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A patient-specific right/left ventricle and patch (RV/LV/patch) combination model with fluid-structure interactions (FSIs) was introduced to evaluate and optimize human pulmonary valve replacement/insertion (PVR) surgical procedure and patch design. Cardiac magnetic resonance (CMR) imaging studies were performed to acquire ventricle geometry, flow velocity, and flow rate for healthy volunteers and patients needing RV remodeling and PVR before and after scheduled surgeries. CMR-based RV/LV/patch FSI models were constructed to perform mechanical analysis and assess RV cardiac functions. Both pre- and postoperation CMR data were used to adjust and validate the model so that predicted RV volumes reached good agreement with CMR measurements (error <3%). Two RV/LV/patch models were made based on preoperation data to evaluate and compare two PVR surgical procedures: (i) conventional patch with little or no scar tissue trimming, and (ii) small patch with aggressive scar trimming and RV volume reduction. Our modeling results indicated that (a) patient-specific CMR-based computational modeling can provide accurate assessment of RV cardiac functions, and (b) PVR with a smaller patch and more aggressive scar removal led to reduced stress/strain conditions in the patch area and may lead to improved recovery of RV functions. More patient studies are needed to validate our findings.
Image-based computational modeling and medical imaging technologies have made considerable advances in biological and clinical research in recent years [1–8]. The use of computer-assisted surgery design procedures is becoming more popular in the clinical decision-making process to replace empirical and often risky clinical experimentation to examine the efficiency and suitability of various reconstructive procedures in diseased hearts. In this paper, a patient-specific right ventricle, left ventricle, and patch (RV/LV/patch) combination model with fluid-structure interactions (FSI) is introduced to optimize human pulmonary valve replacement/insertion (PVR) surgical procedure and patch design. While our purpose is to assess RV cardiac functions with various patch designs and surgical options, LV is included as a support to RV so that more reasonable RV deformation can be obtained from the RV/LV combination model. We are testing the hypotheses that (a) patient-specific image-based modeling can provide accurate information for assessment of RV cardiac function, and (b) a smaller patch in PVR with more aggressive scar removal and RV volume reduction using computer-aided surgery design with optimized postoperative RV morphology and patch design will lead to improved recovery of RV functions .
Right ventricular dysfunction is a common cause of heart failure in patients with congenital heart defects and often leads to impaired functional capacity and premature death. Patients with repaired tetralogy of Fallot (ToF), a congenital heart defect which includes a ventricular septal defect and severe right ventricular outflow obstruction, account for the majority of cases with late onset RV failure. The mechanism of failure is a complex interaction of chronic pulmonary valve regurgitation (present since the original repair), a noncontractile and sometimes aneurysmal RV outflow, ventricular scarring from the incision to remove RV outflow muscle at the original repair, and at times some residual obstruction to RV outflow. The current surgical approach, which includes PVR, has yielded mixed results, with many of the patients seeing little if any improvement in RV function, while in others there is a significant improvement [10,11]. The reason for the unpredictable results is the fact that the PVR surgery only addresses one mechanism for RV dysfunction and dilatation, namely, pulmonary regurgitation. More radical surgical procedures, where scar tissue and even noncontracting segments of the RV muscle are removed, are being performed (NIH-HL63095, del Nido; NIH-NHLBI5P50HL074734, P.I.—Geva; coinvestigator—del Nido). Figure 1 gives sketches of a diseased RV with old patch and scar tissue and illustrations of the conventional and proposed surgical procedures. However, there are currently no evaluation and assessment methods to predict which patients will benefit from the various surgical options, and certainly no methods to tailor the procedure to the individual patient with some confidence of the outcome.
