Theoretical Impact of the Injection of Material Into the Myocardium
A Finite Element Model Simulation
Background— To treat cardiac injuries created by myocardial infarcts, current approaches seek to add cells and/or synthetic extracellular matrices to the damaged ventricle to restore function. Because definitive myocardial regeneration remains undemonstrated, we propose that cardiac changes observed from implanted materials may result from altered mechanisms of the ventricle.
Methods and Results— We exploited a validated finite element model of an ovine left ventricle with an anteroapical infarct to examine the short-term effect of injecting material to the left ventricular wall. The model’s mesh and regional material properties were modified to simulate expected changes. Three sets of simulations were run: (1) single injection to the anterior border zone; (2) therapeutic multiple border zone injections; and (3) injection of material to the infarct region. Results indicate that additions to the border zone decrease end-systolic fiber stress proportionally to the fractional volume added, with stiffer materials improving this attenuation. As a potential therapy, small changes in wall volume (≈4.5%) reduce elevated border zone fiber stresses from mean end-systole levels of 28.2 kPa (control) to 23.3 kPa (treatment), similar to levels of 22.5 kPA computed in remote regions. In the infarct, injection improves ejection fraction and the stroke volume/end-diastolic volume relationship but has no effect on the stroke volume/end-diastolic pressure relationship.
Conclusions— Simulations indicate that the addition of noncontractile material to a damaged left ventricular wall has important effects on cardiac mechanics, with potentially beneficial reduction of elevated myofiber stresses, as well as confounding changes to clinical left ventricular metrics.
Received August 8, 2006; revision received September 27, 2006; accepted October 5, 2006.
Congestive heart failure (CHF) remains a significant problem in the global medical community. More than 5 million Americans currently suffer with CHF, and 500 000 new cases are diagnosed each year.1 Despite an increase in expenditures to treat CHF, with $29.6 billion the estimated associated cost in 2006, mortality remains high, at ≈20% at 1 year and 80% at 8 years. Furthermore, with an increasing population age, the problems associated with CHF are expected to intensify in the coming decades.
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One of the leading causes of CHF is acute myocardial infarction, and aggressive, robust research is ongoing to address such injuries through new medicines, innovative surgeries, and novel tissue engineering approaches. One of the actively pursued approaches to treating CHF associated with acute myocardial infarction is cellular transplantation into the infarct or border zone region to improve regional and global pump function. Many types of cells have been injected into the injured myocardium, such as skeletal myoblasts,2 bone marrow stromal cells,3,4 endothelial precursor cells,5 and embryonic stem cells.6 In addition to cells alone, recent studies have also included extracellular matrix (ECM) materials with or without the cells.6,7
Most of these studies have produced mixed results; survival and engraftment of the implanted cells are poor, conclusive myocyte regeneration remains undemonstrated, and yet most cellular and/or ECM injection approaches are still able to reduce the loss of function after an infarct event. This has led to debate regarding how the addition of cells and/or synthetic ECMs mitigates function loss as quantified by metrics such as the ejection fraction (EF). Although the injection of such cells and materials to the injury may be beneficial in numerous ways, such as through protective angiogenesis8 and cytokine-mediated reduction in apoptosis,9 one specific benefit of these treatments could be simple changes in ventricular geometry and mechanics leading to a reduction of elevated local wall stresses that have been implicated in pathological remodeling.10
In this article, finite element (FE) methods were used to investigate the short-term ventricular mechanical effects of implanted materials such as synthetic ECMs or cellular masses. Using a previously developed and validated FEM of an ovine left ventricle (LV) affected with an anteroapical transmural dyskinetic infarct, we calculated the resulting global function and local stresses for simulated injections of material as a function of volume, stiffness, and location. We tested the hypothesis that even small fractional changes in LV wall volume (≈0% to 5%) can significantly alter cardiac mechanics when properly located, a process we term matrix-assisted myocardium stabilization. We studied the effect of injecting noncontractile material into the border zone and infart, the 2 most common locations for therapy, as well as the global effect of multiple peri-infarct border zone modifications.
