Comparisons of Simulation Results between Passive and Active FSI Models for Left Ventricle in Hypertrophic Obstructive Cardiomyopathy

Background. Patient-specific active Fluid-Structure Interactions (FSI) model is a useful approach to non-invasively investigate the hemodynamics in the heart. However, it takes a lot of effort to obtain the proper external force boundary conditions for active models, which heavily restrained the time-sensitive clinical applications for active computational models. Methods. The simulation results of 12 passive FSI models based on 6 patients’ pre-operative and post-operative CT images were compared with corresponding active models to investigate the differences in hemodynamics and cardiac mechanics between these models. Results. It was found that there was no significant difference in shear stress and pressure difference on mitral valve leaflet (MVL) between passive and active models, but a significant difference was found in wall stress on the inner boundary of left ventricle (Endocardium). It was also found that flow shear stress and pressure difference on the MVL were significantly decreased after successful surgery in both active and passive models. Conclusion . Our results suggested that the passive models may provide good approximated hemodynamic results at 5% RR interval, which is crucial for analyzing the initiation of systolic anterior motion (SAM). Comparing to active models, the passive models decrease the complexity of the modeling construction and the difficulty of convergence significantly. Therefore, with proper boundary conditions and sufficient clinical data, the passive computational model may be a good substitution model for the active model to perform hemodynamic analysis for left ventricle to investigate the mechanisms of the initiation of SAM.


Background
Hypertrophic obstructive cardiomyopathy (HOCM) is characterized by hypertrophic myocardium and obstruction in the left ventricular outflow. Patients with this disease might suffer from severe heart failure and even sudden death. Septal myectomy is the golden standard treatment for the symptomatic patients [1,2]. However, this is a very challenging procedure as the extent of myectomy is very difficult to be determined. This is because that inadequate excision cannot abolish left ventricular outflow obstruction, while the excessive myectomy might produce ventricular septal defect or irregular heart rhythms, such as complete heart block. Therefore, a non-invasive method is significantly necessary for helping surgeons make the optimal design of the surgery.
Several heart models, such as structural finite element models, computational fluid dynamics models, and fluid-structure interactions (FSI) models, have been proposed in the literature to assess the hemodynamics and myocardial functions in heart and become increasingly important in cardiovascular research [3][4][5][6]. Cardiac tissue is generally modeled as a hyper-elastic material [7]. Heart models can be divided into passive and active models to model the myocardial behavior [8][9][10][11][12][13][14][15]. The incompressible elastic solids are generally used to model soft tissue in passive models. The exponential strain energy functions have been widely used to describe the mechanical behavior of passive myocardium [8,11]. Electrical activation is one way to trigger the cardiac active contraction [9,10,[12][13][14]. While this method offers much more insight into the physiological processes, it also requires patient-specific identification of all the parameters inside the electromechanical models. In our case, the left ventricle (LV) is a severely pathological LV which may differ considerably from the ones reported in literature for healthy patients. Applying time-dependent material properties in a solid model is also a method to model active contraction [15,16]. However, patient-specific time-dependent material properties were not able to be measured at the in vivo state due to current technological limitations. In our study, we applied an external force to implement the LV myocardial active contraction. The 3D active FSI models were applied to investigate the biomechanics of the myocardium and the intraventricular flow in LV [17]. However, it takes a lot of effort to obtain the proper external force boundary conditions to match the numerical simulation results with clinical data, which prevents the active computational models from being used in time-sensitive clinical applications.
Comparing to the active model, the pressure boundary conditions of passive models were easier to obtain, which can save modeling time. What's more, it's easier for passive model to obtain the convergent solutions.
In this study, we constructed 12 patient-specific computed-tomography (CT) based passive FSI models for the LV of patients with HOCM, and we compared the numerical simulation results between these passive models and their corresponding active FSI models to investigate the differences.

Results
Based on 6 patients' pre-operative and post-operative LV CT Images, 12 patient-specific active and corresponding passive FSI models were constructed in this study. Figure 1 presents the numerical simulation results of  The maximum/minimum/mean values of wall stress and wall strain of each patient obtained from active models were compared with those from passive models. The comparison results are presented in The details of comparisons results of mean pressure and shear stress values are also listed in Table 4.

Pressure Difference and Shear Stress on MVL were found Significantly Decreased after Successful Surgery in both of Active and Passive Models
It was noticed that, before the surgery, the pressure on the posterior surface of MVL was higher than that on the anterior surface [17]. Therefore, to better investigate the differences between active and passive models, the pressure difference between posterior and anterior surfaces of MVL of the patients before and after surgery between different groups (patients receiving successful surgery vs. failed surgery) were investigated ( Although the values of pressure differences between posterior and anterior surfaces of MVL in passive models were lower than those obtained from active models, the same observations were found from both models (Fig.3).
The pre-operative and post-operative shear stress on MVL obtained from active and passive models were also investigated ( Fig. 4) higher than the mean value of those in Group 1 (Table 5).

