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Computational Biofluid Dynamics Clinic

Michael Brattoli, Christopher Thomas, and Derek Yoder

Mechanical Engineering Rowan University

ABSTRACT

Computational fluid dynamics (CFD) involves the use of advanced computer software to study complex fluid flows using numerical methods. Computational biofluid dynamics (CBD) is an area of fluid mechanics that utilizes three CFD software packages (COMSOL Multiphysics, STAR-CCM+, and SolidWorks Flow Simulation) to assess biological fluid flows for biomedical applications. Two concurrent CBD studies explored cooling blood in the human heart following a heart attack and cooling blood in the brain to treat ischemic stroke. The goal behind the studies was to predict blood temperatures at various locations along the vasculatures of the heart and brain in order to determine the effectiveness of therapeutic hypothermia in the event of heart attacks and strokes. Current outcomes include proficiency in CFD modeling with various software packages, accurate CFD models of basic physiological structures, and two complex vasculature models of the human heart and canine brain.

INTRODUCTION

The primary objectives of this research included modeling flows for practical biomedical applications, and presenting the research at the ASME 2014 Summer Bioengineering Conference in Boston, Massachusetts. Each biomedical application, rapid cooling of the human heart following acute myocardial infarction and localized cooling of the canine brain to treat ischemic stroke, was studied using flow simulation applications. Cooling of the human heart was modeled and studied using SolidWorks. As one of the leading causes of death and disability in the United States, stroke accounts for 1 out of every 18 deaths according to the American Heart Association [1]. Stroke occurs when flow through an artery that supplies blood to the brain is interrupted. There are two types of stroke: hemorrhagic and ischemic. Ischemic stroke results from a blockage, either thrombotic or embolic, in an artery that supplies blood to the brain and accounts for 87% of strokes [1]. Studies show that tissue infarction from ischemic stroke can be reduced by rapidly inducing localized hypothermia in the affected area. Positive neurological effects, reduced reperfusion injury, and increased tissue recovery have been observed in studies with mild temperature reductions of 2-5ºC [2, 3]. The purpose of this research is to validate the thermal fluids finite element model of blood temperatures in the canine middle cerebral artery. The

results will be compared to previous in vivo canine studies and in vitro studies on the FocalCool CoolGuide Cooling System (CCS). Through the completion and validation of simulations that accurately model the canine vasculature with temperature dependent properties and pulsatile flow, the effectiveness of localized hypothermia during ischemic stroke treatment may be proven. Key deliverables for this project included the construction and validation of basic physiological structures that can be found in the human body, as well as two complex models of blood vessels, one in the human heart and one in canine brain. The deliverables are explained in more detail in the Computational Studies section of this report. In the Technological Impact Section, the societal, economic, and environmental effects of this work are further explained. The Conclusion section summarizes the modeling and research, as well as outlines the future work.

COMPUTATIONAL STUDIES

The Computational Studies are divided into two main sections: CFD Modeling and CBD Research. The CFD Modeling division discusses the initial models created to provide a better understanding of methods and best practices of CFD. These models range from simple tutorials to basic physiological models with isothermal and non-isothermal properties. In the CBD Research section, complex physiological models are evaluated and discussed.

CFD MODELING

Planar Backstep Diffuser

A COMSOL tutorial called “Backflow Tutorial” guides the user through defining the geometry, boundary conditions, physics, and mesh. It gives the opportunity for the user to conduct post processing to ensure that the model is validated. The backstep geometry used in this tutorial (Figure 1) is one of the most common geometries studied in the CFD field. The model is run with a fully developed flow profile and turbulent flow physics. The specific boundary conditions are listed in Table 1. The sharp corner at the backstep causes turbulence to occur. As the flow passes through the step, it suffers from flow separation and results in turbulent wake.

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Figure 1: The planar backstep diffuser geometry.

Table 1: COMSOL Backstep Input Parameters This phenomenon is known as a separation bubble (seen in blue in Figure 2). The length of this bubble, also known as a recirculation zone, is main point of comparison when validating a backstep geometry study. As Reynolds number increases, so does the recirculation length due to the flow becoming more turbulent at higher Re.