FE Model Calculations
To determine the effect of material injection to the LV, the 3-dimensional FE method developed by Costa et al11 for large elastic deformations of ventricular myocardium was used, together with the passive diastolic and active systolic mathematical descriptions of Guccione et al12 describing the anisotropic stress-strain relationship of normal and dysfunctional myocardium. All model calculations were performed on a Silicon Graphics O2+ workstation (Mountain View, Calif).
Previously Developed Finite Element Mesh
A previously developed and validated FE model simulation of an ovine heart suffering from an anteroapical infarct13 was used as the starting point for modeling the material injection. This previous work consisted of a 216-element mesh in a 12×18×1 grid (circumferential×longitudinal×transmural) with dimensions and model parameters fit to magnetic resonance imaging–measured cardiac geometry, fiber angle distribution, and mechanical properties of individual LVs that had surgically induced anteroapical transmural infarcts that expanded and became dyskinetic. The mesh had been divided into 3 different regions to best fit the physiological data: remote myocardium with normal passive myocardium properties, a border zone with normal passive myocardium but reduced active contraction, and a dyskinetic infarct with increased stiffness and no active contraction.
Simulation of Synthetic ECM Injections
Simulated Injection Into the Anterior Border Zone
Injection of material to the anterior wall of the infarct border zone was simulated by changing the transmural coordinates of epicardial and endocardial mesh nodes in 3 of the anterior border zone elements to create local bulging in the apical anterior wall. The resulting deformation in the 3 chosen elements and surrounding 9 elements was varied to achieve a total wall volume increase of 0.5 to 1.5 mL (Figure 1A). To simulate the addition of noncontractile volume, for each of the 12 elements with a deformation-induced change of volume, contractility of the element as defined by the active contraction Tmax parameter12 was reduced to an extent proportional to the change in volume.
In addition, to investigate the role that stiffness (stress response to strain) of the injected material contributes to changes in cardiac mechanics, the passive material parameters of the strain energy constitutive equation12 (C, bf, bt, bfs) of the combined material/myocardium elements were modified to model added material with the use of a volume-mixing rule. For these simulations, added material stiffness of 1% to 200% of the average stiffness of passive myocardium was tested. This stiffness range (an elastic modulus range of ≈10 Pa to 20 kPa) was chosen to encompass a wide variety of possible injectable materials, estimated from literature values of shear storage modulus as determined by parallel plate rheology. This simulated range includes derived ECM materials such as fibrin (≈50 Pa),14 Matrigel (30 to 120 Pa for un–cross-linked and cross-linked),15 and type I collagen gels (20 to 80 Pa for 1 to 3 mg/mL),16 as well as newer synthetic ECM materials such as bioactive hydrogels based on N-isopropyl acrylamide (100 to 400 Pa),17,18 alginate (100 Pa to 6 kPa),19 and polyethylene glycol (1 to 3 kPa).20 In addition, because most materials are significantly softer than the upper range tested in the simulations, the higher range also evaluates the likely effect that after injection and integration, materials and/or cells will stiffen beyond their initial properties.
Simulated Multiple Border Zone Injections
A second simulation tested the global effect of injected material as a potential therapy, with a total of 4.4 mL (≈4.5% of total wall volume) added in multiple locations in the infarct border zone. In this simulation, a total of 12 border zone elements in 4 surgically accessible locations (in the anterior, posterior, and septal walls) were modified, with the epicardial nodes scaled by a factor of 1.03 and the endocardial nodes by 0.97, both in the transmural direction, to locally thicken the wall in this region (Figure 1B). In all modified elements, contractility (Tmax) was proportionally decreased to the volume increase, and material stiffness (C, bf, bt, bfs) of the composite elements was reduced by a mixing rule, with the added volume fraction having 20% of the passive stiffness of normal myocardium.
Simulated Injection Into Anterior and Posterior Infarct
A third set of simulations determined the effect of adding material directly to the noncontractile infarct region. In these simulations, 2 regions of the apical infarct mesh were modified by transmural modifications to the epicardial nodes to model the geometry of material added to the infarct wall (Figure 1C). Multiple simulations were performed with varying infarct deformations to test a total volume addition range of 0 to 5.3 mL. Material properties were also modified with the use of a volume-mixing rule for the combined element with the added material having 20% stiffness of passive myocardium.
