Computational modeling of the thermal effects of flow on radio frequency-induced heating of peripheral vascular stents during MRI

Purpose. The goal of this study was to develop and validate a computational model that can accurately predict the influence of flow on the temperature rise near a peripheral vascular stent during magnetic resonance imaging (MRI). Methods. Computational modeling and simulation of radio frequency (RF) induced heating of a vascular stent during MRI at 3.0 T was developed and validated with flow phantom experiments. The maximum temperature rise of the stent was measured as a function of physiologically relevant flow rates. Results. A significant difference was not identified between the experiment and simulation (P > 0.05). The temperature rise of the stent during MRI was over 10 °C without flow, and was reduced by 5 °C with a flow rate of only 58 ml min−1, corresponding to a reduction of CEM43 from 45 min to less than 1 min. Conclusion. The computer model developed in this study was validated with experimental measurements, and accurately predicted the influence of flow on the RF-induced temperature rise of a vascular stent during MRI. Furthermore, the results of this study demonstrate that relatively low flow rates significantly reduce the temperature rise of a stent and the surrounding medium during RF-induced heating under typical scanning power and physiologically relevant conditions.


Introduction
Magnetic resonance imaging (MRI) is widely regarded as a safe technology, but there are unique risks for patients with implanted medical devices, including peripheral vascular stents.These magnetic resonance (MR) safety concerns include magnetically induced displacement force, magnetically induced torque, and radio frequency (RF) induced heating (Woods 2007).There are many material considerations during the design of medical devices that can help improve the MRI safety and visibility of tissue near implanted medical devices (Griebel et al 2023), (Mödinger et al 2023).With respect to RF-induced heating, shorter coronary stents are generally considered safe for MRI (Winter et al 2015), (Santoro et al 2012), (Shellock and Forder 2005), (Levine et al 2007), (Ahmed and Shellock 2001), in contrast to typically longer peripheral vascular stents which may approximate the 3.0 T resonant wavelength (9 cm), and when overlapped they can even reach the 1.5 T resonant wavelength (18 cm) (Yeung et al 2002).Therefore, there is a legitimate concern for RF-induced heating of peripheral vascular stents during routine clinical MRI scans.There is a growing number of patients implanted with these devices, with an estimated 800,000 interventional procedures involving peripheral vascular stents performed in the United States each year (MedSuite 2020).As the number of patients implanted with peripheral vascular stents increases, it is important to consider the safety of these patients when they are clinically indicated for MRI procedures.
Medical device manufacturers use a standard test method, ASTM F2182, to evaluate RF-induced heating of implantable devices for subsequent MR safety labeling (ASTM International 2020).This standard test method uses a static gel phantom that does not account for physiologic cooling mechanisms such as blood flow and perfusion, and therefore may produce overly conservative temperature measurements.These conservative test results have been reported in the labeling of medical devices and could unnecessarily restrict the MRI procedures (e.g.field strength, SAR, length of scan, and zone restrictions for imaging the patient) or may cause some patients to be unnecessarily excluded from MRI procedures altogether.Given many devices have yet to be tested and labeled regarding MRI safety, and current physical testing does not address physiological conditions, appropriate computational modeling is best suited to address these needs with higher quality and reliability at a lower cost.
When electrically conductive materials are subjected to a time-varying magnetic field, electric currents are induced according to Faraday's Law of Induction.These electric currents can cause the temperature to increase in the tissue surrounding the medical device, potentially damaging the tissue (van Rhoon et al 2013).Furthermore, electrically conductive materials (i.e., metallic implants) in a dielectric medium couple with the electric field.This is known as the antenna effect with oscillating currents that can result in a concentration of the electric field near the metallic implant that can cause tissue heating (Acikel and Atalar 2011), (Reiss et al 2021).The extent of reversible or irreversible tissue changes that result from the application of thermal energy is a function of many factors, including tissue sensitivity, temperature, and exposure time (Dewhirst et al 2003), (Pearce 2013).The rate of tissue change can be modeled as a first-order rate process of tissue moving from a natured state N, over an energy of activation barrier Ea, to a denatured state D, at a rate A, over time t governed by the Arrhenius relationship: where R is the universal gas constant and T is temperature (Kahn and Busse 2012).A commonly used threshold of Ω 1 (unitless) may be indicative of irreversible tissue change.Studies have shown that at 42.5 °C cell death occurs in most tissues within 240 min, and the rate of cell death approximately doubles for every degree Centigrade above 43 °C (Yarmolenko et al 2011).This breakpoint at 43 °C (i.e., 6.0 °C above normal human body temperature) is used to extend this Arrhenius model to quantify tissue change, in a nonlinear fashion, in terms of the cumulative equivalent minutes spent at 43 °C (CEM 43 ): Therefore, it is important that any evaluation of the potential for RF-induced heating and tissue damage consider both the time of exposure and temperature.
Previous studies have focused on RF-induced heating of coronary stents in vitro (Shellock and Forder 2005), (Jost and Kumar 1998), (Strohm et al 1999)

