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Validating a Numerical Simulation of Human Heart Motion Using Clinical Data

Validating a Numerical Simulation of Human Heart Motion Using Clinical Data DE GRUYTER Current Directions in Biomedical Engineering 2020;6(3): 20203140 Armin Müller*, Ekaterina Kovacheva, Marc Alexander Fritz, Olaf Dössel, and Axel Loewe Validating a Numerical Simulation of Human Heart Motion Using Clinical Data https://doi.org/10.1515/cdbme-2020-3140 The aim of this work is to compare elastomechanical sim- ulation results with clinical data quantitatively and answer the Abstract: Numerical simulations are increasingly often in- question to what extent can we validate a cardiac simulation volved in developing new and improving existing medical with clinical data. In particular, the clinical data used in this therapies. While the models involved in those simulations are work provide the deformation of the left ventricle over time. designed to resemble a specific phenomenon realistically, the results of the interplay of those models are often not suffi- ciently validated. We created a plugin for a cardiac simula- tion framework to validate the simulation results using clinical 2 Methods MRI data. The MRI data were used to create a static whole- heart mesh as well as slices from the left ventricular short axis, 2.1 Numerical Simulation Framework providing the motion over time. The static heart was a starting point for a simulation of the heart’s motion. From the simula- The cardiac simulation framework that was used to perform tion result, we created slices and compared them to the clinical the validation was CardioMechanics [3]. It was developed at MRI slices using two different metrics: the area of the slices the Institute of Biomedical Engineering (IBT) at Karlsruhe In- and the point distances. The comparison showed global simi- stitute of Technology (KIT). This framework uses the finite larities in the deformation of simulated and clinical data, but element method to simulate the beating of the human heart. also indicated points for potential improvements. Performing this comparison with more clinical data could lead to person- alized modeling of elastomechanics of the heart. 2.1.1 Geometry Keywords: Simulation validation, numerical simulation, The numerical simulation was performed on a whole-heart ge- clinical data, motion deformation, human heart ometry consisting of 7623 points and 42282 tetrahedral vol- ume elements of a heart in end-diastolic state. 1 Introduction Despite a decrease in mortality of cardiovascular diseases, they are still the most common cause of death in Germany [1]. Therefore, finding and improving therapies is a major goal of many researchers. Simulation frameworks support researchers and clinicians in developing and improving medical therapies but need to be verified and validated. Land et al. conducted a verification study on cardiac mechanics simulation software in 2015. They, as well as others, defined verification as “determining how ac- Fig. 1: The whole-heart geometry used for the simulation. On the curate a computer program solves the equations of a mathe- left is the mesh of the heart clipped in the longitudinal axis. The thick layer with the coarser mesh surrounding the four chambers is matical model” and validation is defined as “determining how the pericardial layer. Pictured on the right is the heart without the well a mathematical model represents the real world phenom- pericardial layer. ena it is intended to predict” [2]. *Corresponding author: Armin Müller, Institute of Biomedical The geometrical mesh was created from magnetic reso- Engineering, Karlsruhe Institute of Technology (KIT), Kaiserstr. 12, 76131 Karlsruhe, Germany, e-mail: publications@ibt.kit.edu nance imaging (MRI) data of a healthy 40 year old male vol- Ekaterina Kovacheva, Marc Alexander Fritz, Olaf Dössel, Axel unteer. The MRI data were provided by the University Hospi- Loewe, Institute of Biomedical Engineering, Karlsruhe Institute of tal Heidelberg. The whole-heart geometry comprises the four Technology (KIT), 76131 Karlsruhe, Germany Open Access. © 2020 Armin Müller et al., published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 License. 