Report on the determination of the uncertainty budget for smart implants, the RF exposure system and gradient induced heating

Confidentiality Status: PU - Public, fully open (remember to deposit public deliverables in a trusted repository) Deliverable Cover Sheet Funded by the European Union. Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or EURAMET. Neither the European Union nor the granting authority can be held responsible for them. The project has received funding from the European Partnership on Metrology, co-financed from the European Union’s Horizon Europe Research and Innovation Programme and by the Participating States. 1 of 51 21NRM05 STASIS D6: Report on the determination of the uncertainty budget for smart implants, the RF exposure system and gradient induced heating Organisation name of the lead participant for the deliverable: Czech Institute of Metrology (ČMI) Due date of the deliverable: 30th of September 2025 Actual submission date of the deliverable: 30th of September 2025 21NRM05 STASIS 2 of 51 Glossary AIMD - Active Implantable Medical Device RF - Radiofrequency SAR – Specific Absorption Rate 21NRM05 STASIS 3 of 51 TABLE OF CONTENTS Table of contents .............................................................................................................. 3 Summary .......................................................................................................................... 4 Task A: Finding the correlation between the power deposited into the implant and the following temperature increase ......................................................................................... 5 The standardization background ....................................................................................... 6 1. Definition of the task ..................................................................................................... 7 2. Solution ......................................................................................................................... 8 2.1 Definition of the solved task .................................................................................................... 8 2.2 Theoretical background ........................................................................................................... 8 3 Numerical results ..........................................................................................................12 3.1 Ankle Plate ............................................................................................................................ 12 3.2 Hip ......................................................................................................................................... 13 3.3 Knee ...................................................................................................................................... 15 3.4 Shoulder ................................................................................................................................ 17 3.5 All implants together .............................................................................................................. 19 4 Summary of the task .....................................................................................................20 4.1 Summaritizing the results ...................................................................................................... 20 4.2 What we learned so far? Questions and answers ................................................................ 21 5 Graphical results ...........................................................................................................23 5.1 Ankle plate ............................................................................................................................. 23 5.2 Hip ......................................................................................................................................... 27 5.3 Knee ...................................................................................................................................... 32 5.4 Shoulder ................................................................................................................................ 36 5.5 All four implants together ...................................................................................................... 39 Task B: Performing a statistical analysis of the agreement between the experimental and numerical results. .............................................................................................................41 1. Definition of the task ....................................................................................................41 2. Solution ........................................................................................................................43 2.1 Use of the straight-line function ............................................................................................. 43 2.2 Calculation of the straight-line function parameters .............................................................. 