Materials and methods
A computational model was developed to evaluate the thermal effects of flow on RF-induced heating of a peripheral vascular stent using COMSOL Multiphysics ® and validated with experimental measurements with a flow phantom in a clinical MRI system.

Computational model
The COMSOL Multiphysics finite element software was used to solve the sequentially coupled electromagnetics, fluid dynamics, and transient heat transfer of RF-induced heating of a stent with varied volumetric flow rates.The three physics nodes used in COMSOL were radio frequency electromagnetic waves, laminar flow, and heat transfer in solids and fluids.
The stationary full-field electromagnetic response of the RF coil was solved using the wave equation, which is derived from Maxwell's equations, and describes the propagation of electromagnetic waves through a medium: where E is the electric field, μr is the relative magnetic permeability, ko is the initial wave vector, μr is the magnetic permeability, εr is the relative permittivity, σ is the electrical conductivity, Ω is the angular frequency and εo is the permittivity of free space (Maxwell 1865), (Tipler and Mosca 2004).Implanted metallic devices (e.g., stents, guide wires, pacemaker leads, etc.) alter the electric field distribution and concentrate the electric field at the opposing ends of the device.The overall length of these types of devices plays a major role in the total amplitude of the induced temperature rise.The maximum potential for heating occurs when the length of the conductive object is between the quarter and half RF wavelength in the surrounding medium.The wavelength of the radio frequency waves can be described as: ( ) where λ is the wavelength, Ω is the angular frequency, μ is the magnetic permeability of the medium, ε is the permittivity of the medium and σ is the electrical conductivity of the medium (Yeung et al 2002).The transient heat transfer in solids is solved using the heat equation derived from Fourier's law and conservation of energy: where r is the density of the gel, cp is the specific heat capacity of the gel, T is the temperature in the gel, t is the time, k is the thermal conductivity of the gel and Q is the heat source term (Cannon 1984).The gel is a viscous material therefore the assumption is that convective heat transfer is prevented.The source term, Q, is the density of the gel multiplied by the Specific Absorption Rate (SAR) from the electromagnetic field: where σ is the electrical conductivity of the gel, E is the rms value of the electric field and r is the density of the gel (Jin 1998).The electric field distribution is simulated with the device in the phantom, rather than relying on the incident electric field (i.e., the background electric field distribution with the device is not in the phantom).The heat transfer in fluids is solved using the same heat equation with the addition of a convective flow term.
where r is the density of the fluid, cp is the specific heat capacity of the fluid, T is the temperature in the fluid and u is the fluid velocity field.The laminar flow is modeled as incompressible flow without turbulence, and a no slip wall boundary condition: where r is the fluid density, u is the fluid velocity, p is the pressure, I is the identity tensor, μ is the dynamic viscosity, T is the total stress tensor for the Newtonian fluid, and F is the resultant force (Incropera and Lavine 2011).
The domains, initial values, and boundary conditions for each of the physics are described in table 1.The 3.0 T Siemens Tim Trio RF body coil used in the flow phantom experiment was modeled with quadrature excitation of two voltage ports, appropriate distribution of capacitors, and 16 legs according to proprietary information provided by the MR manufacturer.The RF body coil and shield were assumed to be contained in a sphere of air and modeled with Perfect Electrical Conductor (PEC) boundaries.The RF coil was tuned to resonance at approximately 123 MHz, providing a circularly polarized magnetic field with uniform distribution at isocenter (Jin 2002).Experimental measurements of the temperature rise of a 10 cm long Titanium calibration rod were obtained according to the methods described in ASTM F2182 (ASTM International 2020).A computational model matching the setup of the experiment (i.e., 10 cm Ti rod in the gel phantom) was used to calibrate the voltage ports of the RF coil model to match the experimentally measured temperature rise of the 10 cm calibration rod.
The gel phantom was modeled as 65 cm long, 42 cm wide, and 9 cm deep and centered in the headfoot and left-to-right directions, and the top surface of the phantom was 8.25 cm below isocenter.A Zilver 635 ® Vascular Self-Expanding Stent (Cook Medical Inc., Bloomington, Indiana) with dimensions 10 mm × 95 mm (diameter × length), was modeled at isocenter in the head-foot direction, and offset 19.5 cm to the left, and 12.75 cm below isocenter, matching the experimental conditions described below.The stent geometry was modeled with linear PEC edge segments, without radii at the intersecting struts, on the surface of the flow channel without modeling the thickness of the thin-walled silicone tube.The stent geometry and the domain point probe used to report the temperature measurements (red square) in the simulation are shown in figure 1.The domain point probe was positioned in the static gel near the interface of the PEC stent and the flow channel to match the position of the temperature probe in the physical experiment.The position of the numerical point probe and the temperature probe from the physical experiment are near the point of maximum heating.However, for the purpose of this study, it was more important that the numerical point probe and the temperature probe from the physical experiment positions match.It was not necessary to confirm the global maximum temperature rise since the simulation point probe was being compared to the physical temperature probe measurement and there was sufficient dynamic range to make such a comparison.The thermal and electrical material properties for the air, fluid, and gelled saline domains are listed in table 2. The three-dimensional domains were meshed with tetrahedral elements and triangular elements were used to mesh the RF coil, shield, and flow channel boundaries.The total domain, boundary, and edge elements in the mesh were 626,760, 52,303, and 7,521, respectively.The mesh size varied with an increased mesh density in the phantom and a coarse mesh in the air domains.The final computer simulation solved for 3.9 million degrees of freedom in the electromagnetics physics, 132,000 degrees of freedom in the computational fluid dynamics physics, and approximately 664,000 degrees of freedom in the heat transfer physics.A 64-bit Mac-Book Pro laptop with a 3 GHz Intel Core i7 processor and 16 GB RAM was used for the computer simulations.The average run-time for all the simulations was 34 min.