2 A. Müller et al., Validating a Numerical Simulation of Human Heart Motion Using Clinical Data chambers of a human heart (left and right atrium and left and After the short axis images were manually segmented right ventricle) as well as a layer that mimics the pericardium (ITK-SNAP, www.itksnap.org), surface meshes were created. as shown in Figure 1. Since at first we observed an intra-slices shift, we aligned the short axis slices based on the long axis slices. Furthermore, the orientation of the slices was aligned to the whole-heart geom- 2.1.2 Simulation etry used for the simulation. The aligned MRI slices were used as a ground truth and CardioMechanics calculates the deformation of the input ge- are compared to slices created synthetically from the whole- ometry that results from the interplay of the active and pas- heart simulation. The simulation slices and the MRI slices sive forces in the numerical model [3]. The underlying physics were aligned at the peak systole (at 500 ms). of cardiac biomechanics are described by the governing equa- Since only the slice meshes for the left ventricle were tion for the balance of linear momentum, which reduces to the available, we validated only the deformation of the left ven- equilibrium equation when mass inertia is neglected [4]. tricle at 34 time points across one heartbeat. Here, the numerical model used for the active tension was the model proposed by Stergiopulos et al. [5], while for the passive material properties the transversely isotropic model 2.3 Comparison Plugin proposed by Guccione et al. [6] was used. Since the patient’s pulse was 50 bpm at the time of the MRI acquisition, we used We implemented a plugin for CardioMechanics that compares 1.2 s as the heartbeat cycle length. For the evaluation, we used the slices created from the MR images and those created from the simulation’s fifth heartbeat to ensure that the simulation a simulation. The slices created from the MR images are an and the circulatory system model are in a steady state. input for the plugin. After the simulation is finished, the plugin creates the slices from the simulation results automatically. We decided 2.2 Data Generation to use the seven middle slices generated from the MR images and we named them slice0 (nearest to the heart’s base) to slice6 The MRI data consisted of 639 images with a resolution of (nearest to the heart’s apex) as shown in Figure 2. 256x256 px. 455 of those images were left ventricular short The plugin computes two different metrics on the corre- axis images, distributed over nine slice planes, 40 showed the sponding slices: the total area of the slice surface and the Haus- ventricular long axis with two chambers, and 35 the ventric- dorff metric of the mesh of the slices. ular long axis with four chambers. The last 109 images were The area is calculated for both slices of each pair. The whole-heart images. result was normalized to each slice’s maximum during the cy- cle to compare the development of the area independently of its absolute value. After that, we calculated the difference 𝑒 between the areas of the slices with 𝑒 = (𝑎𝑟𝑒𝑎 − 𝑎𝑟𝑒𝑎 ), 𝐴 𝐵 where 𝐴 and 𝐵 are the two slices that are compared. The Hausdorff metric, also called Hausdorff distance, measures the distance 𝑑(𝐴, 𝐵) between two non-empty com- pact subsets 𝐴, 𝐵 of a metric space 𝐸. It is defined as the great- est of all distances from a point in the first subset to the closest point in the second subset [7]. To calculate the distance between two non-empty sub- sets, the distance 𝛿 between a point 𝑥 and a non-empty com- pact set 𝐾 ⊆ 𝐸 is defined as 𝛿 (𝑥, 𝐾) := 𝑖𝑛𝑓{𝐷(𝑥, 𝑘)|𝑘 ∈ 𝐾}, where 𝐷 is a metric of space 𝐸. The directed Hausdorff distance (dHDD) between two non-empty com- Fig. 2: On the left are the slices generated from the MR images. The right part of the image shows the slices generated from the pact subsets 𝐴, 𝐵 ⊆ 𝐸 is defined as 𝑑 (𝐴, 𝐵) = 𝑑𝐻𝐷𝐷 simulation. On both sides, the simulated left ventricle is shown in 𝑠𝑢𝑝{𝛿 (𝑎, 𝐵)|𝑎 ∈ 𝐴}. Since dHDD is not symmetric, the transparent grey. The colors of slice0, slice2, slice4, and slice6 Hausdorff distance (HDD) is defined as 𝑑 (𝐴, 𝐵) = 𝐻𝐷𝐷 correspond to the colors used in later plots. 𝑚𝑎𝑥{𝑑 (𝐴, 𝐵), 𝑑 (𝐵, 𝐴)}. 𝑑𝐻𝐷𝐷 𝑑𝐻𝐷𝐷 To obtain more evaluations from the comparison with the HDD, we divided each slice into four sections: the top, the bot- A. Müller et al., Validating a Numerical Simulation of Human Heart Motion Using Clinical Data 3 tom, the endocardial and the epicardial face. Thus, we obtain 150 ms), the surface area initially decreased. After that, the four comparison values per slice instead of one. area of those three slices increased. Shortly after that, the area for all slices started decreasing until they reached their mini- mum in the peak systole at 500 ms. The peak systole was de- fined to be the point of maximum contraction. Directly after 3 Results the peak systole, there was an increase of the area up to the slice area’s maximum (at 650 ms for slice0, slice2, and slice4) In Figure 3 and 4, we show the normalized area of the