Figure 2: Fully developed flow profile flowing through backstep diffuser. The recirculation length measured in the COMSOL model is shown in Figure 3. It is a measure of not only the length, but also the point at which the velocity is equal to 0. In order to ensure that the model is valid, the model was run with the same conditions as a published paper written by Nadge and Govardhan.

Figure 3: The recirculation length of COMSOL model. According to Nadge and Govardhan 2014, the recirculation length (Xr/h) is an important characteristic to measure. Nadge and Govardhan have measured recirculation length at different Reynolds numbers with different expansion ratios (outlet diameter/inlet diameter). Reynold’s number is varied and ER fixed to compare with Nadge and Govarhan’s findings in Figure 4.

Figure 4: Nadge and Govarhan’s recirculation lengths at different expansion ratios [4]. Reynolds number was found using Equation (1):

(1) where is the Maximum Inlet Channel Velocity, is Hydraulic Diameter, is Destiny, and is Dynamic Viscosity. The Reynolds number used in this paper is based on the step height, which is a function of the expansion ratio. The velocity at the inlet is also known based on the original COMSOL tutorial and the density is constant throughout the geometry. The dynamic viscosity is altered in order to vary the Reynolds. The results comparing the recirculation length calculated in the tutorial model and the technical paper can be found in Table 2 and Figure 5.

Table 2: Model results versus Nadge and Govardhan.

Figure 5: Model results versus Nadge and Govardhan.

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The percent error is about 7 percent. This is because Nadge and Govarhan studied this geometry in a physical experiment. The COMSOL model is a theoretical calculation of that setup based on the conditions given.

Isothermal y-Bifurcation Model

A computational fluid dynamics (CFD) study of isothermal blood flow through a coronary model was conducted. Figure 6 displays a detailed diagram of the geometry. The geometry was a bifurcation that included a main trunk and a branch that split off at a 55 degree angle. The model boundary conditions shown in Table 3, assume fully developed flow at the inlet along with the no-slip condition for the walls and zero pressure at the outlets. In Table 4, the input parameters for each of the three flow rates analyzed can be found.

Figure 6: Geometry setup for the y-Bifurcation model.

Table 3: Boundary conditions for the y-Bifurcation model.

Table 4: Input parameters for the y-Bifurcation model. Results from each CFD software package were recorded and used to analyze the pressure drop through the main trunk of the model. A scalar plot was created to illustrate the pressure distribution follows the typical linear pattern of flow in a straight tube with the exception of a pressure spike at bifurcation branch. This can be visualized in Figure 7 and 8. In addition to the scalar plot, a normalized pressure plot was created to evaluate the behavior of the pressure for each of the three flow rates, shown in Figure 9. As the flow rate increased from 5 to 20 cm/s, the change in pressure became larger and the effects of the bifurcation split also became greater.

Figure 7: Pressure scalar plot with an inlet flow of 5 cm/s showing the linear behavior of the pressure distribution in STAR-CCM+.

Figure 8: Pressure scalar plot with an inlet flow of 5 cm/s showing how the pressure distribution loses its uniformity at the bifurcation split.

Figure 9: Normalized pressure plot verses axial location divided by diameter comparing all three flows. A dichrotic notch is observed at the bifurcation split and caused by flow disturbances. Flow separation at the split along with reversed flow and area expansion cause the spike in pressure. Validating the results was accomplished by comparing the simulation pressure drop through the first 3 cm of the

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main trunk, where the effects of the bifurcation have not yet integrated, with the theoretically calculated pressure drop from the Poiseuille Flow equation. This can be seen in Equation (2):

(2) where is the pressure drop, is the dynamic viscosity, is the pipe length, is the pipe diameter, and is the flow rate. This method of validation was carried out for each of the three flow rates. Tables 5, 6, and 7 display the break down of the validation for each CFD software package.

Table 5: Pressure drop validation for the first 3 cm of the main trunk with an 1100181-element mesh (STAR-CCM+).