Calculation of End-Systolic and End-Diastolic Pressure-Volume Relationships
For each scenario, FE method diastolic solutions were obtained for LV pressures of 0 to 2.6 kPa (0 to 20 mm Hg), after which active contraction was added and FE method end-systolic solutions were calculated for LV pressures of 0 to 16 kPa (0 to 120 mm Hg). Chamber end-diastolic and end-systolic volume (VED and VES) solutions were used with the corresponding pressures (PED and PES) to plot the end-diastolic and end-systolic pressure-volume relationships (ESPVR and EDPVR, respectively), which were then fit to appropriate polynomial equations. The following linear equation was used to estimate the ESPVR: equation
where EES is the end-systolic elastance and V0 is the volume intercept of the ESPVR, each determined by linear regression of the data.
The polynomial equation used to estimate the EDPVR was as follows: equation
where Ε0,ED, Ε1,ED, and Ε2,ED represent stiffness of the LV diastolic compliance, again determined by linear regression.
Calculation of EF, Stroke Volume/PED, and Stroke Volume/VED Relationships
To determine global changes to pump function, the stroke volume (SV)/PED and SV/VED relationships were calculated and plotted. These relationships were determined by first calculating SV for the in vivo validated cardiac cycle, with PED=1.09 kPa (8.2 mm Hg) and PES=10.24 kPa (76.8 mm Hg). With the use of this calculated SV value and the EDPVR fit parameters, aortic elastance (EA) could be solved for with the use of the following equation:
With the calculated value of EA, SV for all PED as well as the EF, or SV as a percentage of VED, could be determined and the relationships between SV and PED and VED could be plotted.
Calculation of Systolic Fiber Stress
Previously developed FE methods for ventricular mechanics were used to calculate midwall stresses in reference to the local muscle fiber orientation at end systole. For the treatment simulations, the same in vivo measured end-systolic LV pressure of 10.24 kPa (76.8 mm Hg) from the infarct model was chosen as the end-systolic pressure for stress calculation and for comparison of calculated stresses. This chosen end-systolic pressure is based on the assumption that the addition of noncontractile material to the ventricle does not significantly alter the pressure, which is a reasonable assumption because no contractility has been added and no changes in EA from the procedure are expected. In addition, published literature examples of cellular additions to the ventricle do not significantly alter the end-systolic pressure.21
The authors had full access to the data and take full responsibility for their integrity. All authors have read and agree to the manuscript as written.
Simulated Injection Into the Anterior Border Zone
Midwall end-systolic fiber stresses in the local injection area were calculated at an LV pressure of 10.24 (76.8 mm Hg) kPa for a range of injected volumes (0.5 to 1.5 mL) and a range of material properties (1% to 200% of normal diastolic stiffness). There are 12 elements in the volume-altered anterior region of these simulations, 6 of which are infarct elements and 6 of which are remote and border zone. The mean local fiber stress response of the border zone and remote region elements to both variables is depicted in Figure 2A, with cross sections of this surface along with infarct element response shown in Figure 2B and 2C. Mean volume-weighted stress of each of these 2 groups of elements shows a linear decrease with increasing added volume (Figure 2B). Material properties also appear to have an effect, with the higher material stiffness materials bearing more of the load in the softer remote and border zone regions than the stiffer infarct, therefore resulting in an increased reduction in remote and border zone stresses (Figure 2C). The small fractional volumes (0.5% to 1.5%) used in this single-injection simulation have no significant effect on EF or global function.