Experimental model
The RF-induced heating experiments were conducted using a 3.0 T Siemens Tim Trio MR system operating at a frequency of approximately 123 MHz.A plastic container (i.e., the phantom) was constructed according to the ASTM F2182 standard, with interior dimensions of 65 cm long, 42 cm wide, and 19 cm deep.A gelled saline was prepared according to the ASTM F2182 standard with 25 l of distilled water mixed with 1.32 g l −1 NaCl and 10 g l −1 polyacrylic acid (PAA).The electrical and thermal properties of the gel mimic average human tissue with an electrical conductivity (σ) at room temperature of 0.47 ± 10% S/m, a relative electric permittivity (εr) of 80, a thermal diffusivity (α) of • ´- approximately 1.3 ×10 -7 m 2 s −1 , and a heat capacity (cp) of 4150 J kg −1 °C−1 (ASTM International 2020).The viscosity of the gel prevents bulk transport or convective heat transport.The phantom was retrofitted with a flow channel using Masterflex ® L/S ® 18 (Cole-Parmer, Vernon Hills, Illinois) silicone tubing with an inner and outer diameter of 7.9 mm and 11 mm, respectively.Matching the simulation, a Zilver 635 ® Vascular Self-Expanding Stent (Cook Medical Inc., Bloomington, Indiana), 10 mm × 80 mm (diameter × length), was positioned on the exterior of a thin-walled silicone tube (< 1 mm wall thickness) with an outer diameter of 10 mm and connected in-line with the Masterflex L/S 18 silicone tubing.The stent was deployed on the exterior of the thin-walled silicone tube so that it would be in electrical contact with the gel; the magnitude of heating would potentially be reduced if the stent was deployed inside the silicone tube due to the electromagnetic insulating properties of the silicone.The stent lengthened to 95 mm during deployment on the flow channel.
The flow channel was positioned 1 cm from the bottom depth of the phantom and connected with barbed fittings through the sidewalls along the 65 cm dimension of the phantom and approximately 1 cm from the left sidewall.Silicone tubing was routed from the MR equipment room through an RF waveguide and connected to the inlet and outlet of the phantom flow channel.A Masterflex L/S peristaltic pump was used to circulate room-temperature water from a reservoir through the silicone tubing at controlled flow rates.Temperature measurements were recorded using a fiber optic probe system, Luxtron FOT Lab Kit (LumaSense Technologies, Inc., Santa Clara, California), with two STF type probes that take measurements at a frequency of 1 Hz with an accuracy of ±0.2 °C within 20 °C of the calibration temperature (37 °C).One temperature probe was placed within 2 mm of the proximal end of the stent, between the stent and the thin-walled silicone tubing.A second temperature probe was located in the fluid reservoir.The phantom was filled with gel to a depth of 9 cm and positioned on the patient table of the MR system without the spine coil and landmarked along the midlength of the stent and phantom.A schematic of the equipment used in the experiments is shown in figure 2.
A photograph of the experimental setup of the flow phantom on the patient table of the MRI system is shown in figure 3.
The phantom was registered on the MR system as a 158 lb, 5'5' female in the head first-supine position, according to the recommended MR test system parameters listed in ASTM F2182.The RF body coil of the MR system was used to transmit and receive the RF signal.A turbo spin echo sequence was used for the RF-induced heating experiments with a refocusing flip angle of 130°, TR/TE = 269/11 ms, TA = 450 s, turbo factor of 4, and a console reported whole-body Specific Absorption Rate (SAR) of approximately 5.5 W kg −1 achieved by overriding the system SAR monitor.Clinical MRI procedures limit the whole body SAR to no greater than 4 W kg −1 , but the SAR was maximized in this study to increase the dynamic range of the temperature measurements.
The Zilver 635 ® Vascular Self-Expanding Stent is used in the treatment of symptomatic vascular disease of the iliac arteries.The common femoral artery, a continuation of the external iliac artery, has a resting mean volumetric flow rate ranging from 300 ml min −1 to 450 ml min −1 in normal subjects (Hobbs and Edwards 1963), (Pentecost 1964), (Folse 1965a), (Folse 1965b), (Strandness and Sumner 1975).The average volumetric flow rate in the phantom was varied from 12 ml min −1 to 2240 ml min −1 for a total of nine different flow rates in addition to the static condition (0 ml/min).Volumetric flow rates were verified in a separate experiment using a graduated cylinder and a stopwatch.The Luxtron temperature recording software and Masterflex pump were initiated prior to each subsequent RF heating experiment.Temperature measurements at each flow rate were repeated at least three times for a total of forty-one RF heating experiments.The maximum temperature rise was averaged for each experiment and the standard deviation was calculated at each flow rate.The temperature was integrated over 450 s of each experiment and used in the CEM 43 .The average and standard deviation were reported at each flow rate.(-) 1 -1 1 a The thermal properties of the air domains were unnecessary for the simulation because the gel phantom was modeled as perfectly insulated.
b The electrical properties of the stent were unnecessary for the simulation because the stent was modeled as a perfect electrical conductor.

