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 border="1" fo:keep-together.within-page="1" fo:keep-with-next.within-page="always">
	<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.&#160;</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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305 Views.  Kansas State University. 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. 

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

Microfluidic Device for Recreating a Tumor Microenvironment in Vitro

We have developed a microfluidic device that mimics the delivery and systemic clearance of drugs to heterogeneous three-dimensional tumor tissues in vitro. Nutrients delivered by vasculature fail to reach all parts of tumors, giving rise to heterogeneous microenvironments consisting of viable, quiescent and necrotic cell types. Many cancer drugs fail to effectively penetrate and treat all types of cells because of this heterogeneity. Monolayers of cancer cells do not mimic this heterogeneity, making it difficult to test cancer drugs with a suitable in vitro model. Our microfluidic devices were fabricated out of PDMS using soft lithography. Multicellular tumor spheroids, formed by the hanging drop method, were inserted and constrained into rectangular chambers on the device and maintained with continuous medium perfusion on one side. The rectangular shape of chambers on the device created linear gradients within tissue. Fluorescent stains were used to quantify the variability in apoptosis within tissue. Tumors on the device were treated with the fluorescent chemotherapeutic drug doxorubicin, time-lapse microscopy was used to monitor its diffusion into tissue, and the effective diffusion coefficient was estimated. The hanging drop method allowed quick formation of uniform spheroids from several cancer cell lines. The device enabled growth of spheroids for up to 3 days. Cells in proximity of flowing medium were minimally apoptotic and those far from the channel were more apoptotic, thereby accurately mimicking regions in tumors adjacent to blood vessels. The estimated value of the doxorubicin diffusion coefficient agreed with a previously reported value in human breast cancer. Because the penetration and retention of drugs in solid tumors affects their efficacy, we believe that this device is an important tool in understanding the behavior of drugs, and developing new cancer therapeutics.

Microfluidic Device for Recreating a Tumor Microenvironment in Vitro

We present the procedure for fabrication and operation of a microfluidic device that recreates heterogeneous tumor microenvironments in vitro. The variability in apoptosis within tumor tissue was quantified using fluorescent stains and the effective diffusion coefficient of the chemotherapeutic drug doxorubicin into tumor tissue was evaluated.

We have developed a microfluidic device that mimics the delivery and systemic clearance of drugs to heterogeneous three-dimensional tumor tissues in ...

Design of a Cyclic Pressure Bioreactor for the Ex Vivo Study of Aortic Heart Valves

The aortic valve, located between the left ventricle and the aorta, allows for unidirectional blood flow, preventing backflow into the ventricle. Aortic valve leaflets are composed of interstitial cells suspended within an extracellular matrix (ECM) and are lined with an endothelial cell monolayer. The valve withstands a harsh, dynamic environment and is constantly exposed to shear, flexion, tension, and compression. Research has shown calcific lesions in diseased valves occur in areas of high mechanical stress as a result of endothelial disruption or interstitial matrix damage1-3. Hence, it is not surprising that epidemiological studies have shown high blood pressure to be a leading risk factor in the onset of aortic valve disease4. 
The only treatment option currently available for valve disease is surgical replacement of the diseased valve with a bioprosthetic or mechanical valve5. Improved understanding of valve biology in response to physical stresses would help elucidate the mechanisms of valve pathogenesis. In turn, this could help in the development of non-invasive therapies such as pharmaceutical intervention or prevention. Several bioreactors have been previously developed to study the mechanobiology of native or engineered heart valves6-9. Pulsatile bioreactors have also been developed to study a range of tissues including cartilage10, bone11 and bladder12. The aim of this work was to develop a cyclic pressure system that could be used to elucidate the biological response of aortic valve leaflets to increased pressure loads. 
The system consisted of an acrylic chamber in which to place samples and produce cyclic pressure, viton diaphragm solenoid valves to control the timing of the pressure cycle, and a computer to control electrical devices. The pressure was monitored using a pressure transducer, and the signal was conditioned using a load cell conditioner. A LabVIEW program regulated the pressure using an analog device to pump compressed air into the system at the appropriate rate. The system mimicked the dynamic transvalvular pressure levels associated with the aortic valve; a saw tooth wave produced a gradual increase in pressure, typical of the transvalvular pressure gradient that is present across the valve during diastole, followed by a sharp pressure drop depicting valve opening in systole. The LabVIEW program allowed users to control the magnitude and frequency of cyclic pressure. The system was able to subject tissue samples to physiological and pathological pressure conditions. This device can be used to increase our understanding of how heart valves respond to changes in the local mechanical environment.