Due to the complexity of human heart structure and difficulties involved in acquiring human subject data and solving models including FSIs, patient-specific RV models with FSIs for actual surgery planning and optimization based on and verifiable by clinically available data are lacking in the current literature and clinical practice. Early 3D models for blood flow in the heart include Peskin’s model, which introduced fiber-based LV model and the celebrated immersed-boundary method to study blood flow features in an idealized geometry with FSIs . A large amount of effort has been devoted to quantifying heart tissue mechanical properties and fiber orientations mostly using animal models [13–17]. Humphrey’s book provides a comprehensive review of literature . More recent efforts include introduction of magnetic resonance imaging (MRI)-based fluid-only or structure-only 3D models to investigate flow and stress/strain behaviors in the whole ventricle (either RV or LV)[7,18–21]. Stevens et al. introduced a 3D finite element (FE) solid model of the heart based on measurements of the geometry and the fiber and sheet orientations of pig hearts. The end-diastolic deformation of the model was computed using the “pole-zero” constitutive law to model the mechanics of passive myocardial tissue specimens. The sensitivities of end-diastolic fiber-sheet material strains and heart shape to changes in the material parameters were investigated [22,23]. McCulloch and co-workers performed extensive research for 3D ventricular geometry and myofiber architecture of the rabbit heart. Their work included experimental and modeling studies of 3D cardiac mechanics and electrophysiology [20,21,24–26]. The papers by Nash and Hunter  and Hunter et al.  provided comprehensive reviews for heart modeling, including tissue properties, fiber orientation, passive and active mechanical models, electromechanical models, and whole heart models. Those animal models provide insight for human heart mechanics and functions.
In this paper, we propose a novel integrated surgery/modeling process, which combines innovative surgical procedures, noninvasive CMR techniques, and computational modeling to optimize surgical techniques for RV anterior wall volume reduction and remodeling related to PVR. Our new contributions are as follows: (a) our approach is truly interdisciplinary where novel cardiac surgical procedures, CMR techniques, and advanced computational modeling are combined to optimize patch design and RV volume reduction methods for realistic clinical and surgical applications; (b) preoperation patient-specific RV/LV morphology, pressure, and adjusted material properties will be used to construct the model to predict postoperation outcome and model predictions can be verified by postoperation CMR measurements; and (c) the FSIs included in the FSI model will give both flow velocity, shear stress, and structural stress/strain distributions, which will serve as basis for many further investigations. Details of the RV/LV/patch combination model are given below.
Figure 2 gives a sketch of a healthy human heart with RV, LV, a stack of RV contours, and the reconstructed RV/LV geometry obtained from a healthy volunteer. Figure 3 shows preoperation CMR images and segmented MRI contour plots from a patient using protocols approved by Children’s Hospital (Boston, MA) Investigational Review Board and patient consent obtained. Cardiac MRI (CMR) studies were performed in a dedicated MRI suite located in the Department of Cardiology at Children’s Hospital (Boston, MA) to acquire patient-specific ventricle morphology, flow velocity, and flow rate for patients needing pulmonary valve replacement operations before and after scheduled surgeries and healthy volunteers. Thirty RV/LV positions were acquired during one cardiac cycle. Each position contains 10–14 planar slices. 3D RV/LV geometry and computational mesh were constructed under the adina computing environment following the procedures in Refs. [28–30]. The procedure is explained as follows. For each object (made of one material) such as the ventricle, patch, scar, or the fluid domain, we first divide its geometry into enough volumes so that each volume has a more regular shape for mesh/element generation. We next specify an element group for each volume, which includes element style, material, and other information (such as indications assuming large strain or large displacement for the kinematic formulation for the element group). After that, we specify mesh density and mesh style for each volume. Elements of all the volumes were generated using the adina command “Gvolume.” The key here is the proper division of each physical object into computational volumes so that mesh/elements can be generated. This step has a strong influence on the element shape and convergence of the model. For a RV/LV/patch/scar combination model, many volumes are needed. Figure 4 gives the stacked MRI contours and RV/LV inner/outer surface plots showing patch, scar, and valve positions. The location and sizes of the patch and scar tissues were determined by del Nido with his experience and confirmed during actual surgery. Volumes and elements used for this patient-specific model are as follows: normal RV/LV tissue: volumes: 223, elements: 18,896; scar: volumes: 18, elements: 1020; patch: volumes: 11, elements: 880; and fluid: volumes: 138, elements: 152,591. Total volumes for the whole model: 390; total elements: 173,387.