Statistical methods
A paired t-test was used to compare the means and standard deviations of the experimental measurements and computational model.The null hypothesis was that the average of the differences between the paired measurements was zero.If the calculated P-value is less than 0.05, then the mean difference between the paired measurements is significantly different from zero.Furthermore, a correlation analysis was used to measure the strength of the linear relationship between the experimental measurements and the computational model.Bland-Altman analyses are commonly used to compare two different clinical techniques to determine if they sufficiently agree (Bland and Altman 1986).Therefore, Bland-Altman analyses were used in this study to assess the difference between the paired computational model and experimental measurement of temperature rise at all flow rates.The mean difference between the two methods of measurement is referred to as the bias.The agreement interval was calculated based on a 95% confidence interval.Additionally, the paired computational model and experimental measurement of temperature over time were used to calculate CEM 43 at all flow rates.

Results
The experiment and simulation of the maximum temperature rise of the stent with respect to the volumetric flow rate of the fluid were in good agreement.The temperature rise of the stent was over 10 °C without flow, and was reduced by 5 °C with a flow rate of only 58 ml min −1 , corresponding to a reduction of CEM 43 from 45 min to less than 1 min.The fluid reservoir temperature remained constant within 1 °C of room temperature for all experiments.Figure 4 shows the experimental measurements and simulation of temperature rise with maximum flow rate (2240 ml min −1 ) and without flow (0 ml/min) at a measured whole phantom SAR of 5 W kg −1 , and temperature contours of the stent and surrounding gel from the simulation.A summary of the experimental measurements and simulation results with the corresponding CEM 43 thermal dose for the 7.5 min scan time are shown in table 3 and figure 5.
The null hypothesis was not rejected and a statistically significant difference was not identified (P = 0.24) between the experimentally measured temperature and the simulated temperature as a function of the volumetric flow rate.The correlation coefficient (r) and the coefficient of determination (R 2 ) were 0.96 and 0.93, respectively.The results of the Bland-Altman analysis of temperature measurements are shown in figure 6.The bias (i.e., mean difference) was 0.13 °C.The upper and lower limits of agreement were 1.21 °C and −1.47 °C, respectively.The majority of the data fall within the limits of agreement, with the exception of three possible outliers.The variability of the data appears to be consistent across the graph.A   Bland-Altman analysis of CEM 43 calculations are shown in figure 7. The bias (i.e.mean difference) was 0.94 min.The upper and lower limits of agreement were 15.7 min and −17.5 min, respectively.The variability of the data appears to be greater at the highest CEM 43 values.