Design of a Cyclic Pressure Bioreactor for the Ex Vivo Study of Aortic Heart Valves

A cyclic pressure bioreactor capable of subjecting heart valve tissue to physiological and pathological pressure conditions has been designed. A LabVIEW program allows users to control pressure magnitude, amplitude and frequency. This device can be used to study the mechanobiology of heart valve tissue or isolated cells.

The aortic valve, located between the left ventricle and the aorta, allows for unidirectional blood flow, preventing backflow into the ventricle. Aortic ...

A Cre-Lox P Recombination Approach for the Detection of Cell Fusion In Vivo

The ability of two or more cells of the same type to fuse has been utilized in metazoans throughout evolution to form many complex organs, including skeletal muscle, bone and placenta. Contemporary studies demonstrate fusion of cells of the same type confers enhanced function. For example, when the trophoblast cells of the placenta fuse to form the syncytiotrophoblast, the syncytiotrophoblast is better able to transport nutrients and hormones across the maternal-fetal barrier than unfused trophoblasts1-4. More recent studies demonstrate fusion of cells of different types can direct cell fate. The "reversion" or modification of cell fate by fusion was once thought to be limited to cell culture systems. But the advent of stem cell transplantation led to the discovery by us and others that stem cells can fuse with somatic cells in vivo and that fusion facilitates stem cell differentiation5-7. Thus, cell fusion is a regulated process capable of promoting cell survival and differentiation and thus could be of central importance for development, repair of tissues and even the pathogenesis of disease.
Limiting the study of cell fusion, is lack of appropriate technology to 1) accurately identify fusion products and to 2) track fusion products over time. Here we present a novel approach to address both limitations via induction of bioluminescence upon fusion (Figure 1); bioluminescence can be detected with high sensitivity in vivo8-15. We utilize a construct encoding the firefly luciferase (Photinus pyralis) gene placed adjacent to a stop codon flanked by LoxP sequences. When cells expressing this gene fuse with cells expressing the Cre recombinase protein, the LoxP sites are cleaved and the stop signal is excised allowing transcription of luciferase. Because the signal is inducible, the incidence of false-positive signals is very low. Unlike existing methods which utilize the Cre/LoxP system16, 17, we have incorporated a "living" detection signal and thereby afford for the first time the opportunity to track the kinetics of cell fusion in vivo.
To demonstrate the approach, mice ubiquitously expressing Cre recombinase served as recipients of stem cells transfected with a construct to express luciferase downstream of a floxed stop codon. Stem cells were transplanted via intramyocardial injection and after transplantation intravital image analysis was conducted to track the presence of fusion products in the heart and surrounding tissues over time. This approach could be adapted to analyze cell fusion in any tissue type at any stage of development, disease or adult tissue repair.

A Cre-Lox P Recombination Approach for the Detection of Cell Fusion In Vivo

A method to track cell fusion in living organisms over time is described. The approach utilizes Cre-LoxP recombination to induce luciferase expression upon cell fusion. The luminescent signal generated can be detected in living organisms using biophotonic imaging systems with a sensitivity of detection of &tilde;1,000 cells in peripheral tissues.

The ability of two or more cells of the same type to fuse has been utilized in metazoans throughout evolution to form many complex organs, including ...