The RV, LV, scar tissue, and patch material were assumed to be hyperelastic, isotropic, nearly incompressible, and homogeneous. The governing equations for the structure models are (summation convention is used) as follows:
where σ is the stress tensor, ε is Green’s strain tensor, v is solid displacement vector, subscript tt in vi,tt indicates the second-order time derivative, f ·,j stands for derivative of the function with respect to the jth variable, and ρ is material density. Equations (1) and (2) are used for RV/LV muscle, patch, and scar tissues, with parameter values in the constitutive equations (given below) adjusted for each material. The nonlinear Mooney–Rivlin model was used to describe the nonlinear properties of the materials with parameter values chosen to match available experimental data and adjusted to reflect stiffness variation of different materials [16,18]. The strain energy function for the modified Mooney–Rivlin model is given by [7,8,16,32,33]
where I1 and I2 are the first and second strain invariants, C=[Cij]=XTX is the right Cauchy–Green deformation tensor, X=[Xij]=[xi/aj], (xi) is current position, (ai) is original position, and ci and Di are material parameters chosen to match experimental measurements [16,18]. The 3D stress/strain relations can be obtained by finding various partial derivatives of the strain energy function with respect to proper variables (strain/stretch components). In particular, setting material density ρ=1 g cm−3 and assuming
where λ1, λ2, and λ3 are stretch ratios in the (x, y , z) directions, respectively, the uniaxial stress/stretch relation for an isotropic material is obtained from Eq. (3),
The patient-specific stress-stretch curves derived from Mooney–Rivlin models fitting CMR-measured data are given in Fig. 5. Patch and scar stiffness were chosen to be 20 and 10 times of that of RV tissue, respectively (by adjusting c1 and D1 values, D2 was unchanged) so that they were considerably stiffer than RV tissues. There are several types of patch material with different degrees of elasticity in the industry (Dacron, teflon, bovine pericardium, autologous pericardium, etc.). Material parameters in our future patch models will be adjusted (which is easy to do) according to industrial specifications to quantify effects of patch material properties on RV function recovery .
Blood flow was assumed to be laminar, Newtonian, viscous, and incompressible. The Navier–Stokes equations with arbitrary Lagrangian-Eulerian (ALE) formulation were used as the governing equations. Pressure conditions were prescribed at the tricuspid (inlet) and pulmonary (outlet) valves . Since RV muscle was treated as a passive material, pressure conditions were modified so that RV could be inflated properly by fluid forces (Fig. 6). No-slip boundary conditions and natural force boundary conditions were specified at all interfaces to couple fluid and structure models together [32,33]. Putting these together, we have
where u and p are fluid velocity and pressure, ug is mesh velocity, Τ stands for RV inner wall, and σ is structure stress tensor (superscripts r and s indicate different materials: fluid, RV tissue, scar, and patch). Together with Eqs. (1)–(3), we have the completed FSI model.
To simplify the computational model, the cardiac cycle was split into two phases: (a) the filling phase when blood flows into RV, the inlet was kept open, and the outlet was closed; and (b) the ejection phase when blood was ejected out of RV, the outlet was kept open, and the inlet was closed. When the inlet or outlet was closed, flow velocity was set to zero and pressure was left unspecified. We start our simulation cycle when RV has its smallest volume (end of systole) corresponding to the minimal inlet pressure. As the inlet pressure increases, blood flows into RV and its volume increases. When RV reaches its maximal volume, the inlet closes and the outlet opens. Blood is ejected and RV volume decreases. That completes the cycle. While the mechanism driving the motion is different from the real actively contracting heart, our simulated RV motion, deformation, volume change, and fluid flow can provide results matching patient-specific data with properly adjusted material parameters and flow-pressure boundary conditions.