DISSCUSSION
In this study, there were 12 active and corresponding passive FSI models constructed to compare the differences of simulation results between these two models. The numerical simulation results at pre-SAM time point, including wall stress and strain on the inner boundary of LV, and pressure and shear stress on MVL, were extracted to be compared.
It was found that there was a significant difference in wall stress between the passive and active models. The mean value of maximum wall stress in passive models was 29.09% higher than that in active model. However, there were no significant differences of strain values and fluid results between the active and passive models. Based on simulation results obtained from passive models, the pressure difference on coapted MVL and shear stress on MVL were found decreased significantly after successful surgery, but remained still high after failed surgery. These findings are in good agreement with the results obtained from active models [17].
While the mechanisms driving the left ventricle motion in the passive model is different from real heart motion, the simulation of the hemodynamic status, the motion and deformation of LV can still be approached by the passive models. In both of our passive and active models, the boundary conditions were adjusted to match the simulation results with clinical data. That is, at pre-SAM time, the simulation results of average pressure, LV volume, and LVOT velocity were matched with clinical measured data well in both of passive and active models. Our results indicated that, if we focus on the simulation results of left ventricle at some specific time points, the passive model may provide simulation results of blood flow matching well with active models with proper boundary conditions and sufficient clinical data. to obtain the proper boundary conditions for active models comparing to passive models.
In addition, the passive models also decrease the difficulty of convergence significantly.
Since the goal of our study was to perform hemodynamic analysis of LV to investigate the mechanisms of SAM, and the passive models provided good approximated hemodynamic simulations, the passive models may be used as a good substitution model to active models to investigate the initiation of SAM.
Some limitations of this study are acknowledged here. The main limitation of the study is the small sample size which results in limited statistical power. The reason for the small sample size is that the computational modeling method takes large time costs, 1) it takes a lot of effort to find the proper boundary conditions for active models; 2) the construction procedure for both of active and passive models also takes time; 3) it's not easy to obtain patient-specific CT data. Currently, multi-patient studies for heart model simulations is still rare. Adding more patients will be our future effort. Applying commercial software, such as HyperMesh, to automatically create the finite element mesh to save the construction time will be considered. Another limitation is that the valve opening and the chord was not included in our model. From the end of the isovolumic systole to the pre-SAM time point, the mitral valve is almost closed. Therefore, the simulated hemodynamic status of LV, which is very crucial for analyzing the initiation of SAM, should be very similar to the real one.

Conclusion
In this study, based on CT images of 6 HOCM patients before and after surgical septal myectomy, 12 active and corresponding passive FSI models were developed to compare the simulated biomechanics and hemodynamics behaviors between passive and active models. It was found that, between these models, there was a significant difference in wall stress, but the differences in hemodynamic simulation results were not significant.
Compared with active models, the passive models decrease the complexity of the modeling construction and the difficulty of convergence significantly. Therefore, with proper boundary condition, the passive model may be a good approximation to active model with less computational cost to perform hemodynamic analysis for left ventricle to investigate the initiation of SAM. Prospective and large-scale studies are needed to further validate our findings.

Data acquisition
Institution review board approval on human subject research at Fuwai Hospital was obtained for this study.  Table 1.
Cardiac CT images were obtained at every 5% inter-beat (RR) interval. In all these six patients, the beginning time of SAM ranged from 5% to 8% RR interval in the cardiac cycle. Therefore, to investigate the initiation of SAM, the pre-operative and post-operative CT images at 5% RR interval were selected as pre-SAM time point data to construct the computational models. The field of view was 256 mm x 256 mm, the matrix was 512 x 512, and the slice thickness was 0.625mm. More details about the CT images and segmentation for the construction of FSI models can be found from Deng et al [17,18]. Patients' heart rate and blood pressure at the time of CT examinations were used in the simulation. The patient-specific LV volume, pressure and the left ventricular outflow tract (LVOT) velocity at pre-SAM time obtained from echo and MRI data were used to verify the simulation results (Table 2).