Patient-specific Modeling of the Heart: Estimation of Ventricular Fiber Orientations

Patient-specific simulations of heart (dys)function aimed at personalizing cardiac therapy are hampered by the absence of in vivo imaging technology for clinically acquiring myocardial fiber orientations. The objective of this project was to develop a methodology to estimate cardiac fiber orientations from in vivo images of patient heart geometries. An accurate representation of ventricular geometry and fiber orientations was reconstructed, respectively, from high-resolution ex vivo structural magnetic resonance (MR) and diffusion tensor (DT) MR images of a normal human heart, referred to as the atlas. Ventricular geometry of a patient heart was extracted, via semiautomatic segmentation, from an in vivo computed tomography (CT) image. Using image transformation algorithms, the atlas ventricular geometry was deformed to match that of the patient. Finally, the deformation field was applied to the atlas fiber orientations to obtain an estimate of patient fiber orientations. The accuracy of the fiber estimates was assessed using six normal and three failing canine hearts. The mean absolute difference between inclination angles of acquired and estimated fiber orientations was 15.4 &deg;. Computational simulations of ventricular activation maps and pseudo-ECGs in sinus rhythm and ventricular tachycardia indicated that there are no significant differences between estimated and acquired fiber orientations at a clinically observable level.The new insights obtained from the project will pave the way for the development of patient-specific models of the heart that can aid physicians in personalized diagnosis and decisions regarding electrophysiological interventions.

A methodology to estimate ventricular fiber orientations from in vivo images of patient heart geometries for personalized modeling is described. Validation of the methodology performed using normal and failing canine hearts demonstrate that that there are no significant differences between estimated and acquired fiber orientations at a clinically observable level.

Patient-specific  simulations of heart (dys)function aimed at personalizing cardiac therapy are hampered  by the absence of in vivo imaging technology for ...

Tissue Engineering of Tumor Stromal Microenvironment with Application to Cancer Cell Invasion

3D organotypic cultures of epithelial cells on a matrix embedded with mesenchymal cells are widely used to study epithelial cell differentiation and invasion. Rat tail type I collagen and/or matrix derived from Engelbreth-Holm-Swarm mouse sarcoma cells have been traditionally employed as the substrates to model the matrix or stromal microenvironment into which mesenchymal cells (usually fibroblasts) are populated. Although experiments using such matrices are very informative, it can be argued that due to an overriding presence of a single protein (such as in type I Collagen) or a high content of basement membrane components and growth factors (such as in matrix derived from mouse sarcoma cells), these substrates do not best reflect the contribution to matrix composition made by the stromal cells themselves. To study native matrices produced by primary dermal fibroblasts isolated from patients with a tumor prone, genetic blistering disorder (recessive dystrophic epidermolysis bullosa), we have adapted an existing native matrix protocol to study tumor cell invasion. Fibroblasts are induced to produce their own matrix over a prolonged period in culture. This native matrix is then detached from the culture dish and epithelial cells are seeded onto it before the entire coculture is raised to the air-liquid interface. Cellular differentiation and/or invasion can then be assessed over time. This technique provides the ability to assess epithelial-mesenchymal cell interactions in a 3D setting without the need for a synthetic or foreign matrix with the only disadvantage being the prolonged period of time required to produce the native matrix. Here we describe the application of this technique to assess the ability of a single molecule expressed by fibroblasts, type VII collagen, to inhibit tumor cell invasion.

Tissue engineered fibroblast-derived native matrix is an emerging tool to generate a stromal substrate which supports epithelial cell proliferation and differentiation. Here a protocol applying this methodology to assess the impact of different stromal cell types on tumor cell biology is presented.

3D organotypic cultures of epithelial cells on a matrix embedded with mesenchymal cells are widely used to study epithelial cell differentiation and ...

Optimizing Attachment of Human Mesenchymal Stem Cells on Poly(&#949;-caprolactone) Electrospun Yarns

Research into biomaterials and tissue engineering often includes cell-based in vitro investigations, which require initial knowledge of the starting cell number. While researchers commonly reference their seeding density this does not necessarily indicate the actual number of cells that have adhered to the material in question. This is particularly the case for materials, or scaffolds, that do not cover the base of standard cell culture well plates. This study investigates the initial attachment of human mesenchymal stem cells seeded at a known number onto electrospun poly(&#949;-caprolactone) yarn after 4 hr in culture. Electrospun yarns were held within several different set-ups, including bioreactor vessels rotating at 9 rpm, cell culture inserts positioned in low binding well plates and polytetrafluoroethylene (PTFE) troughs placed within petri dishes. The latter two were subjected to either static conditions or positioned on a shaker plate (30 rpm). After 4 hr incubation at 37&#160;oC, 5% CO2, the location of seeded cells was determined by cell DNA assay. Scaffolds were removed from their containers and placed in lysis buffer. The media fraction was similarly removed and centrifuged &#8211; the supernatant discarded and pellet broken up with lysis buffer. Lysis buffer was added to each receptacle, or well, and scraped to free any cells that may be present. The cell DNA assay determined the percentage of cells present within the scaffold, media and well fractions. Cell attachment was low for all experimental set-ups, with greatest attachment (30%) for yarns held within cell culture inserts and subjected to shaking motion. This study raises awareness to the actual number of cells attaching to scaffolds irrespective of the stated cell seeding density.