slices followed by a decrease (up to 750 ms) and a phase with small during one heartbeat. changes until the end of the heartbeat. Slice6 showed a differ- ent behavior. After reaching the minimum in the peak systole, its area increased until the end of the heartbeat. In Figure 4, the surface area of the corresponding slices generated directly from the MR images is shown. The plots were aligned in time so that the peak systole in both plots ap- pear at the same time, at 500 ms. In this plot, the initial de- crease of the slice area is visible (at 320 ms) but it appears later compared to the simulation slices. After that, an increase of the area followed by a decrease up until the peak systole is visible. After the peak systole, there is an increase of the area up to its maximum at 1000 ms. While the simulation slices showed a decrease and a plateau phase after reaching the area’s maxi- mum, the MRI slices showed a decrease of the area until the end of the heartbeat. Fig. 3: Normalized surface area of the slices generated from the simulation. slice0 slice2 slice4 slice6 0 200 400 600 800 1000 1200 Time (ms) Fig. 5: The Hausdorff metric for the endocardial part of the slices. Figure 5 shows the results of the Hausdorff metric over the course of one heartbeat for the endocardial part of the slices. Fig. 4: Normalized surface area of the slices generated from the The four different parts of the slices show a very similar be- MR images. havior for the HDD allowing us to omit the plots for the other three parts. Figure 5 shows that slice2, slice4, and slice6 reach their maximum distance at peak systole (500 ms). The HDD of 20 mm is 26% of the ventricle diameter of 77 mm. After that, Figure 3 shows that for slice0 (between 0 and 70 ms), we observed a plateau phase (750 – 950 ms). This was fol- slice2 (between 0 and 130 ms), and slice4 (between 0 and lowed by an increase of the HDD and finally a decrease at the Hausdorff metric (mm) 4 A. Müller et al., Validating a Numerical Simulation of Human Heart Motion Using Clinical Data end of the heartbeat. Slice0 showed a plateau-phase from 750 5 Conclusion to 850 ms followed by an increase and a drop of the distance at the end of the heartbeat. In this work, we introduced a metric-driven approach to vali- date the deformation of a simulation of the human heart based on clinical data. The results showed that the validation of a car- 4 Discussion diac simulation using clinical data requires further effort. We could observe only global similarities between the simulation The surface area of the slices is affected by two factors: the and the MRI slices. Nevertheless, the comparison also showed wall thickness and the slice diameter. Until peak systole, the that especially the relaxation phase between the simulation and area of both slice sets decreases and after peak systole, the the clinical data differ markedly for this volunteer. area of both sets increases. This indicates global similarities between both slice sets. Author Statement The initial decrease of the surface area is due to the de- Research funding: We gratefully acknowledge funding by crease of the diameter while the wall thickness is rather con- HEiKA. Conflict of interest: Authors state no conflict of in- stant. The increase of the area in the following 150 ms is terest. Informed consent: Informed consent has been obtained caused by the thickening of the wall. After that, the wall thick- from all individuals included in this study. Ethical approval: ening continues while the slice’s diameter further decreases, The research related to human use complies with all the rel- so that the area also decreases until peak systole. In the future, evant national regulations, institutional policies and was per- we plan to quantify the diameter and radius changes. For the formed in accordance with the tenets of the Helsinki Decla- simulation slices, we can then observe an increase in the area ration, and has been approved by the authors’ institutional re- until it reaches its maximum at 650 ms due to the continuing view board or equivalent committee. wall thickening. The maximum of the area for the MRI-slices is reached significantly later, at 1000 ms. The simulation slices show a plateau phase during the relaxation phase until the end of the heartbeat (750 ms – 1200 ms) because of two compen- References sating factors: the thinning of the wall and the increasing of [1] German Heart Report 2018. https://dgk.org the diameter. [2] S. Land, V. Gurev, S. Arens, et al., "Verification of cardiac The ventricle’s deformation during the systole between mechanics software: benchmark problems and solutions the MRI and the