Simulated Multiple Border Zone Injections
In the simulation to investigate the effect of a potential treatment of multiple implantations throughout the peri-infarct border zone, results indicate that the addition of ≈4.5% of the total wall volume (4.4 mL total volume change) to the border zone can bring mean volume-weighted end-systolic fiber stress in the border zone back down to near levels in the remote myocardium (Figure 3A). However, cross-fiber stresses are not dramatically decreased (Figure 3B), and the other 4 stress components are not changed significantly (data not shown). Because mathematical models produce discrete results, statistical analysis is difficult to use to ascertain the significance of computed changes in variables. However, if the groups of elements that form the remote, border zone, and infarct regions are assumed to represent biological variation, their variance can be used to estimate significant differences between the data sets. In this case, with the use of an analysis of variance on the 6 data sets in Figure 3 followed by pairwise Holm t tests, the observed reduction in border zone fiber stress can be considered to be statistically significant (P<0.05), whereas the cross-fiber stress is not significantly reduced.
Figure 4 shows a 3-dimensional color representation of mean end-systolic fiber stress before (Figure 4A) and after (Figure 4B) the injection of material to the ventricle wall, with yellow-red indicating areas of elevated fiber stress compared with the rest of the ventricle. Figure 4 also shows the difference between the 2 (Figure 4C), with blue regions indicating areas of decreased stress as a result of the model changes. Changes in stress are localized in the regions of injection simulation.
In addition, material addition to the border zone in this simulation caused slight shifts to both the ESPVR and EDPVR (Figure 5A1). Meanwhile, global heart function as estimated by SV/PED was not significantly altered by the model changes, with the multiple injections providing no change over the control simulation (Figure 5A2). SV/VED (Figure 5A3) and EF (Figure 6A) were only slightly altered.
Simulated Injection Into Anterior and Posterior Infarct
Results show that direct injection of material to the infarct region can alter the EDPVR and ESPVR proportionally to the amount added (Figure 5B1), moving the EDPVR and ESPVR leftward, with a slight upward change to the slope of the ESPVR. These changes result as a combination of 2 factors, the increased elastance of the ventricle from added material and the changes to ventricular volume. Although not significantly altering the SV/PED relationship (Figure 5B2), these geometric changes can lead to observed differences in SV/VED relationship (Figure 5B3) and the often-reported metric EF (Figure 6B). A modest fractional increase in volume of the infarct (5.3 mL compared with 97 mL total wall volume) is capable of increasing the EF by ≈2 percentage points over the infarct control (24 versus 22) or 10%.
Our studies indicate that a small fractional change (0.5% to 5%) in myocardium wall volume can alter cardiac mechanics, decreasing wall stresses, affecting ESPVR and EDPVR, and increasing EF and SV/VED without improving SV/PED. These short-term mechanical effects are dependent on the location of the injection, the fractional volume of material added, and its relative stiffness to the local myocardium. Although simulating the long-term effect of these changes is beyond the scope of this FE simulation, the short-term calculated effects have direct relevance to ongoing clinical research that involves injecting cells and materials to the ventricle to treat the aftereffects of acute myocardial infarctions.
Small fractional volume additions are important to understand mechanically because they are often used in tissue engineering/regenerative medicine preclinical and clinical studies. For example, in the recent work of Christman et al,7 50 μL of a fibrin gel with or without cells was injected into the LV of Sprague-Dawley rats. These animals have a total heart mass of ≈1 g, and therefore this injection corresponds to ≈5% of the total heart mass (assuming tissue density of ≈1 g/cm3) and to a higher percentage compared with the LV wall alone. Another recent material/cell treatment was in the recent work of Kofidis et al,6 in which a 50-μL volume of noncontractile material with or without cells was injected into the LVs of BALB/c mice. Because BALB mice have a mean LV mass of ≈100 mg,21a this corresponds to the attempted injection of ≈50% of the normal ventricular wall volume.
These small volumes can also be correlated to published cellular transplantation studies by evaluating the cellular volume injected into the myocardium. For example, in the recent Bone Marrow Transfer to Enhance ST-Elevation Infarct Regeneration (BOOST) bone marrow cell transplantation studies,22,23 an average of 26 mL of a highly concentrated cell solution was infused into the infarct region. Because the human LV wall is on average ≈300 mL, the fractional volume of the wall that could be added with these cells is on the order of 5%. In addition, in another relevant cell transplantation study, ≈4 to 6 mL of cells derived from muscle tissue was injected into the ventricles of ischemically injured dogs.21 With mongrel dog LV wall volumes of ≈5 mg/kg24 or ≈100 to 150 mL for the study, this again corresponds to ≈4% to 6% attempted implantation into the LV wall.
