The study was supported by grants from the National Science Foundation (no. 2039014) and the National Cancer Institute (R37CA269622).

1. Build the model of a bipolar radiofrequency system
<ol>
	<li>Preliminary steps to set the interface
	<ol>
		<li>Launch COMSOL Multiphysics and click on Model Wizard.</li>
		<li>Select 3D as Space Dimension.</li>
		<li>Select AC/DC Physics module | Electric Fields and Currents | Electric Currents.</li>
		<li>Select Heat Transfer module | Heat Transfer in Solids.</li>
		<li>Select Mathematics module | PDE interfaces | Coefficient Form PDE.</li>
		<li>Select Study | Time-dependent. Click on Done.</li>
		<li>Once the Comsol working space appears:
		<ol>
			<li>Select Multiphysics | Electromagnetic Heating. With this step, the electromagnetic power loss density is automatically coupled as the heat source for the bioheat transfer equation. 
			NOTE: If Multiphysics does not appear automatically, manually specify the electromagnetic heat source (shown in COMSOL as Volumetric loss density). For more details on how to add the heat source, see &#39;Physics&#39; section, step 2 &#39;Setup for the thermal problem&#39;.</li>
			<li>Select Study from the top ribbon | Study Steps | Frequency Transient.</li>
		</ol>
		</li>
	</ol>
	</li>
	<li>Define the geometries. From the top ribbon, select Geometry, then:
	<ol>
		<li>Define two cones with the dimensions listed in Table 2.</li>
		<li>Position the cones at the distance indicated in Table 2 (spaced dinter-el apart). These two cones will model the two hypodermic needles used for building the bipolar RF system.</li>
		<li>Duplicate the two previous cones to model the insulation of the needles; modify the size of the cone according to the dimensions reported in Table 2.</li>
		<li>Select a cylinder (height, hm, and diameter dm) to model the bulk of muscle placed at z = - 9 mm (x = 0, y = 0). The values of each dimension are listed in Table 2.</li>
		<li>Select a cylinder (height, hs, and diameter ds) to model the thin layer of skin placed at z = 4 mm (x = 0, y = 0). The values of each dimension are listed in Table 2.</li>
		<li>Select a sphere (diameter, dt) to model the subcutaneous tumor placed at z = -0.5 mm (x = 0, y = 0). The size of the tumor is listed in Table 2.</li>
		<li>To facilitate the selection of the geometries in the following steps of the protocol, we recommend the following:
		<ol>
			<li>From the Geometry ribbon, select Virtual operations | Form Composite Domains.</li>
			<li>Select all domains related to the electrically conductive part of the needles to create a composite geometry.</li>
			<li>Repeat the same procedure to create composite domains for the needle insulation geometries.</li>
		</ol>
		</li>
	</ol>
	</li>
	<li>Define the properties of the biological tissue models. 
	NOTE: The following steps describe the procedure to implement the mathematical expressions described by Equations (2)-(7).
	<ol>
		<li>From Component node, right-click to select Definitions.</li>
		<li>Under Functions, select Analytic.
		<ol>
			<li>Specify the name of the Function (e.g., k_muscle or sigma_muscle) and type the mathematical expression consistent with Eq. 2).</li>
			<li>Specify temperature (T) as argument.</li>
			<li>Specify the Units of the function: S/m in the case of electrical conductivity.</li>
			<li>Repeat the previous steps from 1 to 3 to implement Eq. 3, modifying the unit accordingly (i.e., W/(m&#183;K) for thermal conductivity).</li>
			<li>Specify the unit for the argument: K (kelvin) for the temperature. In Plot Parameters, specify the range of values of the function argument (i.e., temperature). To follow this protocol, use a range of 33-100 &#176;C (306.15-373.15 K).</li>
			<li>Repeat the previous steps from 1 to 5 to add the temperature-dependent functions of electrical (Eq. 2) and thermal conductivities (Eq. 3) for each tissue model (i.e., muscle, skin, and tumor) using the nominal values listed in&#8203; Table 1 (normal tissue refers to both muscle and skin).</li>
		</ol>
		</li>
		<li>Under Functions, select Piecewise to implement Equations (4)-(7):
		<ol>
			<li>Specify the name of the function.</li>
			<li>Specify temperature (T) as the argument of the function.</li>
			<li>Type the mathematical expression for each temperature interval consistent with Equations (4)-(7).</li>
			<li>Repeat the previous steps from 1 to 3 to add the temperature-dependent functions of blood perfusion and vascular pressure for each tissue model using the nominal values listed in Table 1&#160;(normal tissue refers to both muscle and skin).</li>
		</ol>
		</li>
	</ol>
	</li>
	<li>Assign material properties to the geometry components.
	<ol>
		<li>From the component node, select Materials.</li>
		<li>Select blank materials to include normal tissue, tumor tissue, blood, PTFE, and stainless steel.</li>
		<li>Enable manual selection and select the geometric entity corresponding to the specified material.
		<ol>
			<li>Normal tissue is associated with geometries modeling muscle and skin.</li>
			<li>Tumor and blood tissues are associated with the tumor geometry.</li>
			<li>PTFE material is associated with the geometries modeling the needle insulator.</li>
			<li>Stainless steel material is associated with the cone geometries modeling the ground and the active needles.</li>
		</ol>
		</li>
		<li>For the temperature-dependent electrical and thermal conductivities23, type the chosen name of the function and the related argument (i.e., T) that appears in the Definitions node.</li>
		<li>For the material properties not depending on temperature, refer to the baseline values27 listed in Table 1. 
		NOTE: We rely on the poroelastic theory to calculate the pressure16,17,26. The following steps show how the properties of a porous material can be assigned to a specific domain.</li>
		<li>From Materials, select More Materials | Porous Material.</li>
		<li>Right-click on Porous Material to select Fluid and Solid components. Select Fluid node and under Fluid properties, select Blood (defined in the previous steps). Select Solid node and under Solid properties, select Tumor (defined in the previous steps). In the Solid node, specify the volume fraction defined as&#160;&#952;S (Table 1).</li>
		<li>Enable manual selection and select the geometric entity corresponding to the specified material. To follow this protocol, assume that only the tumor region is a poroelastic domain.</li>
	</ol>
	</li>
	<li>Meshing
	<ol>
		<li>Under Mesh node, select Size and select a predefined Finer mesh.</li>
		<li>Add Free Tetrahedral feature under Mesh node. This step allows for a refined mesh in the critical areas. 