simulation slices are different. Both, the for testing active and passive material behaviour,” Proceed- change of wall thickening as well as the change in diameter ings. Mathematical, Physical, and Engineering Sciences / the are less prominent for the MRI slices. Therefore, the HDD is Royal Society, vol. 471, no. 2184, p. 2015.0641, 2015. [3] T. Fritz, C. Wieners, G. Seemann, et al., “Simulation of the increasing. After the systole, the HDD for slice2, slice4, and contraction of the ventricles in a human heart model includ- slice6 reach a plateau-phase due to the increase of the diameter ing atria and pericardium: Finite element analysis of a fric- that compensates the thinning of the wall. The observed dif- tionless contact problem,” Biomechanics and Modeling in ferences might be due to a non-optimal choice of material pa- Mechanobiology, vol. 13, no. 3, pp. 627–641, 2014. rameters for the ventricle. Therefore, this comparison method [4] T. Belytschko, W. K. Liu, and B. Moran, "Nonlinear Finite can be included in an optimization framework which will de- Elements for Continua and Structures," Chichester: John Wiley and Sons, Ltd, 2000. termine optimal parameters for the material law so that the [5] N. Stergiopulos, et al., “Determinants of stroke volume and simulated deformation matches the one obtained from clinical systolic and diastolic aortic pressure,” Am J Physiol Heart data. Circ Physiol, vol. 270, no. 6, pp. H2050–H2059, 1996. For the HDD, the closest point was found by selecting the [6] J. M. Guccione, A. D. McCulloch, and L. K. Waldman, “Pas- nearest neighbor from the other set. Selecting the intersection sive material properties of intact ventricular myocardium determined from a cylindrical model,” J. Biomechanical Engi- of the normal of one point with the mesh of the other data-set neering, vol. 113, no. 1, pp. 42–55, 1 1991. might improve results. [7] F. Hausdorff, "Grundzüge der Mengenlehre". Verlag von Veit There were 34 time points per heartbeat available for the und Comp, 1914. creation of the MRI slices. For a thorough comparison, more [8] S. E. Luijnenburg, D. Robbers-Visser, A. Moelker, et al., time points would be desirable. The manual segmentation of "Intra-observer and interobserver variability of biventricular the slices from the MR images is observer-dependent [8]. function, volumes and mass in patients with congenital heart disease measured by CMR imaging,” Int J Cardiovasc Imag- Selecting different slices also impacts the validation re- ing, vol. 26, pp. 57–64, 2010. sults. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Current Directions in Biomedical Engineering de Gruyter

Validating a Numerical Simulation of Human Heart Motion Using Clinical Data

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© 2020 by Walter de Gruyter Berlin/Boston
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DOI
10.1515/cdbme-2020-3140
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Abstract

DE GRUYTER Current Directions in Biomedical Engineering 2020;6(3): 20203140 Armin Müller*, Ekaterina Kovacheva, Marc Alexander Fritz, Olaf Dössel, and Axel Loewe Validating a Numerical Simulation of Human Heart Motion Using Clinical Data https://doi.org/10.1515/cdbme-2020-3140 The aim of this work is to compare elastomechanical sim- ulation results with clinical data quantitatively and answer the Abstract: Numerical simulations are increasingly often in- question to what extent can we validate a cardiac simulation volved in developing new and improving existing medical with clinical data. In particular, the clinical data used in this therapies. While the models involved in those simulations are work provide the deformation of the left ventricle over time. designed to resemble a specific phenomenon realistically, the results of the interplay of those models are often not suffi- ciently validated. We created a plugin for a cardiac simula- tion framework to validate the simulation results using clinical 2 Methods MRI data. The MRI data were used to create a static whole- heart mesh as well as slices from the left ventricular short axis, 2.1 Numerical Simulation Framework providing the motion over time. The static heart was a starting point for a simulation of the heart’s motion. From the simula- The cardiac simulation framework that was used to perform tion result, we created slices and compared them to the clinical the validation was CardioMechanics [3]. It was developed at MRI slices using two different metrics: the area of the slices the Institute of Biomedical Engineering (IBT) at Karlsruhe In- and the point distances. The comparison showed global simi- stitute of Technology (KIT). This framework uses the finite larities in the deformation of simulated and clinical data, but element method to simulate the beating of the human heart. also indicated points for potential improvements. Performing this comparison with more clinical data could lead to person- alized modeling of elastomechanics of the heart. 