Fluid-Structure Interaction Models
The modified non-linear Mooney-Rivlin model was adopted to characterize the mechanical behavior of LV myocardium. The strain-energy function for the isotopic incompressible Mooney-Rivlin model was expressed as, where 1 , and 2 are the first and second strain invariants, is the right Cauchy-Green deformation tensor, where is the current position, is the original position, and 1 , 2 , 1 , and 2 are material constants [16,19]. Details of the determination of the patient-specific material constants have been described in our previous publication [17,18].
The blood in the LV was treated as a laminar, Newtonian, viscous and an incompressible fluid. In this study, we set the viscosity of = 0.04 dyn • cm −2 and density of = 1 g • cm −3 for blood properties. The Navier-Stokes equation with Arbitrary Lagrangian Eulerian formula was used as the governing equation. A no-slip boundary condition between the interfaces was assumed. The structure and fluid models were coupled through their interfaces [16,19,20].

Solution Method
In the construction process of both of active and passive models, the initial shrinkage rate was set as 5% to receive the zero-load geometry which is the starting geometry for the numerical simulation. When the pressure was applied at inlet, the left ventricle expanded in short-axis and long-axis direction, and then regained its in vivo morphology. During this phase, the mitral valve (MV) kept open and the blood filled into LV though MV. At the end of this phase, LV reaches its maximum volume and the pressure in LV increases to end of isovolumic systole pressure. The information of the blood flow and mechanics of LV were received as the starting state of the simulation for the phase from end of systole phase to pre-SAM time point. The details of the pre-shrink process can be found from our previously published paper [17,18].
The finite element meshes was generated by the volume component-fitting method [16,20]. The constructed computational models were solved by commercial software ADINA (ADINA R&D, Watertown, MA), which uses the Newton-Raphson iteration and unstructured finite elements method. The iterative FSI coupling solution method was applied to handle fluid-structure interaction.

Differences between the Passive and Active Models
The simulations of the phase from end of systole phase to pre-SAM time point between active model and passive model were different. In passive models, the inlet (mitral valve) was closed, and the blood was ejected out of LV through the outlet (aortic valve).
The left ventricle muscle was deflated by the patient-specific pressure condition which was scaled based on measured blood pressure conditions, and the pressure difference between LV and aorta which was obtained from ultrasound scanning. In active models, we simulated the LV active contraction by specifying the external forces at epicardium, and the pressure condition at outlet (aortic valve) from the end of isovolumic systole phase to pre-SAM time point (5% RR) [17]. Based on the clinical measured data of LV volume, LV pressure, and LOVT velocity obtained from echo and MRI data at the end of isovolumic systole phase and pre-SAM time point, the external forces were applied on each element at the epicardium, and the pressure condition at outlet at each time step were numerically interpolated. The boundary conditions were manually adjusted accordingly, such that the difference between clinical measured data and the simulation results were less than 5%. The real LV active contraction motion was then implemented.
The adjustment of the boundary conditions was primarily based on the comparisons of numerical results and clinical data at each time step. For more details about the construction of active and passive models, we refer the reader to our previous publications [17].

Data Extraction and Statistical Analysis
The stress, strain, and shear stress are all tensors, therefore, the maximum principal stress (Stress-P 1 ), maximum principal strain (Strain-P 1 ), and maximum shear stress at each node were chosen as wall stress, strain, and shear stress, respectively, for convenience. Data were selected for analysis. The data was expressed as mean ± SD (standard deviation).
The linear Mixed-Effect-Model [21,22] was used to incorporate the non-independent data structure, and compare the simulation results between passive and active models.
The statistical significance was established at a p value of < 0.05. All statistical analyses in this study were conducted using R software (version 3.5.1).

Ethics approval and consent to participate
This study was approved by Institution review board approval on human subject research at Fuwai Hospital.

Consent for publication
Not applicable

Availability of data and materials
The datasets generated during and/or analyzed during the current study are available from the corresponding author at reasonable request.

Competing interests
The authors declare that they have no competing interests.

Funding
The research for this project is funded in part by the Natural Science Foundation of

Authors' contributions
XH and LD designed the study. YS performed the operations. LD collected the clinical data. CY constructed the computational model and performed the numerical simulation.
LD and XH wrote the paper. HZ, ML, and XH perform the statistical analysis. YS, ML, and DT critically reviewed the paper. All the authors read and approved the final manuscript.  Table 2. Table 2. Summary of the comparisons of simulation results of LV pressure, volume, and the left ventricle outflow tract (LVOT) velocity at pre-SAM time obtained from active (Act) and passive (Pas) models, and those from clinical data. Table 3. Summary of comparisons of wall stress and strain values obtained from active and passive models. Diff (%) represents the relative percentage difference based on active models.  Group (Group 2, n=1) obtained from active and passive models. Table 6. Summary of comparisons of the adjustment times for boundary conditions between active models and passive models.