Table 6: Pressure drop validation for the first 3 cm of the main trunk with a 2395887-element mesh (COMSOL).

Table 7: Pressure drop validation for the first 3 cm of the main trunk with a 36288-element mesh (SolidWorks). Each program produced percent error under 5.5%, an acceptable value, where the accuracy slightly decreases with increasing flow speed. Although each model was validated for pressure drop to an acceptable error, the inlet pressures varied based on the number of elements used in the meshing. The larger the mesh size, the more accurate the results obtained. Meshing is an important aspect of CFD modeling. Figure 10 illustrates the mesh for this model at its inlet. The purpose of a mesh study is to optimize a model that balances both accuracy and speed. With a finer mesh applied to a model, the accuracy and solve time increase. The more points used in a mesh study allow for the most efficient results.

Figure 10: Mesh at the inlet of the y-Bifurcation model. As the mesh approaches the wall, it becomes finer to more accurately record results near the surface of the wall due to the flow interactions. The fluid properties can fluctuate considerably due to changes in shear rate and flow development, breakdown, and separation. Mesh studies were created in both COMSOL and STAR-CCM+ to evaluate the model for both accuracy and solving speed. The mesh study was created for the third flow of 20 cm/s and compared the pressure drops in the main trunk to the number of elements in the mesh. The results of this study in STAR-CCM+ can be seen in Figure 11. For this study, six meshes were created with their values displayed in Table 8. The optimal mesh found for this model in STAR-CCM+ was Mesh 3, which had 1100181 elements and was used for the validation process. Likewise, Figure 12 shows the results of the mesh study created in COMSOL and Table 9 shows the eight mesh values used in the COMSOL study. The ideal mesh discovered in COMSOL was Mesh 6, which had 2395887 elements and was used for the validation.

Figure 11: Mesh study of the pressure drop in the main trunk of the y-bifurcation model (STAR-CCM+). The optimum mesh chosen from this study was 1100181 elements.

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Table 8: Mesh values for each of the six meshes run in STAR-CCM+.

Figure 12: Mesh study of the pressure drop in the main trunk of the y-bifurcation model in (COMSOL). The optimum mesh chosen from this study was 2395887 elements. As the plot shows, the final three pressure values are close to one another, which allowed the one with the lowest number of elements to be chosen as the optimal mesh.

Table 9: Mesh values for each of the six meshes run in COMSOL. Non-isothermal Symmetric Bifurcation Model

A CFD model was also created to study isothermal and non-isothermal blood flow in a symmetric bifurcation. A detailed image of the geometry can be seen in Figure 13. The boundary conditions for this model, seen in Table 10, include fully developed flow at the inlet along with no-slip condition for the walls and zero pressure at the outlets. In addition to an initial blood temperature of 28 degrees Celsius, the model applied a constant surface wall temperature of 37 degrees Celsius. Table 11 shows the input parameters for this model.

Figure 13: Geometry setup for the symmetric bifurcation model.

Table 10: Boundary conditions for the non-isothermal symmetric bifurcation model.

Table 11: Input parameters for the symmetrical bifurcation model with constant viscosity. Results for this model were collected in both STAR-CCM+ and COMSOL. The isothermal model evaluated the pressure drop and the non-isothermal model was analyzed for temperatures. A mesh study, which evaluated 8 meshes, was also conducted for this model in STAR-CCM+. The number of elements was optimized at 199259. A pressure plot was generated for the isothermal model and can be seen in Figure 14. At the end of the parent vessel, the spike in pressure occurs and is due to the flow separation and area expansion that ensues at the bifurcation split.

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Figure 14: Pressure plot verse position for the isothermal symmetric bifurcation model. The pressure drop was validated by analyzing the first 12 mm of the parent vessel and was found to have 2.14 percent error from the theoretical pressure drop. The non-isothermal study evaluated the model for average temperature at various locations. Figure 15 shows a cut plot of the temperature distribution throughout the model along with the three areas where the average temperature was analyzed. Additionally, Figure 16 shows a cut plot of the temperature at one of the areas analyzed for average temperature.