2.1.1 Geometry Keywords: Simulation validation, numerical simulation, The numerical simulation was performed on a whole-heart ge- clinical data, motion deformation, human heart ometry consisting of 7623 points and 42282 tetrahedral vol- ume elements of a heart in end-diastolic state. 1 Introduction Despite a decrease in mortality of cardiovascular diseases, they are still the most common cause of death in Germany [1]. Therefore, finding and improving therapies is a major goal of many researchers. Simulation frameworks support researchers and clinicians in developing and improving medical therapies but need to be verified and validated. Land et al. conducted a verification study on cardiac mechanics simulation software in 2015. They, as well as others, defined verification as “determining how ac- Fig. 1: The whole-heart geometry used for the simulation. On the curate a computer program solves the equations of a mathe- left is the mesh of the heart clipped in the longitudinal axis. The thick layer with the coarser mesh surrounding the four chambers is matical model” and validation is defined as “determining how the pericardial layer. Pictured on the right is the heart without the well a mathematical model represents the real world phenom- pericardial layer. ena it is intended to predict” [2]. *Corresponding author: Armin Müller, Institute of Biomedical The geometrical mesh was created from magnetic reso- Engineering, Karlsruhe Institute of Technology (KIT), Kaiserstr. 12, 76131 Karlsruhe, Germany, e-mail: publications@ibt.kit.edu nance imaging (MRI) data of a healthy 40 year old male vol- Ekaterina Kovacheva, Marc Alexander Fritz, Olaf Dössel, Axel unteer. The MRI data were provided by the University Hospi- Loewe, Institute of Biomedical Engineering, Karlsruhe Institute of tal Heidelberg. The whole-heart geometry comprises the four Technology (KIT), 76131 Karlsruhe, Germany Open Access. © 2020 Armin Müller et al., published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 License. 2 A. Müller et al., Validating a Numerical Simulation of Human Heart Motion Using Clinical Data chambers of a human heart (left and right atrium and left and After the short axis images were manually segmented right ventricle) as well as a layer that mimics the pericardium (ITK-SNAP, www.itksnap.org), surface meshes were created. as shown in Figure 1. Since at first we observed an intra-slices shift, we aligned the short axis slices based on the long axis slices. Furthermore, the orientation of the slices was aligned to the whole-heart geom- 2.1.2 Simulation etry used for the simulation. The aligned MRI slices were used as a ground truth and CardioMechanics calculates the deformation of the input ge- are compared to slices created synthetically from the whole- ometry that results from the interplay of the active and pas- heart simulation. The simulation slices and the MRI slices sive forces in the numerical model [3]. The underlying physics were aligned at the peak systole (at 500 ms). of cardiac biomechanics are described by the governing equa- Since only the slice meshes for the left ventricle were tion for the balance of linear momentum, which reduces to the available, we validated only the deformation of the left ven- equilibrium equation when mass inertia is neglected [4]. tricle at 34 time points across one heartbeat. Here, the numerical model used for the active tension was the model proposed by Stergiopulos et al. [5], while for the passive material properties the transversely isotropic model 2.3 Comparison Plugin proposed by Guccione et al. [6] was used. Since the patient’s pulse was 50 bpm at the time of the MRI acquisition, we used We implemented a plugin for CardioMechanics that compares 1.2 s as the heartbeat cycle length. For the evaluation, we used the slices created from the MR images and those created from the simulation’s fifth heartbeat to ensure that the simulation a simulation. The slices created from the MR images are an and the circulatory system model are in a steady state. input for the plugin. After the simulation is finished, the plugin creates the slices from the simulation results automatically. We decided 2.2 Data Generation to use the seven middle slices generated from the MR images and we named them slice0 (nearest to the heart’s base) to slice6 The MRI data consisted of 639 images with a resolution of (nearest to the heart’s apex) as shown in Figure 2. 