For simplicity, LV was included as a structure-only model with the same material parameter values used for both LV and RV tissues. A recorded LV pressure was specified inside the LV so that the LV would expand and contract properly matching CMR data. The inclusion of LV is important to obtain the correct RV motion and deformation. Blood flow in the LV was not included to reduce the computational effort.
We started from a healthy case (Fig. 2) to gain some base line information. The fully coupled FSI RV/LV model was solved by adina (ADINA R&D, Watertown, MA) to obtain full 3D flow, deformation, and stress-strain distributions, which served as the basis for our investigations. Pressure conditions given in Fig. 6(c) were prescribed. Figure 7 gives maximum principal stress (Stress-P1) and maximum principal strain (Strain-P1) plots with a cut surface chosen so that stress/strain behaviors on the RV inner surface could be observed. Maximum Stress-P1/Strain-P1 values were observed near the RV outlet where RV curvature was large. Figure 8 gives four flow velocity plots at different fillings and ejection times, which show interesting patterns with multiple vortexes. The implications of these complex flow velocity and shear stress patterns on RV cardiac functions and disease development will be investigated when more patient data become available. Further solution details are omitted because we are focusing on surgical optimization for diseased RVs in this paper and more results will be reported in the following sections.
With experience learned from the healthy case, a RV/LV/patch model based on preoperation data from a patient was constructed (Figs. (Figs.33 and and4)4) and solved by adina. It should be noted that the diseased RV is considerably larger than the healthy one. This model (M1) would be validated by preoperation data and used to create new patch models to evaluate various surgical and patch options. Figure 9 shows the prescribed pressure conditions and an impressive agreement between the computational and CMR-measured preoperation RV volumes achieved by adjusting material parameters and prescribed pressure conditions in the model. The maximum error (from the 30 time points where MRI data are available) is an impressive 2.7% (11.1 ml/406.9 ml end of diastole), well within the measurement accuracy margin. Figure 10 gives the position of a selected cut surface and Stress-P1/Strain-P1 distributions on the inner RV surface corresponding to maximum/minimum pressure conditions. Once again, maximum Stress-P1/Strain-P1 values occurred at locations with large curvatures. The patch and scar areas had lower strain values (Fig. 10(c)) because the materials were stiffer, as expected.
With the model tuned using the patient-specific preoperation material and pressure data (the volume agreement could be considered as validation by the preoperation data), we were ready to make new patch models to evaluate different patch designs and surgical options. Figure 11 gives sketches of three models: the preoperation model (M1), Patch Model 1 (M2, conventional), and Patch Model 2 (M3, small patch with aggressive trimming). Patch Models M2 and M3 were designed with guidance from del Nido, a cardiac surgeon with more than 20 years of surgical experience. Each slice from the M1 model was shrunk to get the corresponding slices for M2 and M3 and desirable volume reductions. The slices and reconstructed geometries of M2 and M3 were reviewed by del Nido and adjusted as needed before they were used to build the FE models. Figure 12 illustrates how M2 and M3 were constructed from the original M1 contours. With the newly designed patches and RV geometries, the models were solved by adina and solutions were compared and analyzed.
Results reported in Secs. 3.1 and 3.2 indicated that global maximum stress/strain values often occur at locations with large curvatures; therefore, they may not be good indicators for our model/patch comparison and optimization purpose. Our previous experiences from Ref.  suggest that stress/strain variations at selected locations near the patch may be more sensitive indicators for our model comparisons. Figure 13 gives Stress-P1/Strain-P1 variations tracked at selected locations in the patch area for the three cases showing that stress/strain levels around the patch are considerably lower (50% lower for stress and 40% lower for strain) from the small patch model compared to large patch models. This means that the smaller patch would be under lower stress conditions and the ventricle with a smaller patch would not have to work as hard as the ones with larger patches. The significance of this finding needs to be supported by further clinical studies.