		NOTE: For this model, we identified the edges of the tumor and the distal end of the hypodermic needle models as critical areas.</li>
		<li>Select the geometries of interest and customize the maximum (0.25 mm) and minimum element size in a way that the smallest component (e.g., the tip of the needle) is discretized by at least four meshing elements (complete mesh consists of 1,487,828 elements).</li>
	</ol>
	</li>
</ol>
2. Physics
<ol>
	<li>Setup for the electrical problem 
	NOTE: The following steps provide information on how to set the parameters to calculate the electric field distribution (Figure 2, block 1) that will provide the radiofrequency heat source (Q).
	<ol>
		<li>Right-click on the Electric Currents node.</li>
		<li>For the electrical boundary conditions shown in Figure 3A, select Terminal and Ground as boundaries.
		<ol>
			<li>For Terminal, manually select the proximal end (on the top) of one of the two needles. The identified needle will provide the input power.</li>
			<li>Under Terminal, select Power and specify the value according to the desired energy protocol. To follow this protocol, select 0.5 W for mild hyperthermia based on preliminary ex vivo experiments20.</li>
			<li>Select Ground and manually select the proximal surface of the second needle. This needle will act as a return electrode for the returning path of the electrical current.</li>
			<li>Apply electrical insulation to the remaining external surface of the model.</li>
		</ol>
		</li>
	</ol>
	</li>
	<li>Setup for the thermal problem 
	NOTE: The following steps show how to include the temperature-dependent blood perfusion functions (Equations 4 and 5) in the bioheat transfer equation to model the heat sink caused by the blood flow.
	<ol>
		<li>Select Heat Transfer in Solids node and specify 33 &#176;C as the initial value of the temperature.</li>
		<li>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 effect should be considered (i.e., tumor and normal tissue). Select General Source | User defined where the expression for the heat sink can be typed.</li>
		<li>For the thermal boundary conditions shown in Figure 3B, 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 = 15 W/(m2 &#183;K) to model the mechanism of natural heat exchange between the skin and the air28. Specify the external temperature. Use T = 20 &#176;C to model the ambient temperature in the laboratory environment.</li>
	</ol>
	</li>
	<li>Setup for the fluid-dynamics problem 
	NOTE: The following steps describe how to implement the conservation of mass equation illustrated in Figure 2 (Block 3) and how it can be linked to the variation of the temperature.
	<ol>
		<li>Select Coefficient Form PDE node and specify Pressure as the dependent variable. At this stage, the unit Pascal (Pa) is automatically assigned. 
		NOTE: Once the simulation is computed, the results can be displayed and/or exported using the unit of choice. We present the results using mmHg unit for consistency with the literature (see the representative results section).</li>
		<li>Specify Fluid conductance unit 1/s as source term quantity.</li>
		<li>Define the name to identify the variable (Pi, interstitial fluid pressure in this study).</li>
		<li>Right-click on Coefficient Form PDE node and select the Coefficient Form domain. Specify the geometrical entity to which the equation refers (tumor). Repeat the same steps and select the remaining tissue (normal tissue) to which a different PDE will be applied.</li>
		<li>For the tumor model, specify the following coefficients and terms to obtain the conservation of mass equation (Figure 2 block 3): diffusion coefficient Ki of the tumor (Table 1); damping coefficient <img alt="Equation 11" src="/files/ftp_upload/65870/65870eq11.jpg" style="vertical-align: middle;" /> ); source term <img alt="Equation 12" src="/files/ftp_upload/65870/65870eq12.jpg" style="vertical-align: middle;" /> . For the tumor model, neglect the contribution of the lymphatic system. Set all other coefficients equal to zero.</li>
		<li>For the normal tissue model, specify the following coefficients and terms to obtain the conservation of mass equation (Figure 2 block 3): diffusion coefficient Ki&#160;of the normal tissue (Table 1); damping coefficient <img alt="Equation 13" src="/files/ftp_upload/65870/65870eq13.jpg" style="vertical-align: middle;" /> ; source term <img alt="Equation 14" src="/files/ftp_upload/65870/65870eq14.jpg" style="vertical-align: middle;" /> . To consider normal tissue as a normal functioning tissue, consider the contribution of the lymphatic system. Set all other coefficients equal to zero.</li>
		<li>To create the link with the electromagnetic-thermal simulation, express the vascular pressure Pv as a function of the temperature (by means of the blood perfusion variable, see Equations 6 and 7).</li>
		<li>Right-click on Coefficient Form PDE and select Initial Values. Select the geometrical domain (tumor) and repeat the same step for the normal tissue model (normal tissue). Specify Pi0 for tumor and normal tissue according to the values listed in Table 1.</li>
		<li>For the boundary conditions related to the fluid-dynamic study, shown in Figure 3C, right-click on Coefficient Form PDE and select Dirichlet Boundary conditions. Select the external surface of the normal tissue domain and assign the Pi0 value corresponding to the normal tissue (Table 1).</li>
	</ol>
	</li>
</ol>
3. Run the simulations and display the results
NOTE: As a final step before computing, specify the time (simulating the duration of the procedure) and the operating frequency:
<ol>
	<li>Select Frequency-Transient from the Study node.
	<ol>
		<li>Specify the time unit (s).</li>
		<li>From Output Times, select range (on the right side) and specify 0 s as start, 5 s as step, and 900 s as stop.</li>
		<li>Set the Frequency as 500e3 Hz.</li>
	</ol>
	</li>
	<li>Select Compute to run the simulations.</li>
	<li>For the visualization of the results, select Datasets under node Results.
	<ol>
		<li>Right-click to select a cut plane to define the plane to use to visualize 2D distributions (e.g., zx-plane at y = 0).</li>
		<li>Right-click to select a cut point in the 3D volume to display the variation of a parameter across time.</li>
	</ol>
	</li>
	<li>From Results on the top ribbon,
	<ol>
		<li>Select 2D plot group to visualize the two-dimensional distribution of a variable (e.g., temperature) on one of the planes identified in the steps above.</li>
		<li>Select 1D plot group to visualize 1D results (e.g., pressure across the time) at the point or multiple points identified in the steps above. 
		NOTE: The time to run the simulations with the settings described in this protocol is approximately 2.5 h.</li>
	</ol>
	</li>
</ol>