256x256 px. 455 of those images were left ventricular short The plugin computes two different metrics on the corre- axis images, distributed over nine slice planes, 40 showed the sponding slices: the total area of the slice surface and the Haus- ventricular long axis with two chambers, and 35 the ventric- dorff metric of the mesh of the slices. ular long axis with four chambers. The last 109 images were The area is calculated for both slices of each pair. The whole-heart images. result was normalized to each slice’s maximum during the cy- cle to compare the development of the area independently of its absolute value. After that, we calculated the difference 𝑒 between the areas of the slices with 𝑒 = (𝑎𝑟𝑒𝑎 − 𝑎𝑟𝑒𝑎 ), 𝐴 𝐵 where 𝐴 and 𝐵 are the two slices that are compared. The Hausdorff metric, also called Hausdorff distance, measures the distance 𝑑(𝐴, 𝐵) between two non-empty com- pact subsets 𝐴, 𝐵 of a metric space 𝐸. It is defined as the great- est of all distances from a point in the first subset to the closest point in the second subset [7]. To calculate the distance between two non-empty sub- sets, the distance 𝛿 between a point 𝑥 and a non-empty com- pact set 𝐾 ⊆ 𝐸 is defined as 𝛿 (𝑥, 𝐾) := 𝑖𝑛𝑓{𝐷(𝑥, 𝑘)|𝑘 ∈ 𝐾}, where 𝐷 is a metric of space 𝐸. The directed Hausdorff distance (dHDD) between two non-empty com- Fig. 2: On the left are the slices generated from the MR images. The right part of the image shows the slices generated from the pact subsets 𝐴, 𝐵 ⊆ 𝐸 is defined as 𝑑 (𝐴, 𝐵) = 𝑑𝐻𝐷𝐷 simulation. On both sides, the simulated left ventricle is shown in 𝑠𝑢𝑝{𝛿 (𝑎, 𝐵)|𝑎 ∈ 𝐴}. Since dHDD is not symmetric, the transparent grey. The colors of slice0, slice2, slice4, and slice6 Hausdorff distance (HDD) is defined as 𝑑 (𝐴, 𝐵) = 𝐻𝐷𝐷 correspond to the colors used in later plots. 𝑚𝑎𝑥{𝑑 (𝐴, 𝐵), 𝑑 (𝐵, 𝐴)}. 𝑑𝐻𝐷𝐷 𝑑𝐻𝐷𝐷 To obtain more evaluations from the comparison with the HDD, we divided each slice into four sections: the top, the bot- A. Müller et al., Validating a Numerical Simulation of Human Heart Motion Using Clinical Data 3 tom, the endocardial and the epicardial face. Thus, we obtain 150 ms), the surface area initially decreased. After that, the four comparison values per slice instead of one. area of those three slices increased. Shortly after that, the area for all slices started decreasing until they reached their mini- mum in the peak systole at 500 ms. The peak systole was de- fined to be the point of maximum contraction. Directly after 3 Results the peak systole, there was an increase of the area up to the slice area’s maximum (at 650 ms for slice0, slice2, and slice4) In Figure 3 and 4, we show the normalized area of the slices followed by a decrease (up to 750 ms) and a phase with small during one heartbeat. changes until the end of the heartbeat. Slice6 showed a differ- ent behavior. After reaching the minimum in the peak systole, its area increased until the end of the heartbeat. In Figure 4, the surface area of the corresponding slices generated directly from the MR images is shown. The plots were aligned in time so that the peak systole in both plots ap- pear at the same time, at 500 ms. In this plot, the initial de- crease of the slice area is visible (at 320 ms) but it appears later compared to the simulation slices. After that, an increase of the area followed by a decrease up until the peak systole is visible. After the peak systole, there is an increase of the area up to its maximum at 1000 ms. While the simulation slices showed a decrease and a plateau phase after reaching the area’s maxi- mum, the MRI slices showed a decrease of the area until the end of the heartbeat. Fig. 3: Normalized surface area of the slices generated from the simulation. slice0 slice2 slice4 slice6 0 200 400 600 800 1000 1200 Time (ms) Fig. 5: The Hausdorff metric for the endocardial part of the slices. Figure 5 shows the results of the Hausdorff metric over the course of one heartbeat for the endocardial part of the slices. Fig. 4: Normalized surface area of the slices generated from the The four different parts of the slices show a very similar be- MR images. havior for the HDD allowing us to omit the plots for the other three parts. Figure 5 shows that slice2, slice4, and slice6 reach their maximum distance at peak systole (500 ms). The HDD of 20 mm is 26% of the ventricle diameter of 77 mm. After that, Figure 3 shows that for slice0 (between 0 and 70 ms), we observed a plateau phase (750 – 950 ms). This was fol- slice2 (between 0 and 130 ms), and slice4 (between 0 and lowed by an increase of the HDD and finally