Discussion
In a publication with authors from the Center for Devices and Radiological Health at the U.S. Food and Drug Administration, Fujimoto et al (2018) investigated the use of detailed anatomical models for estimating RF-induced heating of stents during MRI.In this publication, the authors state, 'The in vivo blood vessels have blood perfusion and flow which have significant effect on reducing the RF-induced heating.'Therefore, we sought to develop and validate a computational model that incorporates blood flow to enable a more robust assessment of RF safety for patients with implants.
The authors have verified and validated their computational model through multiple venues across numerous studies.This method solves for the sequentially coupled electromagnetics and transient heat transfer.The intermediate electromagnetic step does not need to be independently validated since temperature is the metric of interest.The authors are unaware of any possibility that the results could 'accidentally match' across all the studies that were performed.The same simulation (without flow) in the study was used as part of round robin simulation comparison for the revision of ASTM F2182.The temperature and electric field results were compared across nine independent laboratories using different simulation tools and different RF coils (Murdock et al 2019).Furthermore, after the completion of this study, the simulation (without flow) was qualified by the United States Food and Drug Administration as part of the Medical   2021).This program allows medical device sponsors to use the MDDT in submissions without the need for physical testing for RF-induced heating.This computational method has been used in numerous device submissions for evaluating the RF-induced heating of  devices to replace the physical testing according to ASTM F2182.The data used to qualify this MDDT used over 34 different types of devices and showed agreement between the temperature rise in the simulation and the experiment.The Bland-Altman analysis of temperature measurements with a mean difference of 0.13 °C indicates very good agreement between the simulation and experiment, considering the accuracy of the fiber optic temperature probe is ±0.20 °C.The upper and lower limits of agreement (1.21 °C and −1.47 °C, respectively) are reasonable considering the temperature uncertainty of the experiment.The two data points above the upper limit of agreement were obtained at the highest flow rate where the dynamic range of the temperature measurement is relatively low.The Bland-Altman analysis of CEM 43 with a mean difference of 0.94 min which indicates very good agreement between the two methods considering the clinical insignificance of 1 CEM 43 min.The upper and lower limits of agreement (15.7 min and −17.5 min, respectively) are reasonable considering the variability of the experiment without flow and the difference in the accumulation of CEM 43 over 7.5 min.The variability of the data is greater at the highest CEM 43 values which is expected due to the cumulative nature of CEM 43 .
A physiologically relevant flow rate of 350 ml min −1 results in a temperature reduction of more than 50% to approximately 4 °C, compared to the 10 °C temperature rise of the static condition (0 ml/min).The results demonstrate that a maximum temperature rise of less than 6 °C (absolute temperature 43 °C in vivo) results in minimal CEM 43 thermal doses.Furthermore, this study did not investigate the influence of capillary blood perfusion in the vessel wall and other tissue surrounding the stent, which would be an important consideration for complete occlusions, or complete restenosis in the stented vessel (Dangas et al 2010).Nyenhuis et al (2015) reported that calculations show that capillary blood perfusion is capable of reducing the temperature rise comparable to blood flow.
Idealizations were made in the simulation concerning the experimental conditions.The computational fluid dynamics were simplified by modeling fully developed laminar flow, as opposed to the pulsatile flow from the peristaltic pump used in the experiment, or physiologic pulsatile flow in patients.Another study has shown that there is a negligible difference between the time-averaged unsteady heat flux due to a pulsating blood velocity and an assumed nonpulsating blood velocity; therefore, it is reasonable to assume fully developed laminar flow in the simulation for the purposes of estimating bioheat transfer (Craciunescu and Clegg 2001).Another study has shown that the heat transfer efficiency of blood is higher than that of water, but the differences between them are not significant, and blood can be regarded as a Newtonian fluid in a steady state (Xie and Zhang 2017).The experiments were performed with room-temperature gel and water.The temperature-dependent material properties of the gel and water are not expected to be significant over the range of room temperature to human body temperature.Therefore, the temperature differences relative to room temperature would be the same relative to body temperature.Additional idealizations implemented in the simulation include the phantom walls modeled as perfectly thermally insulated, and the RF coil, shield, and stent modeled as perfect electrical conductors.Previous studies have shown that these idealizations are reasonable and do not adversely affect the accuracy of the thermal solutions in the simulation (Leewood et al 2013), (Leewood et al 2012).A previous study states that the assumption of laminar and fully developed flow is conservative since hydrodynamic entry length for vessels with diameters greater than 2.5 mm may be comparable to or longer than the total length of single or overlapped stents used clinically.Furthermore, turbulent flow in vessels with diameters over 10 mm could result in further reduced temperature by increasing the interaction between the blood and tissue when compared to laminar flows (Shrivastava 2018).Other potential sources of error include the accuracy of temperature probe placement, uncertainty of the material property values, placement of the gel phantom within the MRI scanner, and accuracy of the fiber optic temperature probes.