Simulating the Influence of a Bipolar Radiofrequency Hyperthermia System on Tumors

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M., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Influence+of+injection+technique,+drug+formulation+and+tumor+microenvironment+on+intratumoral+immunotherapy+delivery+and+efficacy.">Influence of injection technique, drug formulation and tumor microenvironment on intratumoral immunotherapy delivery and efficacy.</a> Journal for ImmunoTherapy of Cancer. 9 (2), 0018-0027 (2021).</li><li>Swartz, M. A., Lund, A. W. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Lymphatic+and+interstitial+flow+in+the+tumour+microenvironment:+linking+mechanobiology+with+immunity.">Lymphatic and interstitial flow in the tumour microenvironment: linking mechanobiology with immunity.</a> Nature Reviews Cancer. 12 (3), 210-219 (2012).</li><li>Mehta, A., Oklu, R., Sheth, R. A. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Thermal+ablative+therapies+and+immune+checkpoint+modulation:+can+locoregional+approaches+effect+a+systemic+response.">Thermal ablative therapies and immune checkpoint modulation: can locoregional approaches effect a systemic response.</a> Gastroenterology Research and Practice. 2016, 1-11 (2016).</li><li>Song, C. W., Park, H., Griffin, R. J. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Improvement+of+tumor+oxygenation+by+mild+hyperthermia.">Improvement of tumor oxygenation by mild hyperthermia.</a> Radiation Research. 155 (4), 515-528 (2001).</li><li>Dewhirst, M. W., Oleson, J. R., Kirkpatrick, J., Secomb, T. W. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Accurate+three-dimensional+thermal+dosimetry+and+assessment+of+physiologic+response+are+essential+for+optimizing+thermoradiotherapy.">Accurate three-dimensional thermal dosimetry and assessment of physiologic response are essential for optimizing thermoradiotherapy.</a> Cancers. 14 (7), 1701 (2022).</li></ol>

The authors have no conflicts of interest to disclose.
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We present a computational modeling protocol to couple transient electric-thermal simulations with fluid-dynamic simulations to study the impact of RF-hyperthermia on thermal and interstitial fluid pressure profiles in tumors. The key aspect is in the building of a numerical workflow capable of capturing the relationship existing between temperature and vascular pressure, which in turn drives the changes in interstitial fluid pressure.
We used the relationship between vascular pressure and blo...

