A Computational Modeling Approach to Investigate the Influence of Hyperthermia on the Tumor Microenvironment

So this research is to use computational modeling to study the effect of local radio frequency thermal intervention on the biomechanics of the tumor. We will be focusing particular on high intratumoral pressure driven by abnormal blood flow within the tumor, which is one of the main barrier to the effective distribution of therapeutic agents. Intervention such as radio frequency hyperthermia have been recently explored as a potential tool to perturb tumor microenvironment, for example, increasing blood flow, and thereby decreasing intratumoral pressure.

This may lead to more favorable condition to the distribution of therapeutic agents and potentially improve the patient's response to therapeutic treatments. Currently available to measure intratumoral pressure rely on invasive techniques that provide quantitative information in only a few location within tumors. Computational model may provide the means to assess the special profile of biophysical variables across the entire tumor.

Protocol is the description of a computational workflow that captures the relationship between tissue temperature and blood perfusion driving changes in the intratumoral pressure. The protocol describes a model geometry that, in principle, mirrors in vivo experimental settings designed to approximate clinical thermal intervention. Perspective on how computational models can be employed to advance our understanding of how, by physical parameters of the tumor microenvironment, such as intratumoral pressure, can be affected by local thermal interventions.

To begin select electric fields and currents from AC/DC physics, heat transfer and solids from heat transfer physics, and PDE interfaces from mathematics physics, then, define the geometries by selecting geometry from the top ribbon. Proceed to define two cones with the dimensions displayed in the table on the screen. Position the cones at the distance indicated in the table.

These two cones model the two hypodermic needles used for building the bipolar radio frequency system. Duplicate the two cones to model the insulation of the needles by modifying the cone size. Next, select a cylinder with appropriate height and diameter to model background muscle tissue placed at a Z value of minus nine millimeters while keeping the X and Y values at zero.

Select another cylinder of appropriate dimensions to model the thin layer of skin placed at a Z value of four millimeters with the X and Y values at zero. Then, select a sphere of appropriate diameter to model the subcutaneous tumor placed at a Z value of minus 0.5 millimeters with X and Y values at zero. Next, right click on definitions and select functions, followed by piecewise.

Specify the function name, and specify temperature T as the argument of the function. Type the mathematical expression for each temperature interval consistent with the displayed equations. Repeat the steps using the nominal values listed in the displayed table to add the temperature-dependent functions of blood profusion and vascular pressure for each tissue model.

To create the link with the electromagnetic thermal simulation, express the vascular pressure PV as a function of the temperature. To assign materials properties to the geometry components, go to materials and right click to select more materials, then porous material. Right click on porous material to select fluid and solid components.

Select fluid node, and then, under fluid properties, select blood. Select solid node, and under solid properties, select tumor. In the solid node, specify the volume fraction defined as theta solid.

Enable manual selection and select the geometric entity corresponding to the specified material. To follow this protocol, assume that the tumor region is a poroelastic domain. After building the bipolar radio frequency hyperthermia model, proceed to set up the electrical problem.

Right click on the electric currents node. For the electrical boundary conditions in the displayed figure, select terminal and ground as boundaries. For terminal, manually select the proximal end of the top of one of the two needles.

The identified needle will provide the input voltage. Then, under terminal, select power and specify the appropriate value. For this protocol, select 0.5 watt for mild hyperthermia based on preliminary ex vivo experiments.

Next, select ground and manually select the proximal surface of the second needle, acting as a return electrode for the returning electrical current path. Apply electrical insulation to the remaining external surface of the model. To set up for the thermal problem, select heat transfer and solids node and specify 33 degrees Celsius as the initial value of the temperature.

To model the heat sink effect due to the blood flow, right click on heat transfer in solids, add the heat source domain, and select the geometry where the heat sink effects should be considered, which are tumor and normal tissue. Select general source followed by user-defined and type the expression for the heat sink. For the thermal boundary conditions in the displayed figure, right click on heat transfer, add heat flux as a boundary condition, and specify the external surfaces to which the heat flux is applied.

Select convective heat flux as the flux type. For the heat transfer coefficient, use H equals to 15 watt per meter squared per kelvin to model the mechanism of natural heat exchange between the skin and the air. Specify the external temperature.

Use T equals 20 degrees Celsius to model the ambient temperature in the laboratory environment. To set up the fluid dynamics problem, select coefficient form PDE node and specify pressure as the dependent variable. At this stage, the unit pascal is automatically assigned.

Specify fluid conductance unit one per second as source term quantity. Define the name to identify the variable PI, or interstitial fluid pressure, in this study. Next, right click on coefficient form PDE node and select the coefficient form domain.

Specify the geometrical entity to which the equation refers as tumor. Repeat the same steps and select the remaining tissue as normal tissue, to which a different PDE needs to be applied. For the tumor model, specified the displayed coefficients in terms to obtain the conservation of mass equation.

For the tumor model, neglect the contribution of the lymphatic system. Set all other coefficients equal to zero. Similarly, for the normal tissue model, specify the displayed coefficients in terms to obtain the conservation of mass equation.

For normal tissue, consider the contribution of the lymphatic system. Set all other coefficients equal to zero. Then, right click on coefficient form PDE and select initial values.

Select the geometrical domain as tumor and repeat the same step for the normal tissue model. Specify PI0 for tumor and normal tissue according to the values listed in the displayed table. For the boundary conditions related to the fluid dynamic study shown in the displayed figure, right click on coefficient form PDE and select Dirichlet boundary conditions.

Select the external surface of the normal tissue domain and assign the initial value of interstitial pressure, indicated as PI0, corresponding to the normal tissue. Finally, to run the simulations, select frequency transient from the study node. Specify the time unit as seconds and set the frequency as 500 kilohertz.

After 15 minutes of the simulated heating with 0.5 watt applied power, more than 50%of the tumor volume reached a state of mild hyperthermia, with the temperature in the region of the tumor closest to the needle exceeding 45 degrees Celsius. Compared to the initial conditions, the interstitial fluid pressure gradually decreased from nine millimeters of mercury in the center of the tumor to zero at the edge. Fluid velocity did not exceed 0.2 micron per second within the entire tumor domain, including the periphery.

The interstitial fluid pressure over time changed differently at different radial distances from the heat source. Within three millimeters from the needles, the fluid pressure responded to the rapid increase in the temperature, but finally showed no change at the end of the heating. However, the pressure in the remaining part of the tumor continuously decreased.