44 2.3 Use of the determined straight-line function parameters ...................................................... 45 2.4 Summary to the selected approach ...................................................................................... 46 3 Calculations ..................................................................................................................47 Conclusion 48 21NRM05 STASIS 4 of 51 SUMMARY Determination of the uncertainty in any measurement that is related to the MRI device performance is a complicated task that is affected by a) a complexity of the measurement problem, b) complicated definition of the output quantity, c) problems with the definition of the functional dependence among input quantities and the output quantity, d) determination of the influence quantities, e) quantification of the input quantities and influence quantities. Among others, the heating of the implant due to the electric and magnetic field generated during the MRI device operation is widely investigated to enable safe use of an MRI device also for patients with implants. Within project STASIS several research activities are conducted by different research groups on the topic referring to radiofrequency (RF) induced implant heating and gradient induced implant heating. This document focusses on the uncertainty budget calculations of gradient induced implant heating as mainly investigated by INRIM (Italy), while ČMI and STU Bratislava provide their support in statistical analysis of the obtained data. Therefore this document aims at the two tasks, being carried out by ČMI and STU Bratislava, that were asked for and defined by INRIM. Those two task are a) finding the correlation between the power deposited into the implant under different conditions and the following temperature increase, together with the associated uncertainty, b) Performing the statistical analysis of the deviations between the experimental and numerical results, while accounting for the relevant uncertainties. The details about both tasks are provided directly in the respective chapter. The analysis of the results and their physical interpretation are carried out by INRIM. Therefore, those analyses and interpretations should be sought in the deliverable D4 Report on the technical specifications and guidelines for comprehensive testing of gradient-induced heating of passive implants. RF induced implant heating and the corresponding uncertainty calculations are found in the following documents: • Deliverable D1: Report on the development and calibration of an implant safety concept in MRI, comprised of sensor-equipped smart medical implants and pTx capable MRI scanners that enable to assess and mitigate in situ RF induced implant heating. Lead participant: PTB (Germany). • Deliverable D3: Report on the development of open-source reference harware (RF coil, exciter, modulators, RF power amplifiers) and open-source control software, including traceable measurement procedures that allow testing of implant under parallel transmission (pTx) MR conditions. Lead participant: DKFZ (Germany). • Deliverable D5: Report on the tranlation of in vitro safety testing results to realistic exposure conditions considering combined GC and RF induced heating. Lead participant: IT‘IS (Switzerland). In summary, the aims of the STASIS project deliverable have been successfully achieved, fulfilling Objective 1-3 of the project. 21NRM05 STASIS 5 of 51 Task A: Finding the correlation between the power deposited into the implant and the following temperature increase Scope Determination of the relationship between the induced power and the temperature increase of the implant due to gradient induced implant heating in MRI. Four implants are considered in this document: a. Hip b. Knee c. Shoulder d. Ankle Plate 21NRM05 STASIS 6 of 51 THE STANDARDIZATION BACKGROUND Technical specification ISO/TS 10974 Technical specification ISO/TS 10974 Assessment of the safety of magnetic resonance imaging for patients with an active implantable medical device contains two chapters that deal with harm to the patient by the MRI generated heat: - Chapter 8 Protection from harm to the patient caused by RF-induced heating - Chapter 9 Protection from harm to the patient caused by gradient-induced device heating In the chapter 8, the point 8.4.4.4 states that the local temperature rise T or SAR at a point location in a hot spot produced by the AIMD can be related to the toral power deposition using a calibrated RF power injection method. For each AIMD hot spot, a conversion factor m between T or SAR at the hot spot and injected power is experimentally determined (i.e. T = mPinject or SAR = mPinject). In chapter 9, the standard states that the imaging gradient field dB/dt induces eddy currents on conductive AIMD enclosures and other conductive internal surfaces that result in device heating. The heating will be greatest for implants with a large surface area and high electrical conductivity. Typically, the heating is greatest when the device is oriented so that the gradient field vector is orthogonal to the AIMD surface(s) with the largest conductive area. Device