Elevated interstitial fluid pressure (IFP) is a hallmark of solid tumors1. The leakage of fluid into the interstitium from hyperpermeable blood vessels is imbalanced by the egress of fluid due to compressed intratumoral veins and absent lymphatics1,2,3. In concert with other biophysical parameters that are abnormal within the tumor microenvironment (TME), including solid stress and stiffness, elevated IFP undermines the efficacy of both systemic and local drug delivery4,5,6. Interstitial fluid pressure in solid tumors ranges from 5 mmHg (glioblastoma and melanoma) to 30 mmHg (renal cell carcinoma) compared to 1-3 mmHg in normal tissue2. High IFP is responsible for increasing the fluid flow toward the margin of the tumor and exposes stromal cells, infiltrated cells, and other extracellular components to shear stress1,4. Mechano-biological alterations sustain an immunosuppressive TME, for example, by increasing endothelial sprouting, which supports angiogenesis, cancer cell migration and invasion, transforming growth factor-&#946; (TGF-&#946;) expression, and stromal stiffening7,8,9.
Several studies have explored energy-based therapies with the intent of decreasing IFP, including low-intensity ultrasound, high-intensity focused ultrasound, pulsed electric fields, and thermal therapies5,10,11. Heating to temperatures in the range of 40-43 &#176;C, referred to as mild hyperthermia, has been shown to increase tumor blood perfusion and may thus contribute to expanding compressed veins and reducing vascular pressure by facilitating intravasation and drainage of interstitial fluid11,12. Some recent studies have shown the potential of hyperthermia to reduce IFP and consequently, to facilitate the distribution of drug or contrast agents within a tumor13,14. These studies also show increased T-cell infiltration following hyperthermia compared to no treatment control groups13.
The promising results from in vivo small animal experiments motivate further studies employing computational approaches to advance the understanding of how physical parameters within the TME are affected by physical interventions4,15,16,17. Results from computational models can complement in vivo experimental studies to uncover the cause-effect relationship underlying the local heating (or other external energy sources) and the IFP. This can be particularly instructive given the challenges with measuring spatial variations in IFP with catheter- and needle-based pressure transducers, which typically provide point measurements9,16,18,19. In the context of drug delivery, an understanding of the key biophysical mechanisms is essential to define the appropriate heating protocol as well as the time window for drug injection to enhance the likelihood of effective drug distribution. Quantitative information in terms of changes in biophysical characteristics of the TME, including but not limited to the IFP, could also give insights into the interpretation of the immunological response (e.g., T-cell infiltration) to external stimuli.
We present a protocol for computational modeling of thermally mediated changes to tumor IFP profiles. Specifically, the protocol details how to model a custom small-animal apparatus for delivering controlled thermal therapy with radiofrequency current, simulate transient temperature profiles following heating, and couple fluid dynamic simulations to compute the spatio-temporal variation of tumor IFP in response to thermal therapy. This model mirrors the essential features of the experimental setup we used in a subcutaneous tumor model (McArdle RH7777, ATCC) in a prior experimental study20.
Figure 1 shows the computational model we implemented to calculate thermally induced changes in IFP in a tumor surrounded by normal tissue. A pair of hypodermic needles inserted in the tumor is modeled to deliver heating with&#160;radiofrequency current at 500 kHz. A porous material is assumed in the tumor domain, composed of two phases: the solid phase represents the solid extracellular matrix, and the fluid phase represents the interstitial fluid. In the case of a pressure change or a matrix deformation resulting from an external stimulus, for example increase of temperature, the solid and fluid components rearrange. This causes the movement of the interstitial fluid through the extracellular solid matrix16,17,21.
From the poroelasticity theory, the stress tensor S (Pa) (equation [1]) is the combination of the elastic term describing the change in volume of the solid component relative to the initial conditions, and a porous term describing the stress induced by the hydrostatic pressure of the fluid component.
<img alt="Equation 1" src="/files/ftp_upload/65870/65870eq01.jpg" style="margin: auto;" />&#160; &#160; &#160;(1)
Where, &#955;, &#956; (Pa) are the Lam&#233; parameters, E is the strain tensor, e is the volumetric strain tensor, Pi (Pa) is the interstitial fluid pressure (I is the identity matrix). Steady-state conditions are assumed for the solid component under poroelastic stress, which means that the stress tensor components are orthogonal, <img alt="Equation 15" src="/files/ftp_upload/65870/65870eq15.jpg" style="margin: auto;" />.
Figure 2 shows the system of mathematical equations implemented in the described poroelastic model and the interplay between the components of the presented multi-physics model. The workflow of the computational simulations includes:
Electrical problem equations. The solution of the electrical problem equations provides the time-averaged RF heat source Q (Joule heating). To this end, a quasi-static approximation to Maxwell&#39;s equations is used to calculate the distribution of the time-averaged electric field E (V/m) (Figure 2, block 1).
Thermal problem equations. The solution of the Pennes bioheat equation (Figure 2, block 2) provides the spatial and temporal variation of the temperature T (&#176;C) as a result of the heat source (Q) linked&#160;to the absorbed electromagnetic energy, the passive heating linked to the thermal conduction of the tissues (<img alt="Equation 16" src="/files/ftp_upload/65870/65870eq16.jpg" style="margin: auto;" />), and the heat sink effect of the tissue blood perfusion (cWb(T) (T - Tb)). The heat sink term approximates the heat exchange between the blood flowing in the microvasculature and adjacent tissue where electromagnetic power is absorbed. The heat transfer equation also includes the advection term (<img alt="Equation 17" src="/files/ftp_upload/65870/65870eq17.jpg" style="margin: auto;" />), which describes the change in the temperature caused by the movement of interstitial fluid through the extracellular matrix of the poroelastic model. However, this term has a negligible impact on the temperature profile compared to the other mechanisms responsible for the temperature change.
Fluid-dynamic problem equations. The conservation of mass equation (Figure 2, block 3) combined with Darcy&#39;s law (Figure 2, block 4) gives as an output the spatial and temporal variation of the interstitial fluid pressure Pi resulting from the balance between the source (<img alt="Equation 2" src="/files/ftp_upload/65870/65870eq02.jpg" style="vertical-align: middle;" />) and the sink (<img alt="Equation 03" src="/files/ftp_upload/65870/65870eq03.jpg" style="vertical-align: middle;" /> ) of the fluid. The transient pressure term on the left side of the mass conservation equation, <img alt="Equation 4" src="/files/ftp_upload/65870/65870eq04.jpg" style="margin: auto;" /> , describes the rearrangement of the fluid and solid components in the poroelastic material. This is caused by the variation of the interstitial fluid pressure, Pi, driven by the variation of the vascular pressure Pv as a function of the temperature.
The difference between the vascular pressure (Pv) and the interstitial fluid pressure (Pi) is the source of the fluid that flows through the extracellular matrix. The sink term is linked to the pressure difference between the lymphatic vessels (PL) and the interstitial space (Pi). In normal tissue, the pressure in the lymphatic vasculature (~ -6-0 mmHg) is up to two-fold lower than the interstitial fluid pressure13. This pressure difference ensures the efficacy of the lymphatic vessels to drain the excess of the fluid extravasating from the wall of&#160;blood vessels into the interstitium. For the tumor model presented here, we neglected the contribution of the lymphatic system4,16,22.
Mathematical expressions from Equations (2) to (5) are used to describe the temperature dependence of the electrical and thermal conductivity of tissue and tissue blood perfusion23,24. Two different mathematical models are used to describe the temperature dependence of blood perfusion in the normal and tumor tissue domains, respectively24,25. The models show that the blood perfusion increases with the temperature up to nine times compared to the baseline in the normal tissue and only approximately two times of the baseline value in the tumor domain. For both models, the increase in the blood perfusion is limited to the temperatures within the mild hyperthermia range (below 45 &#176;C). It is worth mentioning that the mathematical expressions, Equations (4) and (5), do not fully describe the mechanisms underlying the temperature-dependent changes in the blood perfusion in the two different types of tissue. However, they help represent the limited perfusion that typically characterizes the tumor microenvironment compared to normal tissues.
<img alt="Equation 5" src="/files/ftp_upload/65870/65870eq05.jpg" style="margin: auto;" />&#160; &#160;&#160; (2)
<img alt="Equation 6" src="/files/ftp_upload/65870/65870eq06.jpg" style="margin: auto;" />&#160; &#160; &#160;(3)
<img alt="Equation 7" src="/files/ftp_upload/65870/65870eq07.jpg" style="margin: auto;" /> (4)
<img alt="Equation 8" src="/files/ftp_upload/65870/65870eq08.jpg" style="margin: auto;" /> (5)
<img alt="Equation 9" src="/files/ftp_upload/65870/65870eq09.jpg" style="margin: auto;" />&#160; &#160; &#160;(6)
<img alt="Equation 10" src="/files/ftp_upload/65870/65870eq10.jpg" style="margin: auto;" />&#160; &#160; &#160;(7)
In this study, we used Equations (6) and (7) to model the vascular pressure as a function of the blood perfusion both for normal and tumor tissue models26. From Equations (4) and (5), the blood flow rate can be expressed as the ratio between the blood perfusion and the blood density. The relationship between blood flow and vascular pressure is well established in the literature3: the blood flow rate and the geometrical resistance (or conductivity, Lp) of the vasculature determine the pressure difference within the blood vessel. The vascular pressure can be expressed as a function of the temperature (Equations (6) and (7)), leveraging on this relationship and the temperature-dependent model of the blood perfusion (Equations (4) and (5)).
The implementation of the computational workflow (Figure 2) and the temperature-dependent properties of the tissue models are described in detail in the following section. All material properties and their descriptions and baseline values (i.e., at body temperature) are listed in Table 1. See the Table of Materials for details about COMSOL Multiphysics installed on a computer used to implement this computational protocol. The electrical problem was modeled using the AC/DC module; bioheat transfer was modeled using heat transfer physics; and the fluid-dynamics problem was modeled using the Mathematics interface.