This article describes a range of set-ups for seeding human mesenchymal stem cells onto materials, in this case electrospun yarns, that do not cover the base of standard culture well plates in order to maximize and quantify the number of cells that initially attach compared to the known seeding density.

Research into biomaterials and tissue engineering often includes cell-based in vitro investigations, which require initial knowledge of the starting cell ...

Concentric Gel System to Study the Biophysical Role of Matrix Microenvironment on 3D Cell Migration

The ability of cells to migrate is crucial in a wide variety of cell functions throughout life&#160;from embryonic development and wound healing&#160;to tumor and cancer metastasis. Despite intense research efforts, the basic biochemical and biophysical principles of cell migration are still not fully understood, especially in the physiologically relevant three-dimensional (3D) microenvironments. Here, we describe an in vitro assay designed to allow quantitative examination of 3D cell migration behaviors. The method exploits the cell&#8217;s mechanosensing ability and propensity to migrate into previously unoccupied extracellular matrix (ECM). We use the invasion of highly invasive breast cancer cells, MDA-MB-231, in collagen gels as a model system. The spread of cell population and the migration dynamics of individual cells over weeks of culture can be monitored using live-cell imaging and analyzed to extract spatiotemporally-resolved data. Furthermore, the method is easily adaptable for diverse extracellular matrices, thus offering a simple yet powerful way to investigate the role of biophysical factors in the microenvironment on cell migration.

The mechanical properties and microstructure of the extracellular matrix strongly affect 3D migration of cells. An in vitro method to study the spatiotemporal cell migration behavior in biophysically variable environments, at both population and individual cell levels, is described.

The ability of cells to migrate is crucial in a wide variety of cell functions throughout life&#160;from embryonic development and wound healing&#160;to ...

PIP-on-a-chip: A Label-free Study of Protein-phosphoinositide Interactions

Numerous cellular proteins interact with membrane surfaces to affect essential cellular processes. These interactions can be directed towards a specific lipid component within a membrane, as in the case of phosphoinositides (PIPs), to ensure specific subcellular localization and/or activation. PIPs and cellular PIP-binding domains have been studied extensively to better understand their role in cellular physiology. We applied a pH modulation assay on supported lipid bilayers (SLBs) as a tool to study protein-PIP interactions. In these studies, pH sensitive ortho-Sulforhodamine B conjugated phosphatidylethanolamine is used to detect protein-PIP interactions. Upon binding of a protein to a PIP-containing membrane surface, the interfacial potential is modulated (i.e. change in local pH), shifting the protonation state of the probe. A case study of the successful usage of the pH modulation assay is presented by using phospholipase C delta1 Pleckstrin Homology (PLC-&#948;1 PH) domain and phosphatidylinositol 4,5-bisphosphate (PI(4,5)P2) interaction as an example. The apparent dissociation constant (Kd,app) for this interaction was 0.39 &#177; 0.05 &#181;M, similar to Kd,app values obtained by others. As previously observed, the PLC-&#948;1 PH domain is PI(4,5)P2 specific, shows weaker binding towards phosphatidylinositol 4-phosphate, and no binding to pure phosphatidylcholine SLBs. The PIP-on-a-chip assay is advantageous over traditional PIP-binding assays, including but not limited to low sample volume and no ligand/receptor labeling requirements, the ability to test high- and low-affinity membrane interactions with both small and large molecules, and improved signal to noise ratio. Accordingly, the usage of the PIP-on-a-chip approach will facilitate the elucidation of mechanisms of a wide range of membrane interactions. Furthermore, this method could potentially be used in identifying therapeutics that modulate protein&#39;s capacity to interact with membranes.