heating could also depend on the gradient waveform characteristics. Technical report ISO/TR 21900 Technical report ISO/TR 21900 Guidance for uncertainty analysis regarding the application of ISO/TS 10974 in its part 4 introduces two methods for uncertainty evaluation (in practice, overlaps between those methods exist): a) Method 1 (part 4.2 of the TR) determines the uncertainty of the measurement system by considering the variability of the system as a whole. In this method, multiple elements of the system are assembled together, and their combined uncertainty is assessed. This is the method that we employed for evaluating the preliminary results, as presented in this report. b) Method 2 (part 4.3 of the TR) dissects the assembly into its parts, determines the uncertainty of individual elements, and then determines the uncertainty of the group by combining the uncertainty of the components. 21NRM05 STASIS 7 of 51 1. DEFINITION OF THE TASK Input data Each implant is associated with an activity1_.mat file containing the following variables: • power_map : Nθ × Nϕ matrix of the total power expressed in watts deposited into the implant for a specific orientation of the unitary harmonic magnetic field expressed in polar coordinates. θ : [0, π/2] is the polar angle (the angle between the magnetic field vector and the z-axis), and ϕ : [−π, π] is the azimuth angle (the angle between the magnetic field vector and the 1 x-axis). Nθ and Nϕ are the numbers of θ and ϕ intervals at which the power has been computed; • power_worst_H : 3-element vector representing the unitary magnetic field that results in the maximum power deposited into the implant; • temp_map_min : Nθ × Nϕ matrix of the maximum temperature increase expressed in kelvin, after minutes of exposure, for a specific orientation of the unitary harmonic magnetic field expressed in polar coordinates with the same criteria used in the power_map matrix; • temp_worst_H_min : 3-element vector representing the unitary magnetic field that results in the maximum temperature increase after minutes of exposure; • external_surface : external surface of the implant expressed in square meters (i.e., the interface between the implant and the background). Each of the particular data files power_map, temp_map_min contains 40,000 data points (for any theta and fi combination it is one data point). The three files temp_map_min were received, for 5 minutes, 15 minutes, and 30 minutes. The task It is expected that the following points are investigated in the framework of the activity: 1. For each implant, the correlation between the magnetic field direction that maximises the power deposition into the implant and that maximises the temperature increase after 5 minutes, 15 minutes, and 30 minutes of exposure; 2. For each implant, the correlation between the power deposited into the implant and the following temperature increase as a function of the magnetic field direction. The correlation should be evaluated by accounting for a temperature increase after 5 minutes, 15 minutes, and 30 minutes of exposure; 3. For each implant, a coefficient, with associated uncertainty/confidence level, that allows estimating the temperature increase after a specified time instant given the power deposited into the implant. 21NRM05 STASIS 8 of 51 2. SOLUTION The following text of this document deals with point 3 of the formulated task, i.e. finding the dependence between the deposited power and a temperature rise, including the respective uncertainty. 2.1 Definition of the solved task Therefore, the task is determining the relationship between the deposited power (denoted as X), and the temperature difference after a given time of 5, 15, and 30 minutes (denoted as Y). It is assumed that this relationship can be approximated by linear regression, i.e. a theoretical model is 𝑌=𝛽 𝑋 or 𝑌=𝛼+ 𝛽 𝑋 The task is to determine: 1. for 𝑌=𝛽 𝑋 a. estimate b the unknown coefficient 𝛽 of the line, b. the uncertainty ub; 2. for 𝑌=𝛼+ 𝛽 𝑋 a. estimates a and b the unknown coefficients 𝛼 and 𝛽 of the line, b. their uncertainties ua, ub, and covariance among them uab. If we determine those parameters, for any given x (the value of power) we can calculate the value of y (the temperature difference) and its corresponding uncertainty uy. Moreover, an additional calculation was carried out, where the deposited power was transferred to energy, and the relation between energy and the temperature increase was investigated. 2.2 Theoretical background The two forms of linear regression will be investigated: a. the linear regression (line) which crosses the zero point (intersection of x and y axes), b. the linear regression (line) which is shifted from the zero point (intersection of x and y axes) 2.2.1 For the linear regression in the form of 𝒀=𝜷 𝑿 1. Employing the least squares method, the unknown coefficient b can be determined as follows: 𝑏= 1 ∑𝑥𝑖2∑𝑥𝑖𝑦𝑖 where xi is the measured power input value (from the supplied data), yi is the measured temperature rise (from the supplied data). 