<table><tbody><tr><td>COMSOL Multiphysics (v. 6.0)</td><td>COMSOL AB, Stockholm, Sweden</td><td></td><td>Software used to implement the computational workflow described in the protocol</td></tr><tr><td>Dell 1.8.0, 11th Gen Intel(R) Core(TM) i7-11850H @ 2.50GHz, 2496 Mhz, 8 Core(s), 16 Logical Processor(s), 32 GB RAM</td><td>Dell Inc.&amp;nbsp;</td><td></td><td>Laptop used to run computational simulations</td></tr></tbody></table>

a computational modeling approach to investigate the influence of hyperthermia on the tumor microenvironment

The biophysical properties of the tumor microenvironment differ substantially from normal tissues. A constellation of features, including decreased vascularity, lack of lymphatic drainage, and elevated interstitial pressure, diminishes the penetration of therapeutics into tumors. Local&#160;hyperthermia within the tumor can alter microenvironmental properties, such as interstitial fluid pressure, potentially leading to improvements in drug penetration. In this context, multi-physics computational models can provide insight into the interplay between the biophysical parameters within the tumor microenvironment and can guide the design and interpretation of experiments that test the bioeffects of local hyperthermia.
This paper describes a step-by-step workflow for a computational model coupling partial differential equations describing electrical current distribution, bioheat transfer, and fluid dynamics. The main objective is to study the effects of hyperthermia delivered by a bipolar radiofrequency device on the interstitial fluid pressure within the tumor.&#160;The system of mathematical expressions linking electrical current distribution, bioheat transfer, and interstitial fluid pressure is presented, emphasizing the changes in the distribution of the interstitial fluid pressure that could be induced by the thermal intervention.

The homogeneous distribution of high interstitial fluid pressure within the tumor and a drop to the normal values (0-3 mmHg) at the periphery are hallmarks of the TME. Figure 4 and Figure 5 show the initial conditions&#160;(t = 0 min) of temperature (A), interstitial fluid pressure (B), and fluid velocity (C). Before starting the heating, when the initial temperature is 33 &#176;C, the value of interstitial fluid pressure within the tumor is approximately 9 mmHg...

Watch this Scientific Journal Video about Author Spotlight: Computing the Effects of a Local Radiofrequency Hyperthermia Intervention on Tumor Biomechanics at JoVE.com

Author Spotlight: Computing the Effects of a Local Radiofrequency Hyperthermia Intervention on Tumor Biomechanics

The article describes a protocol to simulate the transient temperature profiles and the coupled spatiotemporal variation of the interstitial fluid pressure following the heating delivered by a dipolar radiofrequency hyperthermia system. The protocol can be used to assess the response of biophysical parameters characterizing the tumor microenvironment to interventional hyperthermia techniques.

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

The biophysical properties of the tumor microenvironment differ substantially from normal tissues. A constellation of features, including decreased ...

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Research

JoVE Journal

Bioengineering

354 Views.  Kansas State University. Het doel van dit onderzoek is om computationele modellering te gebruiken om het effect van lokale radiofrequente thermische interventie op de biomechanica van de tumor te bestuderen. We zouden ons in het bijzonder richten op hoge intratumorale druk die wordt aangedreven door een abnormale bloedstroom in de tumor, wat een van de belangrijkste barrières is voor de effectieve distributie van therapeutische middelen. Interventies zoals radiofrequente hyperthermie zijn onlangs onderzocht als een ...