The Masterflex peristaltic pump has a manufacturer-reported accuracy of less than 1 ml min −1 , but our independent verification of the flow rate measurements showed that flow rates less than 10 ml min −1 were unreliable and unrepeatable.Therefore, temperature measurements for volumetric flow rates less than 10 ml min −1 were excluded from this study.
The experimental model used temperature measurements via fiber optic probes.The fiber optic probes measure temperature over a small volume and are considered single-point measurements.The spatial positioning of the experimental temperature probes was used in the computational model.The computational model provides three-dimensional temperature distributions that the maximum temperature rise occurs in the gel phantom near the stent.The measurand of the experimental model was temperature, since temperature and time (i.e., thermal dose) are the primary parameters related to patient safety with regards to RF-induced heating of implants during MRI.Intermediate parameters, such as local SAR, were not compared between the experimental and computational models.
The same experimental setup without the flow channel (i.e. the ASTM F2182 phantom) was previously used to evaluate RF heating of the same stent at the same location in the ASTM phantom (Gross and Simonetti 2015).The maximum temperature rise of the stent without the flow channel was 8 °C after 7.5 min at an MR console-reported whole-body SAR of 2 W kg −1 .All else equal, the maximum temperature rise of the stent linearly scales with SAR over the range of achievable values (0-5.5 W kg −1 ), therefore at a SAR of 5.5 W kg −1 a maximum temperature rise of the stent without the flow channel would be 22 °C.In general, scanner-reported SAR cannot be used to make reliable comparisons across different MRI scanners (El-Sharkway et al 2012).The MRI console reported whole body average SAR was not used to calibrate the computational model.The discrepancy between the maximum temperature rise of 10.5 °C with the flow channel (shown in this study) and 22 °C without the flow channel (Gross and Simonetti 2015) appear to be unknown at the time of this publication and such differences could be due to the different boundary conditions around the stent and possibly a difference in the electromagnetic field exposure between the two studies.The silicone flow channel displaces gel from the lumen of the stent and the electrical conductivity of the water inside the flow channel and the silicone itself is several orders of magnitude less than the displaced gel, which could potentially explain the decreased temperature rise of the stent in the presence of the flow channel.This limitation does not impact the validity of the experiments or the ability to compare relative changes in temperature with respect to volumetric flow rates.
The results of this study should also apply to overlapped stents.Similar work by the FDA identified a potentially overlooked clinical scenario, where overlapped stents are separated with a layer of insulation which can affect the location and magnitude of temperature rise near the stent (Serano et al 2016).
Multiple sources in the literature have cited the significant thermal cooling effects of blood flow on RF-induced heating of coronary stents (Elder 2013), (Nyenhuis et al 2015), peripheral vascular stents (Visaria and Shrivastava 2013), and generalized stents (Shrivastava 2018).Elder (2013) and Nyenhuis et al (2015) studied the thermal effects of blood flow on RFinduced heating of coronary stents with experimental measurements and calculations.They observed a temperature reduction of more than 60% for a volumetric flow rate of only 4 ml min −1 .Klocke (1976) reported that coronary artery stenoses of less than 90% maintain normal resting coronary flow of 100 ml min −1 .This suggests that even under conditions of severe coronary stenosis the overwhelming thermal effect of even relatively low volumetric flow rates could dramatically reduce RF-induced heating during MRI.However, this potential temperature reduction may be impacted by the shape and size of the stenoses since they could change the blood flow pattern and affect the ability of the flow to be in direct contact with the stent.In a recent study without experimental validation, simulation of RF-induced heating of a peripheral vascular stent predicted a temperature reduction from 10 °C without flow to less than 3 °C with a volumetric flow rate of 3% of the normal physiological flow rate (Visaria and Shrivastava 2013).The Zilver Vascular Stent used in this study is indicated for use in the iliac artery.The physiologic flow rate in the external iliac artery of normal individuals at rest is approximately 350 ml min −1 (Strandness and Sumner 1975).Shrivastava (2018) found that stent heating is reduced by 80% or more when the stent diameter is greater than 15 mm and the flow rate is at least 25% of the mean physiological flow without restenosis.The diameters varied from 1 mm to 30 mm, lengths from 25 mm to 300 mm, and considered normal and reduced (i.e., 25%) physiological flow rates for zero restenosis and 75% restenosis.Notably, a 'standing wave' assumption was used does not include the electromagnetic simulation of a radiofrequency coil and does not include any experimental measurements.Furthermore, the stent geometry and stent material properties were not modeled.