2. The uncertainty ub of the coefficient b can be determined as follows: 21NRM05 STASIS 9 of 51 𝑢𝑏=1 √∑𝑥𝑖2𝑠, where s can be estimated by a formula for sample residual variance 𝑠=√1 𝑛−1∑[𝑦𝑖−(𝑏𝑥𝑖)]2 𝑛 𝑖=1 3. The uncertainty uy of the calculated value y = bx can be determined as follows: 𝑢𝑦=𝑥 𝑢𝑏=𝑥 1 √∑𝑥𝑖2𝑠 4. Coefficient of determination R2 is a statistical measure of how well the regression predictions approximate the real data points 𝑅2=1−∑ (𝑦𝑖−𝑏𝑥𝑖)2 𝑛𝑖=1 ∑ (𝑦𝑖−𝑦)2 𝑛𝑖=1 5. Confidence intervals (UCL, LCL) 𝑦±𝑡𝑛−1,1−𝛼/2 𝑢𝑦 𝑦±𝑡𝑛−1,1−𝛼/2 𝑠√x ∑𝑥𝑖2 6. Prediction intervals (UPL, LPL) 𝑦±𝑡𝑛−1,1−𝛼/2 𝑠√1 + x ∑𝑥𝑖2 7. Tolerance intervals (UTL, LTL) 𝑦±𝑘2,1−𝛼/2,𝑝,𝑛 𝑠 8. Uncertainty of conversion is determined as follows. The expanded uncertainty Uy,conv of the temperature increase ∆T obtained by conversion from deposited power is defined as half the interval between the upper and lower tolerance limits (UTL resp. LTL), the interval that represents (1-α)∙100 = 95% certainty that there is a p∙100 = 90% chance, that the correct prediction of ∆T lies between the upper and lower limits of the tolerance interval, i.e. 𝑈𝑦,conv=𝑘2,1−𝛼/2,𝑝,𝑛 𝑠 where 𝑘2,1−𝛼/2,𝑝,𝑛=𝑘2,0,975,0,9,𝑛 2.2.2 For the linear regression in the form of 𝒀=𝜶 + 𝜷 𝑿 1. Employing the least squares method, the unknown coefficients a, and b can be determined as follows: 21NRM05 STASIS 16 of 51 4. Linear regression 𝑌=𝛽 𝑋 for temperature increase depending on the energy (in J) (n – number of points) (1−𝛼=0,95,𝑝=0,9,𝑛=12∙104) bknee_energy_b = 0.00146018 K/J ubknee_energy_b = 1.1829946310-6 K/J Rknee_energy_b2 = 0.68011614 sknee_energy_b = 1,4954181610-9 K 𝑘2,0,975,0,9,120 000=1,6449 Uy,convknee_energy_b = 2,4598110-9 K Remark: Please note that the correlation coefficient indicates a weak linear relationship, compared to the dependence of temperature increase on the deposited power after 5, 15, and 30 minutes. Please compare with the correlation coefficient for 𝑌=𝛽 𝑋. 3.3.2 For the linear regression in the form of 𝒀=𝜶 + 𝜷 𝑿 1. Linear regression 𝑌=𝛼+ 𝛽 𝑋 for temperature increase depending on the deposited power, exposure of 5 minutes (n – number of points) (1−𝛼=0,95,𝑝=0,9,𝑛=4∙104) aknee5m_ab = 3.365910-11 K uaknee5m_ab = 3.636210-12 K bknee5m_ab = 1.135547694 K/W ubknee5m_ab = 0.001170572 K/W ua,bknee5m_ab = -3.8910410-15 K2/W Rknee5m_ab2 = 0.9592295 sknee5m_ab = 2.9479510-10 K 𝑘2,0,975,0,9,40 000=1,6449 Uy,convknee5m_ab = 4,8490810-10 K 2. Linear regression 𝑌=𝛼+ 𝛽 𝑋 for temperature increase depending on the deposited power, exposure of 15 minutes (n – number of points) (1−𝛼=0,95,𝑝=0,9,𝑛=4∙104) aknee15m_ab = -9.1403910-12 K uaknee15m_ab = 4.8616110-12 K bknee15m_ab = 1.780577858 K/W ubknee15m_ab = 0.001565058 K/W ua,bknee15m_ab = -6.9555410-15 K2/W Rknee15m_ab2 = 0.970024943 sknee15m_ab = 3.9414210-10 K 𝑘2,0,975,0,9,40 000=1,6449 Uy,convknee15m_ab = 6,4832410-10 K 3. Linear regression 𝑌=𝛼+ 𝛽 𝑋 for temperature increase depending on the deposited power, exposure of 30 minutes (n – number of points) (1−𝛼=0,95,𝑝=0,9,𝑛=4∙104) aknee30m_ab = -3.2243210-11 K uaknee30m_ab = 5.4247210-12 K bknee30m_ab = 2.288048166 K/W ubknee30m_ab = 0.001746334 K/W ua,bknee30m_ab = -8.6601410-15 K2/W Rknee30m_ab2 = 0.977230186 sknee30m_ab = 4.3979410-10 K 𝑘2,0,975,0,9,40 000=1,6449 Uy,convknee30m_ab = 7,2341810-10 K 4. Linear regression 𝑌=𝛼+ 𝛽 𝑋 for temperature increase depending on the energy (in J) (n – number of points) (1−𝛼=0,95,𝑝=0,9,𝑛=12∙104) aknee_energy_ab = 1.9700352010-9 K uaknee_energy_ab = 5.2594130310-12 K 21NRM05 STASIS 17 of 51 bknee_energy_ab = 0.00104006 K/J ubknee_energy_ab = 1.4412788710-6 K/J ua,bknee_energy_ab = -5.8988354910-18 K2/J Rknee_energy_ab2 = 0,81272095 sknee_energy_ab = 1.1442336110-9 K 𝑘2,0,975,0,9,120 000=1,6449 Uy,convknee_energy_ab = 1,8821510-9 K 3.4 Shoulder 3.4.1 For the linear regression in the form of 𝒀=𝜷 𝑿 1. Linear regression 𝑌=𝛽 𝑋 for temperature increase depending on the deposited power, exposure of 5 minutes (n – number of points) (1−𝛼=0,95,𝑝=0,9,𝑛=4∙104) bshould5m_b = 2.28773545 K/W ubshould5m_b = 0.00040099 K/W Rshould5m_b2 = 0.988382321011267 sshould5m_b = 3.6729410-11 K 𝑘2,0,975,0,9,40 000=1,6449 Uy,convshould5m_b = 6,0416310-11 K 2. Linear regression 𝑌=𝛽 𝑋 for temperature increase depending on the deposited power, exposure of 15 minutes (n – number of points) (1−𝛼=0,95,𝑝=0,9,𝑛=4∙104) bshould15m_b = 3.56581087 K/W ubshould15m_b = 0.0005406969 K/W Rshould15m_b2 = 0.99128182 sshould15m_b = 4.9526210-11 K 𝑘2,0,975,0,9,40 000=1,6449 Uy,convshould15m_b = 8,1465610-11 K 3. Linear regression 𝑌=𝛽 𝑋 for temperature increase depending on the deposited power, exposure of 30 minutes (n – number of points) (1−𝛼=0,95,𝑝=0,9,𝑛=4∙104) bshould30m_b = 4.45101618 K/W ubshould30m_b = 0.00061052 K/W Rshould30m_b2 = 0.99280986 sshould30m_b = 5.59223810-11 K 𝑘2,0,975,0,9,40 000=1,6449 Uy,convshould30m_b = 9,1986710-11 K 4. Linear regression 𝑌=𝛽 𝑋 for temperature increase depending on the energy (in J) (n – number of points) (1−𝛼=0,95,𝑝=0,9,𝑛=12∙104) bshould_energy_b = 0.00287617 K/J ubshould_energy_b = 2.3593049210-6 K/J Rshould_energy_b2 = 0.54590741 sshould_energy_b = 4.3970863210-10 K 𝑘2,0,975,0,9,120 000=1,6449 Uy,convshould_energy_b = 7, 3277210-10 K Remark: Please note that the correlation coefficient indicates a weak linear