Figure 15: This is a cut plot showing the temperature distribution in symmetric bifurcation with description of the three areas analyzed for average temperature. As expected the thermal boundary at the wall increases through the parent vessel of the model.

Figure 16: Cut plot of the temperature distribution in symmetric bifurcation at the outlet of the parent vessel.

When considering viscosity with non-isothermal conditions, there are variables that cause viscosity to change. In this simulation, temperature was evaluated. The model was run with both a constant viscosity and a variable viscosity, which implemented a polynomial function that accounts for the temperature of the fluid at every point in the model. The polynomial equation that was used can be seen in Equation (3).

(3)

The average temperature data was recorded and compared between a constant viscosity model as well as a variable viscosity model run in both STAR-CCM+ and COMSOL. Table 12 shows the percent difference of the variable viscosity models to the constant viscosity model at the three areas that already referenced.

Table 12: Percent difference of temperature at three locations between the constant viscosity model and the STAR-CCM+ and COMSOL models with variable viscosity.

CBD RESEARCH

Rapid Heart Cooling

Ischemia, a restriction of blood flow in the heart is the usually caused by myocardial infarction, more commonly known as a heart attack. A balloon can be used to

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expand the blocked artery to allow cooled blood to flow into the area of the heart that is not receiving any blood flow; the damaged area will be prepared and treated to reduce damage locally. For this study, the left coronary artery was the primary subject of investigation. By running flow through and extracting data from points along the left coronary artery it is possible to determine the effectiveness of the use of cooled blood. Before attempting to find this information, it was necessary to understand each geometry in increasing complexity up to a geometry as complex as the left coronary artery. Heat transferred from the walls of the vessel into the blood inside the vessel is an important condition to consider when testing and validating flow simulation in the coronary artery. A test was run with blood entering the artery at different temperatures lower than body temperature. The test had a uniform inlet mass flow of 0.00154 kg/s, outlet pressure of 12600 Pa, with laminar Newtonian flow. The walls were set at 37°C with no slip condition. The test was run at 20°C less than body temperature. At the outlet, 1 mm in of the parent branch, 126.86 mm from the inlet along the spline, it was found that temperature of the blood had reached a temperature of 29°C. From the inlet, the blood had increased 12°C. The second test, run at 25°C at the inlet, resulted in the blood reaching a temperature of 35.7°C, an increase of 10°C.

Figure 17: Model of the left coronary arter (human). Verticle slices in the branches reveal temperature plots of blood within. Red is 37°C, blue represents 17°C.

Table 13: Summary of results from simulated model of human left coronary artery. The heart model tested is not accurate to documented dimensions, and has no experimental data to reference.

Using FOCALCOOL’s data from an experiment conducted on a swine heart from an 80 kg pig on December 3, 2009, a new model has been constructed, and will be tested and compared. The experiment simulated a myocardial infarction by cutting off blood flow to the left coronary artery for a period of time. Cold blood was then pumped into the left coronary artery via a catheter and thermocouples recorded blood temperature at the outlets of the primary branches. This model is based on the measurements and photographs of the swine heart and angiograms of the left coronary artery of an 80 kg pig. The results from this model can be compared to the experimental data.

Figure 18: Photograph of the heart of an 80kg pig in the chest cavity. Experiments were run with cooled blood entering the LCA seen in the upper left of the image. The thermocouples are reading temperatures of the blood in the heart as cold blood is being pumped in. Localized Brain Tissue Cooling

Previous research indicates that localized hypothermia may be useful for the treatment of stroke victims. Ischemia, which accounts for 87% of all strokes, commonly occurs in the middle cerebral artery (MCA) [1]. The MCA is part of the cerebral circulatory anastomosis, known as the Circle of Willis, which connects the blood flow in the brain. The MCA is a daughter bifurcation stemming from the parent internal carotid artery (ICA), which branches off from the common carotid artery (CCA). Simple geometrical models (i.e. straight tube and bifurcations), have been developed to understand arterial blood flow before approaching the ultimate goal of modeling an anatomically accurate structure that accounts for temperature dependent blood properties and pulsatile flow so that the effects of cooled blood on localized brain tissue can be analyzed.