Video: Auteur in de schijnwerpers: het berekenen van de effecten van een lokale radiofrequente hyperthermie-interventie op de biomechanica van tumoren

A Mimic of the Tumor Microenvironment: A Simple Method for Generating Enriched Cell Populations and Investigating Intercellular Communication

Understanding the early heterotypic interactions between cancer cells and the surrounding non-cancerous stroma is important in elucidating the events leading to stromal activation and establishment of the tumor microenvironment (TME). Several in vitro and in vivo models of the TME have been developed; however, in general these models do not readily permit isolation of individual cell populations, under non-perturbing conditions, for further study. To circumvent this difficulty, we have employed an in vitro TME model using a cell growth substrate consisting of a permeable microporous membrane insert that permits simple generation of highly enriched cell populations grown intimately, yet separately, on either side of the insert&#39;s membrane for extended co-culture times. Through use of this model, we are capable of generating greatly enriched cancer-associated fibroblast (CAF) populations from normal diploid human fibroblasts following co-culture (120 hr) with highly metastatic human breast carcinoma cells, without the use of fluorescent tagging and/or cell sorting. Additionally, by modulating the pore-size of the insert, we can control for the mode of intercellular communication (e.g., gap-junction communication, secreted factors) between the two heterotypic cell populations, which permits investigation of the mechanisms underlying the development of the TME, including the role of gap-junction permeability. This model serves as a valuable tool in enhancing our understanding of the initial events leading to cancer-stroma initiation, the early evolution of the TME, and the modulating effect of the stroma on the responses of cancer cells to therapeutic agents.

We adapted a permeable microporous membrane insert to mimic the tumor microenvironment (TME). The model consists of a mixed cell culture, allows simplified generation of highly enriched individual cell populations without using fluorescent tagging or cell sorting, and permits studying intercellular communication within the TME under normal or stress conditions.

Understanding the early heterotypic interactions between cancer cells and the surrounding non-cancerous stroma is important in elucidating the events ...

Cancer Research

Protocol for Long Duration Whole Body Hyperthermia in Mice

Hyperthermia is a general term used to define the increase in core body temperature above normal. It is often used to describe the increased core body temperature that is observed during fever. The use of hyperthermia as an adjuvant has emerged as a promising procedure for tumor regression in the field of cancer biology. For this purpose, the most important requirement is to have reliable and uniform heating protocols. We have developed a protocol for hyperthermia (whole body) in mice. In this protocol, animals are exposed to cycles of hyperthermia for 90 min followed by a rest period of 15 min. During this period mice have easy access to food and water. High body temperature spikes in the mice during first few hyperthermia exposure cycles are prevented by immobilizing the animal. Additionally, normal saline is administered in first few cycles to minimize the effects of dehydration. This protocol can simulate fever like conditions in mice up to 12-24 hr. We have used 8-12 weeks old BALB/Cj female mice to demonstrate the protocol.

This paper describes a protocol for whole body hyperthermia in mice that can stimulate fever like conditions up to 12-24 hr.

Hyperthermia is a general term used to define the increase in core body temperature above normal. It is often used to describe the increased core body ...

Medicine

Quantifying the Brain Metastatic Tumor Micro-Environment using an Organ-On-A Chip 3D Model, Machine Learning, and Confocal Tomography

Brain metastases are the most lethal cancer lesions; 10-30% of all cancers metastasize to the brain, with a median survival of only ~5-20 months, depending on the cancer type. To reduce the brain metastatic tumor burden, gaps in basic and translational knowledge need to be addressed. Major challenges include a paucity of reproducible preclinical models and associated tools. Three-dimensional models of brain metastasis can yield the relevant molecular and phenotypic data used to address these needs when combined with dedicated analysis tools. Moreover, compared to murine models, organ-on-a-chip models of patient tumor cells traversing the blood brain barrier into the brain microenvironment generate results rapidly and are more interpretable with quantitative methods, thus amenable to high throughput testing. Here we describe and demonstrate the use of a novel 3D microfluidic blood brain niche (&#181;mBBN) platform where multiple elements of the niche can be cultured for an extended period (several days), fluorescently imaged by confocal microscopy, and the images reconstructed using an innovative confocal tomography technique; all aimed to understand the development of micro-metastasis and changes to the tumor micro-environment (TME) in a repeatable and quantitative manner. We demonstrate how to fabricate, seed, image, and analyze the cancer cells and TME cellular and humoral components, using this platform. Moreover, we show how artificial intelligence (AI) is used to identify the intrinsic phenotypic differences of cancer cells that are capable of transit through a model &#181;mBBN and to assign them an objective index of brain metastatic potential. The data sets generated by this method can be used to answer basic and translational questions about metastasis, the efficacy of therapeutic strategies, and the role of the TME in both.

Here, we present a protocol for preparing and culturing a blood brain barrier metastatic tumor micro-environment and then quantifying its state using confocal imaging and artificial intelligence (machine learning).

Brain metastases are the most lethal cancer lesions; 10-30% of all cancers metastasize to the brain, with a median survival of only ~5-20 months, ...

Modeling Breast Cancer in Human Breast Tissue using a Microphysiological System

Breast cancer (BC) remains a leading cause of death for women. Despite more than $700 million invested in BC research annually, 97% of candidate BC drugs fail clinical trials. Therefore, new models are needed to improve our understanding of the disease. The NIH Microphysiological Systems (MPS) program was developed to improve the clinical translation of basic science discoveries and promising new therapeutic strategies. Here we present a method for generating MPS for breast cancers (BC-MPS). This model adapts a previously described approach of culturing primary human white adipose tissue (WAT) by sandwiching WAT between adipose-derived stem cell sheets (ASC)s. Novel aspects of our BC-MPS include seeding BC cells into non-diseased human breast tissue (HBT) containing native extracellular matrix, mature adipocytes, resident fibroblasts, and immune cells; and sandwiching the BC-HBT admixture between HBT-derived ASC sheets. The resulting BC-MPS is stable in culture ex vivo for at least 14 days. This model system contains multiple elements of the microenvironment that influence BC including adipocytes, stromal cells, immune cells, and the extracellular matrix. Thus BC-MPS can be used to study the interactions between BC and its microenvironment. 
We demonstrate the advantages of our BC-MPS by studying two BC behaviors known to influence cancer progression and metastasis: 1) BC motility and 2) BC-HBT metabolic crosstalk. While BC motility has previously been demonstrated using intravital imaging, BC-MPS allows for high-resolution time-lapse imaging using fluorescence microscopy over several days. Furthermore, while metabolic crosstalk was previously demonstrated using BC cells and murine pre-adipocytes differentiated into immature adipocytes, our BC-MPS model is the first system to demonstrate this crosstalk between primary human mammary adipocytes and BC cells in vitro.