relationship, compared to the dependence of temperature increase on the deposited power after 5, 15, and 30 minutes. Please compare with the correlation coefficient for 𝑌=𝛽 𝑋. 21NRM05 STASIS 18 of 51 3.4.2 For the linear regression in the form of 𝒀=𝜶 + 𝜷 𝑿 1. Linear regression 𝑌=𝛼+ 𝛽 𝑋 for temperature increase depending on the deposited power, exposure of 5 minutes (n – number of points) (1−𝛼=0,95,𝑝=0,9,𝑛=4∙104) ashould5m_ab = -7.3825577710-11 K uashould5m_ab = 4.9214646310-13 K bshould5m_ab = 2.44132357 K/W ubshould5m_ab = 0.00107459 K/W ua,bshould5m_ab = -5.0389435510-16 K2/W Rshould5m_ab2 = 0.99231007 sshould5m_ab = 2.9883168010-11 K 𝑘2,0,975,0,9,40 000=1,6449 Uy,convshould5m_ab = 4,9154810-11 K 2. Linear regression 𝑌=𝛼+ 𝛽 𝑋 for temperature increase depending on the deposited power, exposure of 15 minutes (n – number of points) (1−𝛼=0,95,𝑝=0,9,𝑛=4∙104) ashould15m_ab = -1.1529653510-10 K uashould15m_ab = 6.0297758610-13 K bshould15m_ab = 3.80567595 K/W ubshould15m_ab = 0.00131658 K/W ua,bshould15m_ab = -7.5640273910-16 K2/W Rshould15m_ab2 = 0.99523567 sshould15m_ab = 3.6612841610-11 K 𝑘2,0,975,0,9,40 000=1,6449 Uy,convshould15m_ab = 6,0224510-11 K 3. Linear regression 𝑌=𝛼+ 𝛽 𝑋 for temperature increase depending on the deposited power, exposure of 30 minutes (n – number of points) (1−𝛼=0,95,𝑝=0,9,𝑛=4∙104) ashould30m_ab = -1.3627949110-10 K uashould30m_ab = 6.5323085910-13 K bshould30m_ab = 4.73453459 K/W ubshould30m_ab = 0.00142631 K/W ua,bshould30m_ab = -8,8773663210-16 K2/W Rshould30m_ab2 = 0.99638305 sshould30m_ab = 3,9664223910-11 K 𝑘2,0,975,0,9,40 000=1,6449 Uy,convshould30m_ab = 6,5243710-11 K 4. Linear regression 𝑌=𝛼+ 𝛽 𝑋 for temperature increase depending on the energy (in J) (n – number of points) (1−𝛼=0,95,𝑝=0,9,𝑛=12∙104) ashould_energy_ab = 6.8328786710-10 K uashould_energy_ab = 1.4661182210-12 K bshould_energy_ab = 0.00184608 K/J ubshould_energy_ab = 2.7250765010-6 K/J ua,bshould_energy_ab = -3,2404823110-18 K2/J Rshould_energy_ab2 = 0,79272417 sshould_energy_ab = 2.9707816110-10 K 𝑘2,0,975,0,9,120 000=1,6449 Uy,convshould_energy_ab = 4,8866410-10 K 21NRM05 STASIS 19 of 51 3.5 All implants together As a sample, evaluation for all data coming from all four implants at 30 minutes exposure were evaluated and the overall parameters were calculated. 3.5.1 For the linear regression in the form of 𝒀=𝜷 𝑿 1. Linear regression 𝑌=𝛽 𝑋 for temperature increase depending on the deposited power, exposure of 30 minutes (n – number of points) (1−𝛼=0,95,𝑝=0,9,𝑛=16∙104) ball30m_b = 2,40313060 K/W uball30m_b = 0,00067089 K/W Rall30m_b2 = 0,97086364 sall30m_b = 5,6976766210-10 K 𝑘2,0,975,0,9,40 000=1,6449 Uy,convall30m_b = 9,3721110-10 K 2. Linear regression 𝑌=𝛽 𝑋 for temperature increase depending on the deposited power divided by the implant surface, exposure of 30 minutes (n – number of points) (1−𝛼=0,95,𝑝=0,9,𝑛=16∙104) ball30m_bS = 0,05714077 K/Wm2 uball30m_bS = 0,00001001 K/Wm2 Rall30m_bS2 = 0,98843460 sall30m_bS = 3,5897194210-10 K 𝑘2,0,975,0,9,40 000=1,6449 Uy,convall30m_bS = 5,9047310-10 K 3.5.2 For the linear regression in the form of 𝒀=𝜶 + 𝜷 𝑿 1. Linear regression 𝑌=𝛼+ 𝛽 𝑋 for temperature increase depending on the deposited power, exposure of 30 minutes (n – number of points) (1−𝛼=0,95,𝑝=0,9,𝑛=16∙104) aall30m_ab = 4,4545298510-10 K uaall30m_ab = 1,9013836710-12 K ball30m_ab = 2,25120807 K/W uball30m_ab = 0,00089554 K/W ua,ball30m_ab = -1,2329907810-15 K2/W Rall30m_ab2 = 0.99231007 sall30m_ab = 2.9883168010-11 K 𝑘2,0,975,0,9,40 000=1,6449 Uy,convall30m_ab = 8,6282310-10 K 2. Linear regression 𝑌=𝑎+ 𝛽 𝑋 for temperature increase depending on the deposited power divided by the implant surface, exposure of 30 minutes (n – number of points) (1−𝛼=0,95,𝑝=0,9,𝑛=16∙104) aall30m_abS = 6.8328786710-10 K uaall30m_abS = 1.3583111110-12 K ball30m_abS = 0.05640815 K/W uball30m_abS = 1.5142550810-5 K/W ua,ball30m_abS = -1.5525632510-18 K2/W Rall30m_abS2 = 0.98860143 sall30m_abS = 3.5637560710-10 K 𝑘2,0,975,0,9,120 000=1,6449 Uy,convall30m_abS = 5,8620210-10 K 21NRM05 STASIS 20 of 51 4 SUMMARY OF THE TASK 4.1 Summaritizing the results The following tables compare the results of the two approaches: a. with a linear regression in the form of 𝑌=𝛽 𝑋 b. with a linear regression in the form of 𝑌=𝛼+ 𝛽 𝑋 The main idea is comparing the declination of the regression line, i.e. the parameter b, regardless the shift of the line (represented by a parameter a) is considered. To do so, the deposited power in W was transferred to energy in J. Four cases were compared - three related to the time (5, 15, and 30 minutes), and one for the whole set of 120000 points (for any combination of the angles  and  it is one data point). For the deposited power Table 4.1 For the linear regression in the form of 𝑌=𝛽 𝑋 Parameter 5 minutes 15 minutes 30 minutes Ankle Plate bankpla_b / K/W 1,4712125 2,115517798 2,552769599 Hip bhip_b / K/W 1,133156432 1,897958636 2,49762561 Knee bknee_b / K/W 1,145453 1,777887961 2,278559419 Shoulder bshould_b / K/W 2,28773545 3,56581087 4,45101618 Table 4.2 For the linear regression in the form of 𝑌=𝛼+ 𝛽 𝑋 Parameter 5 minutes 15 minutes 30 minutes Ankle Plate aankpla_ab / K 2.2983610-11 