Conclusions
The computational model developed in this study was validated with experimental measurements and accurately predicts the influence of flow on the RF-induced temperature rise of a vascular stent during MRI.As expected, the results of this study demonstrate that flow significantly reduces the temperature rise of a stent and the surrounding medium during RFinduced heating, and therefore should be considered in the MR safety evaluation of vascular medical devices.A temperature reduction of more than 50% was observed for a flow rate of less than 20% of the expected physiological flow rate.By accounting for the thermal effects of flow, the maximum temperature rise and CEM 43 thermal dose were not concerning when compared to the relatively high maximum temperature rise and CEM 43 thermal dose without flow.A maximum temperature rise of less than 6 °C over a 15minute MRI scan results in a minimal CEM 43 thermal dose.This research will support the future utilization of advanced simulation tools that incorporate physiological flow rates in the assessment of the MR safety of medical devices implanted in the vasculature.
tissue thermal sensitivity, T is the average temperature during Δt, which is the time spent at temperature T in minutes (van Rhoon et al 2013), (Sapareto and Dewey 1984), (Yung et al 2010).The CEM 43 thermal dose concept was introduced in the 1970s to quantify the effects of tumor hyperthermia and was initially based on cell survival data for Chinese Hamster Ovary (CHO) cells (Sapareto and Dewey 1984), (Dewey 2009).In recent years, CEM 43 has been used extensively and successfully in clinical trials to assess the efficacy of tumor ablation (Maguire et al 2001), (Jones et al 2005), (Leopold et al 1993), (Leopold et al 1992), (Sherar et al 1997).Multiple summaries of the literature are provided (Goldstein et al 2003), (Yarmolenko, 2011).Recently, researchers and regulators have suggested the utility of CEM 43 for evaluating the potential for tissue damage caused by RFinduced heating of implanted medical devices during MRI (van Rhoon et al 2013), (Kainz 2007), and background heating in porcine tissue (Nadobny et al 2015).
, (Hug et al 2000), and also in simulation (Winter et al 2015), (Elder 2013), (Nyenhuis et al 2015).Coronary stents are typically shorter in length than peripheral vascular stents (Kastrati et al 2001), (Elezi et al 1998), (Krankenberg et al 2007), (Dake et al 2011), (Visaria and Shrivastava 2013) and therefore less likely to heat during MRI scans at 1.5 T and 3.0 T. Still other in vitro and in silico studies have focused on stent-like objects, hollow cylinders and wires (Ho 2001), (Bassen et al 2006), (Leewood et al 2013).The goal of this study is to validate a computer simulation of RF-induced heating that incorporates flow through a peripheral vascular stent.The results of the simulation are compared to experimental temperature measurements during MRI of the stent embedded in a gel phantom with varying flow through the stent.This validation represents an important step towards accurate simulations of in vivo conditions that include blood flow in the context of thermal dose and CEM 43 .
Figure 1.A schematic of the geometrical domains (air, gel phantom, and flow channel) used in the simulation.The diameter of the RF coil is 60 cm and the longest dimension of the phantom is 65 cm.The red square denotes the temperature point probe location used in the simulation.

