# Direct Temperature Measurements of Cardiac Stent during MRI Examinations
## 2 Materials and Methods
### Temperature Data Analysis and SAR Computation  
The SAR can be expressed as follows:  
\[SAR=\frac{\sigma\langle E^{2}\rangle_{t}}{2\rho} \tag{1}\]  
where \(\sigma\) is the electrical conductivity and \(\rho\) is the mass density of the considered tissue; the angle brackets represent the temporal averaging and \(E\) is the induced electric field.  
The possible tissue hazard is related to power deposition and its temperature increasing. In vivo conditions, changing in tissue temperature is balanced of heat diffusion, perfusion cooling, metabolic heat and external heat, represented by \(SAR\). Tissue parameters can vary by orders of magnitude among tissue types [27]. In case the heat loss due to thermal diffusion, heat radiation, or thermoregulation (blood flow, sweating, etc.) is absent or not significant, the temperature rise \(dT/dt\) is directly related to \(SAR\) as follows:  
\[c\frac{dT}{dt}=SAR \tag{2}\]  
where \(c\) is the heat capacity.  
According to Equation (2), local SAR at the chosen locations was calculated by multiplying the initial slope of the temperature rise with the specific heat capacity of the phantom material. For our phantom, the heat capacity was considered close to that of water, 4184 J/kg \({}^{\circ}\)C [17]. To avoid errors in the SAR estimation, we selected the initial linear portion of the temperature rise, choosing as the starting point the first temperature increment step (>0.2 \({}^{\circ}\)C) and using the number of samples that maximized the R coefficient of the regression model (Pearson coefficient) [28]. The SAR estimation was considered reliable if R > 0.95. Each sample represented the average of three temperature measurements.  
Figure 1: (**a**) Experimental setup for direct temperature measurements; (**b**) enlargement of the details on the stent highlighting the positioning of the temperature probes.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline  & **\#1** & **\#2** & **\#3** & **\#4** & **\#5** & **\#6** & **\#7** & **\#8** & **\#9** & **\#10** \\ \hline Son duration (s) & 19 & 29 & 40 & 43 & 50 & 23 & 246 & 102 & 130 & 18 \\ \hline Whole body (SAR/R/ level (W/kg) & \(<\)0.2\(\,\)/normal & \(<\)0.2\(\,\)/normal & \(<\)0.2\(\,\)/normal & \(<\)0.2\(\,\)/normal & \(<\)0.2\(\,\)/normal & \(<\)0.1\(\,\)/normal & \(<\)0.1\(\,\)/normal & \(<\)0.1\(\,\)/normal & \(<\)0.1\(\,\)/normal & \(<\)0.1\(\,\)/normal & \(<\)0.1\(\,\)/normal \\ \hline Max B1 + ms (s) & 2.38 & 2.34 & 2.39 & 2.38 & 2.34 & 2.33 & 1.60 & 1.28 & 1.81 & 1.54 \\ \hline Sequence & T2W\_TSL_Cor_BH 1T2W/SAR/Cor_BH 1T2W/SAR/Cor_BH 1T2W\_TSL_BH 1T2W\_STAR_BH 1T2W\_STAR_BH 1T2W\_STAR_BH 1T2W\_BH 1T2W\_STAR_BH 1T2 We also reported the difference between the baseline and the highest temperature reached during the test for each probe (dTmax (\({}^{\circ}\)C)).  
Using a thin-plate smoothing spline interpolation [29], we reconstructed the temperature trend along the entire length of the stent.  
Since the thermal damage to tissue depends not only on the temperature rise but also on tissue sensitivity and exposure time, cumulative equivalent minutes can be used as a metric for thermal dose assessment [7]. To calculate this parameter, we converted our temperature vs. time trends to an equivalent number of minutes of heating at 43 \({}^{\circ}\)C (CEM43\({}^{\circ}\)C), according to this equation:  
\[\text{CEM43}^{\circ}\text{C}=\sum_{i=1}^{n}t_{i}*R^{(43-T_{i})} \tag{3}\]  
where \(t_{i}\) is the \(i\)-th time interval, \(R\) is a constant equal to 0.25 for \(T<43\)\({}^{\circ}\)C and 0.5 for \(T>43\)\({}^{\circ}\)C, and \(T_{i}\) is the average temperature during the \(t_{i}\) interval.  
We assumed that the temperatures at the interface between tissue and device were similar. Also, the initial value of temperature (22 \({}^{\circ}\)C) was scaled to 37 \({}^{\circ}\)C (assuming normal human body temperature).