3.11163310-11 3.5856610-11 bankpla_ab / K/W 1.230235528 1.788778401 2.17682236 Hip ahip_ab / K 1.2057610-10 1.1376910-9 1.387910-9 bhip_ab / K/W 1.09149561 1.504872446 2.018085947 Knee aknee_ab / K 3.365910-11 -9.1403910-12 -3.2243210-11 bknee_ab / K/W 1.135547694 1.780577858 2.288048166 Shoulder ashould_ab / K -7.3825577710-11 -1.1529653510-10 -1.3627949110-10 bshould_ab / K/W 2.44132357 3.80567595 4.73453459 For energy Table 4.3 For the linear regression in the form of 𝑌=𝛽 𝑋 Parameter Value Ankle Plate bankpla_energy_b / K/J 0.00167640 Hip bhip_energy_b / K/J 0.001580637 Knee bknee_energy_b / K/J 0.00146018 Shoulder bshould_energy_b / K/J 0.00287617 Table 4.4 For the linear regression in the form of 𝑌=𝛼+ 𝛽 𝑋 Parameter Value Ankle Plate aankpla_energy_ab / K 5.4104990110-11 bankpla_energy_ab / K/J 0.00126533 Hip ahip_energy_ab / K 2.5969710-9 21NRM05 STASIS 21 of 51 bhip_energy_ab / K/J 0.000930428 Knee aknee_energy_ab / K 1.9700352010-9 bknee_energy_ab / K/J 0.00104006 Shoulder ashould_energy_ab / K 6.8328786710-10 bshould_energy_ab / K/J 0.00184608 Example As an example, the following table compares results for one case of exposure time and the same regression model. The last line represents the results for deposited energy divided by the surface. Table 4.5 Comparison of parameters for 30 minutes exposure time and a model 𝑌=𝛽 𝑋 Implant Model ∆𝑇×10−8/ K 𝑈(∆𝑇)×10−8/ K 𝑏 Deposited power ×10−9 Ankle plate ∆𝑇=𝑏 𝑃 0,003 – 0,06 0,006 2,55 K/W 0,01 – 0,09 W Hip ∆𝑇=𝑏 𝑃 0,5 - 1 0,138 2,50 K/W 2 – 4 W Knee ∆𝑇=𝑏 𝑃 0,06 – 1,1 0,072 2,28 K/W 0,5 – 5 W Shoulder ∆𝑇=𝑏 𝑃 0,018 – 0,35 0,009 4,45 K/W 0 – 1 W All 4 implants ∆𝑇=𝑏 𝑃 0,05– 1,1 0,094 2,40 K/W (0,5 – 5) ×10−9 W All 4 implants ∆𝑇=𝑏 𝑃𝑆 0,1– 1,1 0,0013 0,057 Km2 W (1,1 – 19) ×10−8 W/m2 It is worth noting from a physical point of view, one can observe a natural process of heating and heat transfer to the environment - the non-linear section of the graph indicates the heating of the implant itself from the moment the gradient coil is turned on, and the linear section demonstrates the transfer of heat from the implant to the surrounding tissues. With increasing time, the direction of the magnetic field for maximum temperature rise approaches the direction of maximum energy storage in the implant. At the time of 30 minutes, they are already close. 4.2 What we learned so far? Questions and answers Following is a short summary of facts, what we learned so far by processing the obtained data, and what is still needed to do. What we obtained in general? The linear relationship between the deposited power (energy, power divided by surface) and the temperature rise. Which form gets this relationship? This relationship we can approximate by linear regression in the form Y = b X (of a line crossing through the zero point) or Y = a + b X (a line shifted from the zero point) With which restrictions? For each implant, we took all information on power and the respective temperature increase as data points, regardless of the combination of angles and also the time of exposure. In other words, we did not investigate the way data were obtained, and purely statistical methods were applied What is the usefulness of obtained relationship? We can select the maximum temperature increase and we can derive the deposited power related to that temperature increase What we cannot say from the obtained relationship? We cannot say a) the way the deposited power was brought to the implant. In other words, we know the relationship 21NRM05 STASIS 22 of 51 between the temperature increase and the magnitude of the incoming power, but we do not know the time of exposure and parameters of the magnetic field which generated the incoming power b) the influence of angles c) the influence of implant geometry with one exception, when we divided the incoming power by the surface of individual implants d) the maximum temperature at any given particular point of the implant. In other words, we know the general temperature rise in dependence on the acting power, either at one particular time or in a time interval, but not the temperature at any point of the implant e) the influence of time of exposure What is needed in future investigations? For further use of the model and its better complexity, the following information needs to be obtained and implemented: a) A model relationship between the measured MRI machine input parameters and the generated power, acting on the implant b) Influence of implant geometry on thermal distribution c) Limits for permissible temperature increase, time limits, and other limitations for implant exposure (what is the longest exposure of the implant) d) Other 21NRM05 STASIS 23 of 51 5 GRAPHICAL RESULTS 5.1 Ankle plate 5.1.1 Ankle plate - linear regression in the form of 𝒀=𝜷 𝑿 21NRM05 STASIS 24 of 51 21NRM05 STASIS 25 of 51 5.1.2 Ankle plate - linear regression in the form of Y =  +  X 21NRM05 STASIS 32 of 51 5.3 Knee 5.3.1 Knee - linear regression in the form of 𝒀=𝜷 𝑿 21NRM05 STASIS 33 of 51 21NRM05 STASIS 34 of 51 5.3.2 Knee - linear regression in the form of Y =  +  X 21NRM05 STASIS 35 of 51 21NRM05 STASIS 36 of 51 5.4 Shoulder 5.4.1 Shoulder - linear regression in the form of 𝒀=𝜷 𝑿 Figures for individual times are missing 21NRM05 STASIS 37 of 51 5.4.2 Shoulder - linear regression in the form of Y =  +  X 21NRM05 STASIS 38 of 51 21NRM05 STASIS 39 of 51 5.5 All four implants together 5.5.1 All four implants together - linear regression in the form of 𝒀=𝜷 𝑿 21NRM05 STASIS 40 of 51 5.5.2 All four implants together - linear regression in the form of 𝒀=𝜶 + 𝜷 𝑿 21NRM05 STASIS 41 of 51 Task B: Performing a statistical analysis of the agreement between the experimental and numerical results. 