This protocol describes the construction of an in vitro microphysiological system for studying breast cancer using primary human breast tissue with off the shelf materials.

Breast cancer (BC) remains a leading cause of death for women. Despite more than $700 million invested in BC research annually, 97% of candidate BC drugs ...

Modeling the Effects of Hemodynamic Stress on Circulating Tumor Cells using a Syringe and Needle

During metastasis, cancer cells from solid tissues, including epithelia, gain access to the lymphatic and hematogenous circulation where they are exposed to mechanical stress due to hemodynamic flow. One of these stresses that circulating tumor cells (CTCs) experience is fluid shear stress (FSS). While cancer cells may experience low levels of FSS within the tumor due to interstitial flow, CTCs are exposed, without extracellular matrix attachment, to much greater levels of FSS. Physiologically, FSS ranges over 3-4 orders of magnitude, with low levels present in lymphatics (&#60;1 dyne/cm2) and the highest levels present briefly as cells pass through the heart and around heart valves (&#62;500 dynes/cm2). There are a few in vitro models designed to model different ranges of physiological shear stress over various time frames. This paper describes a model to investigate the consequences of brief (millisecond) pulses of high-level FSS on cancer cell biology using a simple syringe and needle system.

Here we demonstrate a method to apply fluid shear stress to cancer cells in suspension to model the effects of hemodynamic stress on circulating tumor cells.

During metastasis, cancer cells from solid tissues, including epithelia, gain access to the lymphatic and hematogenous circulation where they are exposed ...

Magnetic Resonance-Guided High Intensity Focused Ultrasound Generated Hyperthermia: A Feasible Treatment Method in a Murine Rhabdomyosarcoma Model

Magnetic resonance-guided high intensity focused ultrasound (MRgHIFU) is an established method for producing localized hyperthermia. Given the real-time imaging and acoustic energy modulation, this modality enables precise temperature control within a defined area. Many thermal applications are being explored with this noninvasive, nonionizing technology, such as hyperthermia generation, to release drugs from thermosensitive liposomal carriers. These drugs can include chemotherapies such as doxorubicin, for which targeted release is desired due to the dose-limiting systemic side effects, namely cardiotoxicity. Doxorubicin is a mainstay for treating a variety of malignant tumors and is commonly used in relapsed or recurrent rhabdomyosarcoma (RMS). RMS is the most common solid soft tissue extracranial tumor in children and young adults. Despite aggressive, multimodal therapy, RMS survival rates have remained the same for the past 30 years. To explore a solution for addressing this unmet need, an experimental protocol was developed to evaluate the release of thermosensitive liposomal doxorubicin (TLD) in an immunocompetent, syngeneic RMS mouse model using MRgHIFU as the source of hyperthermia for drug release.

Presented here is a protocol to use controlled hyperthermia, generated by magnetic resonance-guided high intensity focused ultrasound, to trigger drug release from temperature-sensitive liposomes in a rhabdomyosarcoma mouse model.

Magnetic resonance-guided high intensity focused ultrasound (MRgHIFU) is an established method for producing localized hyperthermia. Given the real-time ...

Preparing a Microfluidics-Based Vascularized Human Micro-Tumor Model

Establishing a Physiologic Human Vascularized Micro-Tumor Model for Cancer Research

A lack of validated cancer models that recapitulate the tumor microenvironment of solid cancers in vitro remains a significant bottleneck for preclinical cancer research and therapeutic development.&#160;To overcome this problem, we have developed the vascularized microtumor (VMT), or tumor chip, a microphysiological system that realistically models the complex human tumor microenvironment. The VMT forms de novo within a microfluidic platform by co-culture of multiple human cell types under dynamic, physiological flow conditions. This tissue-engineered micro-tumor construct incorporates a living perfused vascular network that supports the growing tumor mass just as newly formed vessels do in vivo. Importantly, drugs and immune cells must cross the endothelial layer to reach the tumor, modeling in vivo physiological barriers to therapeutic delivery and efficacy. Since the VMT platform is optically transparent, high-resolution imaging of dynamic processes such as immune cell extravasation and metastasis can be achieved with direct visualization of fluorescently labeled cells within the tissue. Further, the VMT retains in vivo tumor heterogeneity, gene expression signatures, and drug responses. Virtually any tumor type can be adapted to the platform, and primary cells from fresh surgical tissues grow and respond to drug treatment in the VMT, paving the way toward truly personalized medicine. Here, the methods for establishing the VMT and utilizing it for oncology research are outlined. This innovative approach opens new possibilities for studying tumors and drug responses, providing researchers with a powerful tool to advance cancer research.

Author Spotlight: Creating Human Vascularized Micro-Tumors as Models for Translational Cancer Research 

This protocol presents a physiologically relevant tumor-on-a-chip model to perform high-throughput basic and translational human cancer research, advancing drug screening, disease modeling, and personalized medicine approaches with a description of loading, maintenance, and evaluation procedures.

A lack of validated cancer models that recapitulate the tumor microenvironment of solid cancers in vitro remains a significant bottleneck for preclinical ...