Together, these referenced studies show an attempted injection range of volumes that are 4% to 50% of the LV wall, with the majority being ≈5% to 10%. Because the direct injection of material into the beating myocardium will likely result in significant losses (upward of 50%) owing to material being expelled during the cardiac cycle or to poor cellular engraftment, the range of 0.5% to 5% chosen for our simulations represents an attempt to depict a realistic clinical scenario of added noncontractile volume to the LV wall.
Therefore, any mechanical changes in ventricular performance that these small volume additions may effect could have important implications for current tissue engineering applications. Our results demonstrate that wall thickening achieved by injection and integration of a cell population or the use of an in situ forming biomaterial may help to normalize cardiac wall stress in an injured ventricle. Thus, therapies such as injection of biomaterials or cellular transplantation with noncontractile cells may be valuable as clinical methods to reduce elevated fiber stresses. However, it is important to note that these improvements are not associated with an improvement in global pump function as determined by the SV/PED relationship and that SV/VED and EF changes are not necessarily indicative of functional improvement.
This stress reduction potential of injected material is highly significant because in a dyskinetic transmural infarct, the elevated stresses in the infarct border zone region are thought to contribute significantly to pathological remodeling in the postinfarct heart.10,25,26 Reducing these stresses may in turn minimize stress-induced apoptosis and border zone extension and expansion, reducing further remodeling and preventing the progression into CHF. Although the average level of stress reduction is on the order of 20%, it is important to note that the resulting border zone fiber stress levels are equivalent to those calculated in the remote region. Although the cross-fiber stress remains elevated, this reduction of 1 fiber stress component in this sensitive area may be an effective means to mitigate postinfarct loss of cardiac function.
This possibility has implications for many ongoing studies because it indicates that improvements in the long-term mechanics of ischemically injured ventricles may be achieved by reductions in local stress instead of the intended addition of contractile elements into the injured region. Comparing the results obtained from our modeling with experimental results reported in the literature strengthens this hypothesis because, despite claims of actual regeneration, attenuation of progressive loss of ventricular function is primarily observed in numerous in vivo studies of cell and synthetic ECM implantation. For example, Christman et al7 demonstrated that injecting fibrin glue with or without skeletal myoblasts into a rat LV with an infarct/reperfusion injury helped to maintain wall thickness and fractional shortening after 5 weeks, and postulated mechanical stability may be a contributing cause. Similarly, Kofidis et al6 injected the ECM material Matrigel and/or embryonic stem cells into mice LVs with ligated left anterior descending coronary arteries and again reported the positive result of higher fractional shortening and wall thickness at 2 weeks after treatment compared with controls. Such results could easily be explained by a mechanism of mechanical stabilization from added material instead of the claimed large-scale functional regeneration resulting from the transplanted cells.
Furthermore, material added directly to the ventricle presents a different analysis challenge because altering the ventricular geometry with noncontractile material may give the appearance of improved performance without meaningful functional benefit. Our modeling results clearly indicate that the global pressure-volume relationships, the SV/VED, and the often-reported cardiac metric EF can be affected by adding noncontractile material. This means that studies involving cellular transplantation that have reported changes in pressure-volume relationships, SV/VED, or EF need to be critically analyzed to confirm that the benefit is not simply a result of the mechanical or geometric change to the heart caused by material placement. For instance, the same type of slight shifts in EDPVR and ESPVR with accompanying changes in EF that have been modeled in these studies have also been reported in the literature in recent in vivo cellular transplantation studies. He et al21 demonstrated a very similar upward and leftward shift in the ESPVR and EDPVR when upward of 6% of the LV wall mass of skeletal myoblasts was injected into injured canine ventricles. More importantly, in the recent BOOST study, a pivotal human clinical study of marrow stromal cell transfer to treat cardiac damage, the key finding was that LVEF increased over the control group by ≈6 percentage points at 6 months and 2 percentage points at 18 months by intracoronary delivery of a volume of cells approximately equal to 5% of human adult LV wall mass,22,23 in agreement with the small changes in EF that were seen in this modeling work (1 to 2 percentage points), as well as other studies such as the pioneering bone marrow stromal cell work by Orlic et al.27 Such changes may unfortunately not be indicative of true ventricular performance improvement but may only be due to changes in local ventricular geometry or mechanics that arise from a transplanted cell mass.