An ongoing CFD study of simulated blood flow through the vasculature of a canine brain is being conducted to evaluate flow distribution, blood temperature, and tissue temperatures at various locations in the model. Boundary conditions for this model were fully developed flow at the inlet, no-slip condition at the walls, and zero pressure at the outlets. Figure 19 shows the model

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geometry along with labels of key elements. Table 14 shows the input parameters for this isothermal canine model.

Figure 19: Geometry setup for the complex canine model. All outlets assume are zero pressure.

Table 14: Isothermal input parameters for the canine model.

Initial results were produced from the isothermal flow model, which singled out the fluid region of the model and ignored the artery wall thickness, to examine the flow rates at each of the inlet and outlet boundaries. The results were validated by comparing the flow percentages from the model with the results from a previous study with the same geometry and conditions. This comparison can be found in Table 15.

Table 15: Flow rate comparison between isothermal canine model and previous model with same geometry and conditions. The models compared relatively well yielding a difference below 5% with the exception of location 6. Using a finer mesh on that region of the model could reduce this error.

The study also evaluated the model under non-isothermal conditions with constant and variable viscosity. The model was studied in both COMSOL and STAR-CCM+ using the input parameters in Table 16. A mesh of 1006521 elements was used in STAR-CCM+ for this study. At constant viscosity, the temperature is calculated based on the conduction through the vessel

walls as the blood travels further from the inlet and the convection through the blood. Figure 20 illustrates the change in blood temperature as it travels through the geometry.

Table 16: Non-isothermal Input Parameters for Canine Model.

Figure 20: Split plots measuring temperature at 50 slices along the geometry. Post processing was performed in COMSOL and STAR-CCM+ to calculate the temperature at the inlet and each outlet of the canine model. The results compared to within 4% of each other (see Table 17). The temperature at boundary 9 as calculated by COMSOL is warmer than would be possible since the flow is not fast enough to create enough friction to heat the blood to a temperature greater than the temperature of the vessel wall. Further investigation is needed to determine the cause.

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Table 17: COMSOL Versus CCM+ Canine Model Average Temperature Results At Each Boundary Using Constant Viscosity.

The model was also studied using variable viscosity based on Equation (3) show earlier. This produced a more refined average temperature than the constant viscosity model at each boundary condition since temperature affects the viscosity of the fluid (see table 18). The results of the two software packages were within 3% of each other. It is prudent to say that the programs can be used interchangeably without an increased risk of error.

Table 18: COMSOL Versus CCM+ Canine Model Average Temperature Results At Each Boundary Using Variable Viscosity.

In this particular geometry under the parameters of the model, the difference between temperatures in the constant viscosity and variable viscosity canine models were minimal. In the future, variable viscosity should not only consider the effects of temperature but also take shear rate into account along with other material property factors to ensure that viscosity is not affected more than this study indicates.

TECHNOLOGICAL IMPACT STATEMENT

Use of therapeutic hypothermia is not new to the medical field, but the use of therapeutic hypothermia in these specific instances is not yet widely used or understood. Hopefully, with the research conducted in this clinic and by professionals who invest their time and energy into this subject, others will be inspired to use, or see the

benefits of using this treatment in their practices. Adding to the field of knowledge surrounding the subject will raise further questions to the limits of its use and how it can be improved.

Use of therapeutic hypothermia to treat ischemia would help save and extend the lives of those who suffer from it. Should this research inspire hospitals to make this method a standard treatment option for ischemia, those who produce the tools to apply this technique would readily receive funding from hospitals that purchase the equipment. Engineers around the world would then strive to produce the best equipment to make treatment as easy, accessible, and cheap as possible, ultimately creating jobs to design and manufacture the parts while improving the quality of care and treatment for patients.