To assess RV cardiac functions and evaluate possible outcome of different surgical options, two commonly used measures of RV functions were used:
where RVEDV=RV end of diastole volume and RVESV=RV end of systole volume, respectively. Our results indicated that while maximum RV volumes for the three models were different as expected, their volume variations in a cardiac cycle had similar patterns mostly determined by the specified pressure conditions (see Fig. 9). RVEDV, RVESV, SV, and EF values for the three models are summarized in Table 1, which indicates that the proposed small patch design would provide about 10% improvement in EF compared to the conventional patch model (38.5% versus 35.3%). The improvement in EF was more than 100% compared to the preoperation ventricle, when pulmonary regurgitation was taken into consideration (38.5% versus 18.3%, see Sec. 3.4 for CMR data). As part of the RV remodeling clinical trial (P.I.—Geva), the patient was randomized to take either conventional patch reduction + PVR, or RV remodeling with patch reduction, scar tissue removal, + PVR.
One advantage of our approach is that postoperation data can be obtained to validate computational predictions based on preoperation data. When needed, the computational model can be adjusted to better match postoperation CMR measurements. The CMR-measured postoperation RV volume and computer-predicted RV volume based on preoperation data are given by Fig. 14(a). The error margin of volume predictions was 9.4%. Noticing the differences in the volume profiles and that it is the same patient with the same ventricle, we modified the prescribed pressure profile and kept the material parameters unchanged. Figure 14(b) shows that the modified model predicted RV volume with much improved accuracy (new predicted maximum volume: 190.2 ml, error for the entire cycle <3%). RV cardiac functions (stroke volume and ejection fractions) were calculated and compared with actual postoperation CMR measurements. The ejection fraction for the modified small patch model was 39.2% (see Table 1).
Pulmonary regurgitation seriously affects RV cardiac function and should be taken into consideration when assessing RV ejection fraction before surgery to obtain the true improvement in EF after surgery. For the patient considered in this paper, CMR-measured averaged flow rate and accumulated outflow volume at the pulmonary valve are given by Fig. 15. The total recorded outflow in one cardiac cycle was 159.63 ml; pulmonary regurgitation: 81.83 ml; PR rate: 51.26%; and net outflow: 74.6 ml. When pulmonary regurgitation was combined in the calculation, the EF improvement of the proposed patch model was more than 100% compared to the preoperation model (see Table 1). The PR-adjusted ejection fraction (EFPR-adj) given by
provides a more accurate measure of RV functions and was used in Table 1.
Our model is a first attempt to introduce patient-specific RV/LV/patch/scar combination models with FSIs for realistic computer-aided surgical design and optimization. Several simplifications were made when we selected our model: Active heart contractions, fiber orientations, and anisotropic properties were not included in our model. These model simplifications were made for the following reasons: (a) we want to use clinically measurable data so that our model can be used in patient-specific surgery design and realistic clinical applications, (b) the model should be simple enough to be constructed and solved for a quick turnaround time (ideally within 24–48 h when implemented for clinical use), and (c) the model should capture key factors so that we can assess RV cardiac function (RV stroke volume and ejection fraction) and make accurate and verifiable predictions needed in the surgery design. Since material parameters can be adjusted so that model-predicted RV volumes can match CMR-measured RV volumes (which can be considered validation by patient data), our model can be used for accurate RV cardiac function assessment based on SV and EF calculations. It should be understood that predicted stress distributions will be more model dependent and should be interpreted with caution. However, comparative stress studies can still provide useful information because relative differences will be less model dependent.
Several improvements can be added to our models in the future for better accuracy and applicability: (a) Valve mechanics. Valves can be added into our model for better flow control at the inlet and outlet.(b) Fiber orientation and anisotropic material properties. Patient-specific fiber orientation data cannot be measured with the current technology. However, single and multilayered (epicardium, midlayer, and endocardium) anisotropic models can be introduced to seek possible improvement in computational prediction accuracies. (c) Active contraction model. One way to add active contraction into our model is to introduce an external force field, which is tied to fiber structure and orientations. Measurement and validation of the external force field are not currently available. Another way to induce contraction is to make the RV material stiffer during systole. These improvements will be our future directions; each will take considerable effort to implement. Compared with these improved models, we still expect that the SV and EF predictions by our model will have similar accuracies since calculation of SV and EF involves RV volumes and the improved models will also be adjusted to match CMR-measured data.