Intravital Microscopy of Tumor-associated Vasculature Using Advanced Dorsal Skinfold Window Chambers on Transgenic Fluorescent Mice

Tumor and tumor vessel development, as well as tumor response to therapeutics, are highly dynamic biological processes. Histology provides static information and is often not sufficient for a correct interpretation. Intravital evaluation, in which a process is followed in time, provides extra and often unexpected information. With the creation of transgenic animals expressing cell-specific markers and live cell tracers, improvements to imaging equipment, and the development of several imaging chambers, intravital microscopy has become an important tool to better understand biological processes. This paper describes an experimental design for the investigation of tumor vessel development and of therapeutic effects in a spatial and temporal manner. Using this setup, the stage of vessel development, tip cell and lumen formation, blood flow, extravasation, an established vascular bed, and vascular destruction can be visualized and followed. Furthermore, therapeutic effects, intratumoral fate, and the localization of chemotherapeutic compounds can also be followed.

This protocol describes the intravital imaging of transgenic mice expressing cell-specific fluorescent markers. Intravital imaging provides a non-invasive method for high-resolution observations in living animals using implantable windows through which the microscopic visualization of processes is possible. This method is especially useful to study longitudinal processes.

Tumor and tumor vessel development, as well as tumor response to therapeutics, are highly dynamic biological processes. Histology provides static ...

Microfluidic Co-Culture Models for Dissecting the Immune Response in in vitro Tumor Microenvironments

Complex disease models demand cutting-edge tools able to deliver physiologically and pathologically relevant, actionable insights, and unveil otherwise invisible processes. Advanced cell assays closely mimicking in vivo scenery are establishing themselves as novel ways to visualize and measure the bidirectional tumor-host interplay influencing the progression of cancer. Here we describe two versatile protocols to recreate highly controllable 2D and 3D co-cultures in microdevices, mimicking the complexity of the tumor microenvironment (TME), under natural and therapy-induced immunosurveillance. In section 1, an experimental setting is provided to monitor crosstalk between adherent tumor cells and floating immune populations, by bright field time-lapse microscopy. As an applicative scenario, we analyze the effects of anti-cancer treatments, such as the so-called immunogenic cancer cell death inducers on the recruitment and activation of immune cells. In section 2, 3D tumor-immune microenvironments are assembled in a competitive layout. Differential immune infiltration is monitored by fluorescence snapshots up to 72 h, to evaluate combination therapeutic strategies. In both settings, image processing steps are illustrated to extract a plethora of immune cell parameters (e.g., immune cell migration and interaction, response to therapeutic agents). These simple and powerful methods can be further tailored to simulate the complexity of the TME encompassing the heterogeneity and plasticity of cancer, stromal and immune cells subtypes, as well as their reciprocal interactions as drivers of cancer evolution. The compliance of these rapidly evolving technologies with live-cell high-content imaging can lead to the generation of large informative datasets, bringing forth new challenges. Indeed, the triangle &#39;&#39;co-cultures/microscopy/advanced data analysis&#34; sets the path towards a precise problem parametrization that may assist tailor-made therapeutic protocols. We expect that future integration of cancer-immune on-a-chip with artificial intelligence for high-throughput processing will synergize a large step forward in leveraging the capabilities as predictive and preclinical tools for precision and personalized oncology.

In the age of immunotherapy and single-cell genomic profiling, cancer biology requires novel in vitro and computational tools for investigating the tumor-immune interface in a proper spatiotemporal context. We describe protocols to exploit tumor-immune microfluidic co-cultures in 2D and 3D settings, compatible with dynamic, multiparametric monitoring of cellular functions.

Complex disease models demand cutting-edge tools able to deliver physiologically and pathologically relevant, actionable insights, and unveil otherwise ...

Immunology and Infection

In Vitro and In Vivo Delivery of Magnetic Nanoparticle Hyperthermia Using a Custom-Built Delivery System

Hyperthermia has long been used in the treatment of cancer. Techniques have varied from the intra-tumoral insertion of hot iron rods, to systemically delivered tumor antibody-targeted magnetic nanoparticles, at temperatures from 39 &#730;C (fever-level) to 1,000 &#730;C (electrocautery) and treatment times from seconds to hours. The temperature-time relationship (thermal dose) dictates the effect with high thermal doses resulting in the tissue ablation and lower thermal doses resulting in sublethal effects such as increased blood flow, accumulation of drugs and immune stimulation. One of the most promising current medical therapies is magnetic nanoparticle hyperthermia&#160; (mNPH). This technique involves activating magnetic nanoparticles, that can be delivered systemically or intratumorally, with a non-invasive, non-toxic alternating magnetic field. The size, construct and association of the magnetic nanoparticles and the frequency and field strength of the magnetic field are major heating determinants. We have developed sophisticated instrumentation and techniques for delivering reproducible magnetic nanoparticle hyperthermia in large and small animal models and cultured cells. This approach, using continuous, real time temperature monitoring in multiple locations, allows for the delivery of well-defined thermal doses to the target tissue (tumor) or cells while limiting non-target tissue heating. Precise control and monitoring of temperature, in multiple sites, and use of the industry standard algorithm (cumulative equivalent minutes at 43 &#730;C /CEM43), allows for an accurate determination and quantification of thermal dose. Our system, which allows for a wide variety of temperatures, thermal doses, and biological effects, was developed through a combination of commercial acquisitions and inhouse engineering and biology developments. This system has been optimized in a manner that allows for the rapid conversion between ex vivo, in vitro, and in vivo techniques. The goal of this protocol is to demonstrate how to design, develop and implement an effective technique and system for delivering reproducible and accurate magnetic nanoparticle therapy (mNP) hyperthermia.

This protocol presents techniques and methodology necessary for the accurate delivery of magnetic nanoparticle hyperthermia using a sophisticated delivery and monitoring system.

Hyperthermia has long been used in the treatment of cancer. Techniques have varied from the intra-tumoral insertion of hot iron rods, to systemically ...

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

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