1. DEFINITION OF THE TASK The STASIS project proposal reads Results from A3.1.6 and A3.2.2 were collected by INRIM. These correspond to temperature increase experiments together with the relevant results obtained from numerical simulations. Both experimental and numerical data are associated with an uncertainty value. The task is to perform a statistical analysis in order to establish how much experimental results match with the numerical results also accounting for the relevant uncertainties. In other words, following data are available (see Fig. B1) a. Temperature rise in K of a particular implant, simulation point, obtained by simulation in discrete samples of the exposition time (green line, unceratinty limits are also illustrated), b. The corresponding temperature rise in K of the same implant, the same measurement point and an overall experimental setup, obtained by experiment in discrete samples of the exposition time (orange line, uncertainty limits are also illustrated). Figure B1. Graphical representation of the task (Shown are data for Hip(RE), column 1 (measurement point 1)) The following implants were considered for the analysis: femur, hip, knee, shoulder, tibia. A total of 21 .mat files were received for analysis. Each .mat file refers to a specific experiment (experimental data + relevant simulation data). The filename reports the implant involved in the experiment, the type of experiment, the implant position (when relevant) and the used MR sequence. Each single Matlab file contains 6 arrays: 1. Experimental data: time_resampled(:,1) Column vector with time samples ch_resampled(:,1:nc) Column vector with temperature samples; Each column refers to a temperature channel (measurement point) 21NRM05 STASIS 48 of 51 Table B.1 Results of the straight-line function for the data set obtained a b u(a) u(b) Covariance u(a,b) r Task 1 All data -0.004907905185139 0.924327743761982 0.002693956867838 0.025767880339540 -3.054564128133216e-05 16.356225461292260 Task 2 Femur 200 s -0.004730217587454 0.764718356179748 0.008910662518204 0.054692237926329 -3.943972340959600e-04 12.628808844127024 400 s 0.005484039284024 0.794856667329768 0.016632775139442 0.057877198517401 -7.891698747274929e-04 6.153752039199373 600 s 0.008816646973441 0.846492742818379 0.023261674414261 0.060293704812444 -0.001143871188974 2.934548380175607 900 s 0.019996056335162 0.902026680656433 0.032540845293747 0.063432356664473 -0.001668952276106 1.518828987277543 Hip 200 s 0.032811974462212 0.675617192505557 0.007072946246634 0.026867613797268 -1.478000675677771e-04 71.048007289867640 400 s 0.084510037995691 0.706981615857333 0.012459134533751 0.029064187803765 -2.818537343583272e-04 43.416643501154084 600 s 0.111144500822584 0.734546879023881 0.037975359708094 0.039849506044676 -0.001234784942520 9.852844269361958 900 s 0.142266773037649 0.770801042214080 0.051051413169259 0.042812645885891 -0.001806335746488 9.384097184437433 Knee 200 s -0.032700997000726 1.363775029442935 0.014226073886945 0.100974986207993 -0.001258899417226 56.425459240637615 400 s -0.086568159309177 1.599471865771367 0.031151828999689 0.132949206001708 -0.003777865631926 47.715613021277810 600 s -0.016167458845686 0.948402139155403 0.068575618419529 0.176310022995135 -0.010795593998282 1.398042607547288 900 s -0.008410344367889 0.975509217870057 0.101381672501821 0.202210521678653 -0.018725419437812 0.937575813899910 Shoulder 200 s 0.092348790812444 0.605476218531904 0.021853895529061 0.044989454137160 -8.810759574447535e-04 63.192080641849046 400 s 0.135806389583340 0.664324351155069 0.035654762816244 0.049739998863051 -0.001602071216622 38.862364904973470 600 s -6.942268151502020 6.662260323516325 5.259269630098430 4.422615337265153 -23.252142515793548 6.609665129465449 900 s -8.448816378108440 6.852350502801359 7.111394417175920 5.045863739893506 -35.872930040495824 5.012914868532930 Tibial 200 s 0.007981113298991 0.747216771432548 0.018756384837045 0.032845168480118 -5.036758959273508e-04 15.039333715460039 400 s -0.012373094230415 0.851839266200256 0.028255461147689 0.036981250849329 -8.595562018906676e-04 9.990926533472772 600 s -0.043726806293060 0.925261632810579 0.035578652206837 0.039586481317741 -0.001160989179935 4.878173260086101 900 s -0.058557238649261 0.972882215768814 0.043985242614225 0.041628823001058 -0.001513425989819 3.502485857130775 All implants 200 s 0.019404360162885 0.747732444719381 0.004004268972022 0.014975736364059 -4.409892159967782e-05 3.298069621031615e+02 400 s 0.047282489207037 0.797156939505872 0.007333200626946 0.016940397573535 -9.519947247492448e-05 2.630251338560409e+02 21NRM05 STASIS 49 of 51 600 s 0.012029267473151 0.843408051415499 0.014173075703090 0.020017327043491 -2.192219973245130e-04 57.266271836093990 900 s 0.023309698882737 0.879474979322333 0.019556198278792 0.021759148159872 -3.371221376833681e-04 51.079917132521660 Task 3 Femur All data -0.006232712451246 0.974316799768952 0.002636770831267 0.015137320761821 -1.785595462315558e-05 22.031284019898187 Hip All data -0.010127130291883 0.981961439309857 0.003091733874135 0.037031500592081 -8.783850728521455e-05 8.663269118337070 Knee All data -0.025655599242253 0.635730970788776 0.004724296366429 0.025062916742844 -8.769111124247974e-05 40.491842193596625 Shoulder All data -0.007870851702194 0.602963188245692 0.002278225200328 0.019661337835525 -2.033082567756539e-05 28.873495789406000 Tibial All data -0.029140236234364 0.846196607619542 0.003503254322056 0.013505486922342 -3.597166595319500e-05 53.408775848999454 Task 4 Femur (RE) Column 1 -0.006232718194965 0.974316840921663 0.002636770204518 0.015137311789100 -1.785593812292627e-05 22.031284019276782 (RE) Column 2 -0.008476106084576 1.094590662635126 0.002057347855561 0.027751097606440 -4.055233576945168e-05 7.523012472448466 (RE) Column 3 -0.005898772150929 0.934139807147304 0.001142507077300 0.022498232107492 -1.583725406549432e-05 16.890858701944012 (WO) Column 1 -0.014480766272367 0.819962538854963 0.003120426729800 0.007300288348353 -6.840082202684264e-06 2.157251420955415e+02 (WO) Column 2 -0.025935624908013 0.882618375809857 0.001865718639896 0.009087580699284 -1.200322437929293e-05 1.277057052346939e+02 (WO) Column 3 -0.017089974693584 0.801482938072242 0.001096810204045 0.010254121944293 -7.193855497312013e-06 1.493173819253223e+02 Hip (RE) Column 1 -0.016743859722609 1.105160605337667 0.002636829337239 0.019618394120527 -3.627700103513687e-05 26.234347983448260 (RE) Column 2 -0.057813095789869 0.771213156107088 0.003902334649557 0.009282837603295 -2.421292971189638e-05 2.036805548965392e+02 (RE) Column 3 -0.023709808684009 0.707954247349384 0.001870730219673 0.007596874347081 -7.300274677495872e-06 1.333386488648540e+02 (WO) Column 1 -0.018073454641214 1.236555055376612 0.001919757451050 0.017692451049411 -2.034602034536907e-05 74.326988493140850 (WO) Column 2 -0.052194553032637 0.835559397697266 0.004194794132810 0.005473999054752 -1.473461300988362e-05 1.616714292884419e+02 (WO) Column 3 -0.033560775212565 0.838425625804233 0.002162951775858 0.005504634667619 -6.080451653533217e-06 2.057898045903108e+02 Knee (RE) Column 1 -0.043192999226446 0.825570125801035 0.004467118540836 0.016276953256501 -4.994158398155970e-05 1.135774387648894e+02 (RE) Column 2 -0.034538552005863 1.017801716943328 0.005382778567051 0.018862084421613 -6.719419224789433e-05 57.858114601268085 (RE) Column 3 -0.004030894372869 0.931333152977411 0.001772915161297 0.022608818513522 -2.505432986681995e-05 15.584181236160006 Shoulder (RE) Column 1 -0.011368711127394 0.700416319819935 0.002232891632581 0.012204125617612 -1.017234028905895e-05 64.443861744462030 (RE) Column 2 -0.014974527951590 0.869540334505379 0.003651757261737 0.013406528752676 -1.909794711220192e-05 47.972676598516190 (RE) Column 3 -0.007459415085771 0.930055126903404 0.002330648427774 0.012099748784110 -9.194749181638742e-06 29.768809127857107 (WO) Column 1 -0.030981907741031 0.615641030688305 0.002055573339668 0.005539338887334 -6.254061891484881e-06 3.316615129318416e+02 21NRM05 STASIS 50 of 51 (WO) Column 2 -0.056188927881634 0.791370820236438 0.003103801211024 0.006036364482795 -1.185521993983736e-05 4.079458835598822e+02 (WO) Column 3 -0.015783600211746 0.962898933063130 0.001961545555037 0.006200481008795 -5.628324898417632e-06 1.049761210610379e+02 Tibial (RE) Column 1 -0.029140148368575 0.846196270801262 0.003503268711441 0.013505577273523 -3.597206005349667e-05 53.408775893887970 (RE) Column 2 -0.036696178580039 0.828405139241780 0.003857732286419 0.014700399118551 -4.213683677797982e-05 92.797142743558070 (RE) Column 3 -0.017247590112678 0.909471049544661 0.002918067420570 0.014883774207750 -3.251342842190504e-05 22.514565823455534 (WO) Column 1 -0.084158194884998 0.864489155796940 0.004431159689568 0.005524489017350 -1.703726454715574e-05 6.613607628106338e+02 (WO) Column 2 -0.079704878088096 0.839609160589047 0.004164139515233 0.005569931423752 -1.504637522552644e-05 6.559714187593834e+02 (WO) Column 3 -0.044828414879061 0.965986355332829 0.003549813677295 0.006034187194786 -1.347092352156828e-05 2.381353580279230e+02 51 of 51 CONCLUSION In summary, an open-source reference hardware consisting of an 8-channel 3T pTx body coil, performant parallel transmission RF exposure hardware and operating software have been developed, which is suitable, amongst others, for offline implant testing by manufacturers or test houses. More detailed information on the reference hardware and software can be found in the public repositories, and its application is further detailed in deliverable D1 of the STASIS project. The aims of the STASIS project deliverable have been successfully achieved, fulfilling Objective 2 of the project.