Here we present a supported lipid bilayer in the context of a microfluidic platform to study protein-phosphoinositide interactions using a label-free method based on pH modulation.

Numerous cellular proteins interact with membrane surfaces to affect essential cellular processes. These interactions can be directed towards a specific ...

Workflow Based on the Combination of Isotopic Tracer Experiments to Investigate Microbial Metabolism of Multiple Nutrient Sources

Studies in the field of microbiology rely on the implementation of a wide range of methodologies. In particular, the development of appropriate methods substantially contributes to providing extensive knowledge of the metabolism of microorganisms growing in chemically defined media containing unique nitrogen and carbon sources. In contrast, the management through metabolism of multiple nutrient sources, despite their broad presence in natural or industrial environments, remains virtually unexplored. This situation is mainly due to the lack of suitable methodologies, which hinders investigations.
We report an experimental strategy to quantitatively and comprehensively explore how metabolism operates when a nutrient is provided as a mixture of different molecules, i.e., a complex resource. Here, we describe its application for assessing the partitioning of multiple nitrogen sources through the yeast metabolic network. The workflow combines information obtained during stable isotope tracer experiments using selected 13C- or 15N-labeled substrates. It first consists of parallel and reproducible fermentations in the same medium, which includes a mixture of N-containing molecules; however,a selected nitrogen source is labeled each time. A combination of analytical procedures (HPLC, GC-MS) is implemented to assess the labeling patterns of targeted compounds and to quantify the consumption and recovery of substrates in other metabolites. An integrated analysis of the complete dataset provides an overview of the fate of consumed substrates within cells. This approach requires an accurate protocol for the collection of samples&#8211;facilitated by a robot-assisted system for online monitoring of fermentations&#8211;and the achievement of numerous time-consuming analyses. Despite these constraints, it allowed understanding, for the first time, the partitioning of multiple nitrogen sources throughout the yeast metabolic network. We elucidated the redistribution of nitrogen from more abundant sources toward other N-compounds and determined the metabolic origins of volatile molecules and proteinogenic amino acids.

This protocol describes an experimental procedure to quantitatively and comprehensively investigate the metabolism of multiple nutrient sources. This workflow, based on a combination of isotopic tracer experiments and an analytical procedure, allows the fate of consumed nutrients and the metabolic origin of molecules synthetized by microorganisms to be determined.

Studies in the field of microbiology rely on the implementation of a wide range of methodologies. In particular, the development of appropriate methods ...

Calorespirometry: A Powerful, Noninvasive Approach to Investigate Cellular Energy Metabolism

Many cell lines used in basic biological and biomedical research maintain energy homeostasis through a combination of both aerobic and anaerobic respiration. However, the extent to which both pathways contribute to the landscape of cellular energy production is consistently overlooked. Transformed cells cultured in saturating levels of glucose often show a decreased dependency on oxidative phosphorylation for ATP production, which is compensated by an increase in substrate-level phosphorylation. This shift in metabolic poise allows cells to proliferate despite the presence of mitochondrial toxins. In neglecting the altered metabolic poise of transformed cells, results from a pharmaceutical screening may be misinterpreted since the potentially mitotoxic effects may not be detected using model cell lines cultured in the presence of high glucose concentrations. This protocol describes the pairing of two powerful techniques, respirometry and calorimetry, which allows for the quantitative and noninvasive assessment of both aerobic and anaerobic contributions to cellular ATP production. Both aerobic and anaerobic respirations generate heat, which can be monitored via calorimetry. Meanwhile, measuring the rate of oxygen consumption can assess the extent of aerobic respiration. When both heat dissipation and oxygen consumption are measured simultaneously, the calorespirometric ratio can be determined. The experimentally obtained value can then be compared to the theoretical oxycaloric equivalent and the extent of the anaerobic respiration can be judged. Thus, calorespirometry provides a unique method to analyze a wide range of biological questions, including drug development, microbial growth, and fundamental bioenergetics under both normoxic and hypoxic conditions.

This protocol describes calorespirometry, the direct and simultaneous measurement of both heat dissipation and respiration, which provides a noninvasive approach to assess energy metabolism. This technique is used to assess the contribution of both aerobic and anaerobic pathways to energy utilization by monitoring the total cellular energy flow.