Therefore, when procedures are evaluated in which geometry of the ventricle may have been altered, more relevant metrics of performance, such as the SV/PED, should be used instead of EF or SV/VED. The SV/PED relationship, which mathematically compensates for procedurally induced ventricular volume changes, is necessarily a better metric than EF or SV/VED, which are directly dependent on LV volume and hence susceptible to misinterpretation when LV volume is altered. This has been noted previously because investigations into the Batista procedure28,29 revealed that improvements in EF could be obtained by geometric changes to the ventricle, but in fact the more meaningful SV/PED relation was depressed through the procedure. The same type of reasoning should be applied in current and future implantation studies; researchers must realize that the addition of cells and/or ECM-like materials can also have enough of an effect on LV volume and elastance to cause analysis complications when EF is considered as an end point.
Although this model captures many aspects of LV mechanics, with a representative 3-dimensional geometry and validated diastolic and systolic material properties for an actual imaged heart, limitations still exist. One significant limitation is the lumped element approach to modeling the injection of material to the wall. A more accurate method would be to refine the mesh to allow for intramural elements of injected material to delineate myocardial stresses that are generated on the myocytes compared with those that are generated on added material during cardiac function. This approach would likely be able to determine the effect of material properties of the implanted material in a more precise manner, especially with low stiffness materials. Future studies along these lines are suggested as computing power becomes more available and model convergence time on a refined mesh model becomes more reasonable.
A study was undertaken with the use of FE methods to examine the mechanical effects of the injection of noncontractile material to the myocardium. The main purpose of this work was to provide insight into the types of functional changes that could be expected when ECM materials and/or cell masses are injected into an injured ventricle and to use these results to devise novel treatments as well as to interpret the ambiguous results that have been obtained with similar clinical techniques. Simulation output indicates that the injection of small volumes of material can change cardiac mechanics in a volume-, stiffness-, and location-dependent manner, with border zone placement the most likely to reduce pathological wall stresses and infarct placement able to change performance metrics with no meaningful pump function improvement. These results indicate that there is both the significant potential for therapeutic application of material implantation to the myocardium as well as potential confounding mechanical effects. In particular, this work highlights the need for critical evaluation of past and present studies that alter ventricular geometry through implantation of cells and/or ECM-like materials while using LV volume-dependent metrics such as EF to evaluate clinical success.
Sources of Funding
This work was supported by National Institutes of Health grants 5R01 HL063348-03 and HL77921, National Biomedical Computation Resource grant PA1 RR08605, and a Whitaker Foundation Graduate Fellowship.
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The injection of stem cells and/or synthetic extracellular matrices into the damaged left ventricular (LV) wall has been proposed as a way to restore function in patients with systolic LV failure. Cell transplantation into the LV wall has been shown to improve ejection fraction; however, the effect of therapeutic cellular or extracellular matrix injection on other indices of LV function has been less clear. In this work, we used a realistic finite element model of the LV with an anteroapical infarct to theoretically determine the effect of injecting a noncontractile material into the infarct border zone and infarct. Simulated border zone injections were found to reduce elevated end-systolic myofiber stresses. Furthermore, simulated injection into the infarct reduced end-systolic and end-diastolic volume and, as a consequence, improved ejection fraction and the stroke volume/end-diastolic volume relationship. However, there was no effect on the stroke volume/end-diastolic pressure relationship. These findings suggest that clinical changes in ventricular function found after intramyocardial injection of stem cells or extracellular matrices may be a mechanical consequence of noncontractile thickening of the LV wall and not a result of directly improving LV pump function through myocardial regeneration.