deformation, the nonlinear variation of hydraulic conductivity with deformation, and contact with a rigid, impermeable skull using a recently developed algorithm. The model was capable of achieving over a 700 percent ventricular enlargement, which is much greater than in previous studies, primarily due to the use of an anatomically realistic skull recreated from magnetic resonance imaging rather than an artificial skull created by offsetting the outer surface of the cerebrum. The choice of softening or stiffening behavior of brain tissue, both having been demonstrated in previous experimental studies, was found to have a significant effect on the volume and shape of the deformed ventricle, and the consideration of the variation of the hydraulic conductivity with deformation had a modest effect on the deformed ventricle. The model predicts that noncommunicating hydrocephalus occurs for ventricular fluid pressure on the order of 1300 Pa.

Convection-enhanced delivery is a technique to infuse therapeutic agents into the brain under positive pressure for the treatment of disorders of the central nervous system. Recent clinical trials [1] have shown limited efficacy of this procedure, attributed to poor distribution of the infused agent that may be due to backflow, in which the infused fluid preferentially flows along the outside of the catheter toward the surface of the brain.

An axisymmetric biphasic finite element model is proposed to simulate the backflow that develops around the external boundary of the catheter during flow-controlled infusions. The model includes both material and geometric nonlinearities and special treatments for the nonlinear boundary conditions used to represent the forward flow from the catheter tip and the axial backflow that occurs in the annular gap that develops as the porous medium detaches from the catheter. Specifically, a layer of elements with high hydraulic conductivity and low Young’s modulus was used to represent the nonlinear boundary condition for the forward flow, and another layer of elements with axial hydraulic conductivity consistent with Poiseuille flow was used to represent the backflow. Validation of the model was performed by modifying the elastic properties of the latter layer to fit published experimental values for the backflow length and maximum fluid pressure obtained during infusions into agarose gels undertaken with a 0.98-mm-radius catheter. Next, the finite element model predictions showed good agreement with independent experimental data obtained for 0.5-mm-radius and 0.33-mm-radius catheters. Compared to analytical models developed by others, this finite element model predicts a smaller backflow length, a larger fluid pressure, and a substantially larger percentage of forward flow. This latter difference can be explained by the important axial flow in the tissue that is not considered in the analytical models. These results may provide valuable guidelines to optimize protocols during future clinical studies. The model can be extended to describe infusions in brain tissue and in patient-specific geometries.

Initial experimental characterization of brain tissue assumed it was a single-phase material and modeled the nonlinear mechanical behavior observed under finite deformation using the incompressible Ogden strain energy function. For the modeling of some diseases of the brain, it is necessary to represent brain tissue as a biphasic medium with solid and fluid phases. Two forms of a compressible Ogden-like strain energy functions are currently available in the popular finite element solvers FEBIO and ABAQUS. We assessed the ability of these functions to reproduce physically expected behavior under uniaxial, biaxial, and triaxial loading. For some nonlinear material parameter sets, the compressible Ogden-type strain energy function of ABAQUS yielded stiffening behavior in tension for uniaxial loading that became markedly softer for triaxial deformation. In contrast, the compressible Ogden-type strain energy function of FEBIO showed no such reversal of the trends. Considering that stress fields in brain tissue are rarely uniaxial, a complete evaluation of compressible strain energy functions under multiaxial loading is necessary for accurate modeling of biphasic brain tissue.

A nonlinear, coupled biphasic-mass transport model that includes transvascular fluid exchange is proposed for flow-controlled infusions in brain tissue. The model accounts for geometric and material nonlinearities, a hydraulic conductivity dependent on deformation, and transvascular fluid exchange according to Starling's law. The governing equations were implemented in a custom-written code assuming spherical symmetry and using an updated Lagrangian finite-element algorithm. Results of the model indicate that, using normal physiological values of vascular permeability, transvascular fluid exchange has negligible effects on tissue deformation, fluid pressure, and transport of the infused agent. As vascular permeability may be increased artificially through methods such as administering nitric oxide, a parametric study was conducted to determine how increased vascular permeability affects flow-controlled infusion. Increased vascular permeability reduced both tissue deformation and fluid pressure, possibly reducing damage to tissue adjacent to the infusion catheter. Furthermore, the loss of fluid to the vasculature resulted in a significantly increased interstitial fluid concentration but a modestly increased tissue concentration. From a clinical point of view, this increase in concentration could be beneficial if limited to levels below which toxicity would not occur. However, the modestly increased tissue concentration may make the increase in interstitial fluid concentration difficult to assess in vivo using co-infused radiolabeled agents.