Application of this treatment would require a catheter to deliver the blood to the desired region as well as a method of cooling the blood that is to be delivered into the body. A catheter would have to be disposed of with other biologically contaminated waste generating medical waste. Such waste has its own rules and regulations for disposal. This will prevent some material from being recycled effectively; however this will not significantly add to the waste produced by hospitals already. The equipment used to cool blood can be handled in ways that reduce the amount of waste produced and saving the users money by not having to replace and use so many parts.

CONCLUSION

The study of computational fluid dynamics using advanced computer software to investigate complex fluid flows has applications in the biomedical field. In this CBD clinic project, students have gained a solid foundation of CFD principles and best practices in SolidWorks, COMSOL, and STAR-CCM+. These skills allowed more complex geometries to be studied such as the heart and canine models and will be useful in future CFD modeling projects. The overarching goal for this semester was to apply these skills to two specific biomedical applications: rapid cooling of the human heart following acute myocardial infarction and localized cooling of the canine brain using therapeutic hypothermia to treat ischemic stroke. The tutorials that taught these fundamentals have been refined and will serve those who continue this body of work in the future. The basic bifurcation models will provide a standard for comparison for those who complete the same models in the future as they build their skills to carry this body of work forward – ensuring that their results are validated and that new skills have been learned. All models have been well documented and stored in model inventories to pass on this work to future clinic projects. Progress was made in both the heart and canine modeling. Initial results from the heart model have been

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gathered and continued work is needed to fully understand the effects of localized hypothermia. The canine model initial results have been compared in two software package and yielded similar results. In order to progress the study forward, more robust parameters such as variable viscosity dependent upon both temperature and shear rate must be introduced into the model. Creating geometry to mimic the true shape of the canine vasculature using DICOM images as well as producing a new model of the swine heart is part of the future work for this project. Meshing practices must also be implemented with these models to insure the validity of the results. Additionally, as stated before further investigation into variable viscosity is needed as well as the addition of pulsatile flow to increase the accuracy of these models compared to functioning vasculature. These improvements will bring the models closer to physiological accuracy and will increase the confidence others have in the potential of this research for use in the human body. Modeling flows for practical biomedical applications is crucial for the advancement in treatment of patience undergoing life-threatening events. ACKNOWLEDGMENTS

We appreciate the continued support from our advisor Dr. Merrill. We also acknowledge Ryan Sikorski for his assistance in the effort to complete and validate a thermal fluids finite element model of hypothermic blood flow in the canine brain. We thank NIH and the Department of M.E. for the computer workstations as well as Chuck Linderman and Karl Dyer for setting up the lab. Lastly, we acknowledge the support teams from both CD-adapco and COMSOL for their support of our efforts.

REFERENCES [1] Llyod-Jones, D., Adams, R., and Carnethon, M.,

2011, “Heart Disease and Stroke Statistics – 2009 Update: A Report From the American Heart Association Statistics Committee and Stroke Statistics Subcommittee,” Circulation, pp. 459-463.

[2] van der Worp, H. B., Sena, E. S., Donnan, G. A., Howells, D. W., and Macleod, M. R., 2007, “Hypothermia in Animal Models of Acute Ischaemic Stroke: a Sys- tematic Review and Meta-Analysis,” Brain: A journal of neurology, pp. 3063–3074.

[3] Holzer, M., Bernard, S. A., Hachimi-Idrissi, S., Roine, R. O., Sterz, F., and Millner, M., 2005, “Hypothermia for Neuroprotection After Cardiac Arrest: Systematic Review and Individual Patient Data Meta-Analysis,” Critical Care Medicine, pp. 414–418.

[4] Nadge, M, Pankaj and Govardhan, R.N. “High Reynolds number flow over a backward-facing step: structure of the mean separation bubble”, Exp Fluids 2014. Springer-Verlag Berlin Heidelberg. 55:1657.

DEFINITIONS, ACRONYMS, ABBREVIATIONS

ASME: American Society of Mechanical Engineers CBD: Computational Biofluid Dynamics CCA: Common Carotid Artery CFD: Computational Fluid Dynamics CCS: CoolGuide Cooling System ICA: Internal Carotid Artery MCA: Middle Cerebral Artery Re: Reynolds Number

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