a decrease at the Hausdorff metric (mm) 4 A. Müller et al., Validating a Numerical Simulation of Human Heart Motion Using Clinical Data end of the heartbeat. Slice0 showed a plateau-phase from 750 5 Conclusion to 850 ms followed by an increase and a drop of the distance at the end of the heartbeat. In this work, we introduced a metric-driven approach to vali- date the deformation of a simulation of the human heart based on clinical data. The results showed that the validation of a car- 4 Discussion diac simulation using clinical data requires further effort. We could observe only global similarities between the simulation The surface area of the slices is affected by two factors: the and the MRI slices. Nevertheless, the comparison also showed wall thickness and the slice diameter. Until peak systole, the that especially the relaxation phase between the simulation and area of both slice sets decreases and after peak systole, the the clinical data differ markedly for this volunteer. area of both sets increases. This indicates global similarities between both slice sets. Author Statement The initial decrease of the surface area is due to the de- Research funding: We gratefully acknowledge funding by crease of the diameter while the wall thickness is rather con- HEiKA. Conflict of interest: Authors state no conflict of in- stant. The increase of the area in the following 150 ms is terest. Informed consent: Informed consent has been obtained caused by the thickening of the wall. After that, the wall thick- from all individuals included in this study. Ethical approval: ening continues while the slice’s diameter further decreases, The research related to human use complies with all the rel- so that the area also decreases until peak systole. In the future, evant national regulations, institutional policies and was per- we plan to quantify the diameter and radius changes. For the formed in accordance with the tenets of the Helsinki Decla- simulation slices, we can then observe an increase in the area ration, and has been approved by the authors’ institutional re- until it reaches its maximum at 650 ms due to the continuing view board or equivalent committee. wall thickening. The maximum of the area for the MRI-slices is reached significantly later, at 1000 ms. The simulation slices show a plateau phase during the relaxation phase until the end of the heartbeat (750 ms – 1200 ms) because of two compen- References sating factors: the thinning of the wall and the increasing of [1] German Heart Report 2018. https://dgk.org the diameter. [2] S. Land, V. Gurev, S. Arens, et al., "Verification of cardiac The ventricle’s deformation during the systole between mechanics software: benchmark problems and solutions the MRI and the simulation slices are different. Both, the for testing active and passive material behaviour,” Proceed- change of wall thickening as well as the change in diameter ings. Mathematical, Physical, and Engineering Sciences / the are less prominent for the MRI slices. Therefore, the HDD is Royal Society, vol. 471, no. 2184, p. 2015.0641, 2015. [3] T. Fritz, C. Wieners, G. Seemann, et al., “Simulation of the increasing. After the systole, the HDD for slice2, slice4, and contraction of the ventricles in a human heart model includ- slice6 reach a plateau-phase due to the increase of the diameter ing atria and pericardium: Finite element analysis of a fric- that compensates the thinning of the wall. The observed dif- tionless contact problem,” Biomechanics and Modeling in ferences might be due to a non-optimal choice of material pa- Mechanobiology, vol. 13, no. 3, pp. 627–641, 2014. rameters for the ventricle. Therefore, this comparison method [4] T. Belytschko, W. K. Liu, and B. Moran, "Nonlinear Finite can be included in an optimization framework which will de- Elements for Continua and Structures," Chichester: John Wiley and Sons, Ltd, 2000. termine optimal parameters for the material law so that the [5] N. Stergiopulos, et al., “Determinants of stroke volume and simulated deformation matches the one obtained from clinical systolic and diastolic aortic pressure,” Am J Physiol Heart data. Circ Physiol, vol. 270, no. 6, pp. H2050–H2059, 1996. For the HDD, the closest point was found by selecting the [6] J. M. Guccione, A. D. McCulloch, and L. K. Waldman, “Pas- nearest neighbor from the other set. 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Journal

Current Directions in Biomedical Engineering – de Gruyter

Published: Sep 1, 2020

Keywords: Simulation validation; numerical simulation; clinical data; motion deformation; human heart

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