Figure 2 .
Figure 2. A schematic showing the location of the equipment in the MR scanner room and the adjacent equipment room.The fiber optic temperature probe and silicone tubing from the peristaltic pump and reservoir were routed through the RF waveguide between the two rooms.

Figure 3 .
Figure3.A photograph of the experimental setup includes the flow phantom without gel, the vascular stent positioned on the exterior of the flow channel inside the phantom, and temperature probes.Two additional probes are shown in the photograph that were not used during the experimental measurements.The probe on the right side of the phantom (background) and the probe at the distal end of the stent were not used during the experiment when the phantom was filled with gel and positioned at isocenter in bore of the MRI system.The flow phantom is shown on the patient table of the MRI system prior to advancing to isocenter in the bore of the MRI system.

Figure 4 .
Figure4.The experimental measurements of RF-induced temperature rise versus time without flow (dashed grey line) and with a flow rate of 192 ml min −1 (dashed black line), 2240 ml min −1 (dashed grey line), and computer simulation without flow (solid lines) at each flow rate, with temperature contours of the stent and gel from the simulation, all at a console-reported SAR of 5.5 W kg −1 .

Figure 5 .
Figure 5.The MR-powered RF temperature rise of the stent at varied volumetric flow rates for the experimental measurements (grey circles) and computer simulation (red diamonds) in the context of thermal dose, CEM 43 (dashed horizontal line).The physiologic flow rate in the external iliac artery of normal subjects at rest is approximately 0.35 l min −1 (Strandness and Sumner 1975).Klocke (1976) reported that coronary artery stenoses of less than 90% maintain normal resting coronary flow of 100 ml min −1 .The error bars denote ±1σ for the experimental measurements.

Figure 6 .
Figure6.A Bland-Altman analysis shows the agreement of the simulation with the experimental measurements at all volumetric flow rates.The mean difference (solid black line) between the simulation and experiment was −0.13 °C and the limits of agreement (black dashed lines) are −0.13°C ± 1.96(SD), where SD is the standard deviation (σ = 0.6827).The upper and lower limits of agreement are 1.21 °C and −1.47 °C, respectively.

Figure 7 .
Figure 7.A Bland-Altman analysis showing the average CEM 43 values from the experiment and simulation at each volumetric flow rate.The mean difference (solid black line) between the simulation and experiment was −0.94 min and the limits of agreement (black dashed lines) are −0.94min ± 1.96(SD), where SD is the standard deviation (σ = 8.4660).The upper and lower limits of agreement are 15.7 min and −17.5 min, respectively.
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Table 1 .
The domains and input values used in the computational model.

Table 2 .
The thermal and electrical properties of the materials used in the computational model.

Table 3 .
The measured and simulated maximum temperature rise and thermal dose at varied volumetric flow rates.