Our results indicated that the best patch material would be materials that have similar elastic properties to that of ventricle tissues. However, we are limited by market availability. There are several types of patch material with different degrees of elasticity (Dacron, teflon, bovine pericardium, autologous pericardium, etc.). Material parameters in the patch models can be adjusted according to industrial specifications to quantify effects of patch material properties on RV function recovery .
Since there are many factors involved and model construction is very time consuming and labor intensive, an incremental adjustment approach will be followed in future clinical practice, subject to surgical and anatomical constraints, and with guidance from the surgeon. Starting from the current most conservative Patch Model 1 (minimum to no removal of scar tissue and a conventional patch) to the most aggressive Patch Model 2 (maximum resection surgically possible and safe of scar and patch), a middle-ground model will be designed based on patient-specific anatomy, blood pressure, and other relevant factors. Results from the three models will be presented to the surgeon after the surgery for his review. When postoperation data are obtained, model adjustments will be made as needed to optimize the predicted outcome (see Table 1). Experience learned from analyzed cases will be applied to new cases so that factors such as RV remodeling and pressure adjustments after surgery can be included in future model design for more accurate predictions. Our preliminary results indicate that the small patch model (Patch Model 2) leads to improved RV function recovery and lowered stress/strain variations, which may also be helpful for the ventricle to save energy and improve its function. More studies are needed to validate these initial observations.
Preoperation data (morphology, cardiac motion in one cycle, pressure, and RV volume) were used not only for constructing the model, but also for validation of the model and computational results. RV pressure and volume data were used to determine patient-specific material parameter values to fit CMR RV volume data. The validated model matching preoperation data (patient-specific RV/LV morphology, material parameters, and pressure conditions) were used to perform patch-design simulations and predict postoperation RV cardiac function. The model (mainly the pressure condition) was adjusted again to match postoperation CMR-measured RV data for more accurate predictions. While the ventricles are the same (other than the patch and scar tissue removal), the flow mechanical environment is considerably different, which leads to pre- and postoperation RV pressure differences. More case studies will help us to better predict postoperation RV pressure prior to surgery so that the first-time prediction accuracy can be improved. In a way, our modeling process will “learn” to improve as more experience is gained.
Our preliminary data indicate that MRI-based FSI RV/LV/patch models validated by preoperation data have great potential to make accurate assessment of RV cardiac functions and may be used to replace expensive and risky surgical experiments. PVR surgical procedure with a smaller patch and more aggressive scar removal may lead to reduced stress/strain conditions in the patch area and improved recovery of RV functions. Integration of surgical, imaging, and modeling components could lead to considerable potential gain not only in surgical planning and patient outcome assessment, but also in our understanding of the mechanisms involved in RV failure. Scientifically, the 3D flow, RV stroke volume, ejection fraction, and 3D RV stress/strain distributions from patients and healthy volunteers will add to the current literature and form a database for future research and investigations. More patient studies are needed to validate our findings.
This research was supported in part by NIH-HL63095 (PJdN), NIH-NHLBI 5P50HL074734 (P.I.—Geva; coinvestigator—del Nido), and NSF of China Project Nonlinear PDEs in Geometry (10371001).
Dalin Tang, Mathematical Sciences Department, Worcester Polytechnic Institute, Worcester, MA 01609.
Chun Yang, Mathematical Sciences Department, Worcester Polytechnic Institute, Worcester, MA 01609; Mathematics Department, Beijing Normal University, Beijing, P.R.C.
Tal Geva, Department of Cardiology, Children’s Hospital, Boston, MA 02115; Department of Pediatric, Harvard Medical School, Boston, MA 02115.
Pedro J. del Nido, Department of Cardiac Surgery, Children’s Hospital, Harvard Medical School, Boston, MA 02115.