The Role of Infarct Stiffness in Cardiac Patch Therapy: A Computational Study Using an Idealized Left Ventricular Geometry Open Access

Myocardial infarction (MI) is the leading cause of death worldwide, affecting almost 10% of all individuals aged over 60 [1]. When the heart survives the acute phase of MI, in about 15–30% of patients, progressive adverse ventricular remodeling compromises ventricular function to the extent that it results in heart failure (HF) 1-yr post-MI [2–4].

Cardiac patches are tissue-engineered scaffolds designed to be functionalized with cells. When these scaffolds are seeded with cardiomyocytes and exposed to appropriate physical and biological cues, they induce growth of mature, contractile tissue in vitro [5]. Through their mechanical properties, cardiac patches may offer long-lasting structural support to the damaged myocardium, improve cardiac function, and attenuate left ventricular (LV) remodeling. Experimental studies have shown that cardiac patches, implanted in animal models of acute MI, can increase cardiac function in remote tissue and the border zone and reduce the progression of adverse ventricular remodeling [6–10]. The attenuation of LV remodeling has been attributed to paracrine factors that promote cardiac regeneration through several mechanisms, including cardiomyocyte proliferation, stimulation of angiogenesis, and limitation of inflammatory and profibrotic processes. The cardiac patch influences these paracrine factors through the newly introduced cells and by changing tissue load, for example, by reducing global LV wall stress and overstretching of native cells. However, while these improvements in cardiac function were found in acute MI, they were not observed after implantation of a cardiac patch in animal models of chronic MI [11–13]. Since these studies also differ from each other in the animal model used, it is hard to isolate and understand the effect of infarct tissue properties on patch functionality.

Computational models of the patch-supported heart allow for isolated variations in infarct properties and may contribute to understanding the relation between infarct stiffness and patch functionality. In a previous numerical study, we showed that a cardiac patch, disposed over a chronic MI, functions optimally when fibers within the patch are oriented parallel to the fibers in the subepicardial layers in the LV [14]. The restoration of overall cardiac function was attributed to a mechanical contribution of the cardiac patch but mostly to improved functionality in the healthy tissue surrounding the infarct region. The same study also showed that mechanical tethering to the relatively stiff infarct tissue limits the functionality of the patch. Furthermore, our study on the evolution of acute MI toward a chronically remodeled state showed that the increase in infarct tissue stiffness in this process alters stress and strain courses over the cardiac cycle in the infarct and the adjacent tissue in a spatially heterogeneous way [15]. These findings may also have implications for the mechanically tethered cardiac patch and help explain why the aforementioned experimental studies found functional improvements in an animal model of acute MI but not in chronic MI.

In this study, we adapt the computational framework outlined in Ref. [14] of cardiac mechanics in MI supported by a cardiac patch in order to study the impact of remodeling of the infarct region on patch functionality. In that study, we assumed an isotropic tenfold increase in tissue stiffness in the infarcted region to mimic the material properties associated with chronic MI. in vivo, changes in tissue stiffness arise from scar tissue formation in the infarct area in the weeks to months post-MI [16]. Tissue stiffness of the infarct area therefore varies over time, while we assumed a constant value in the upper limit of experimental observations from ovine, porcine, and murine animal models [17–20]. Furthermore, the ventricular wall may thin by up to 50% in chronic MI which effectively reduces the stiffness of the infarct as a whole and may result in a region of weakened myocardium that is prone to bulging during systole [18]. Indeed, changes in stiffness of the infarct as a whole arise from a combination of both changes in tissue properties and wall thickness.

In this study, we investigate how infarct tissue stiffness and wall thickness influence the ability of a contractile cardiac patch to restore cardiac function. The insights gained might help to better interpret experimental findings and identify the conditions that support optimal patch performance.

In this study, the finite element model of cardiac mechanics in MI, supported by a cardiac patch from Ref. [14], was employed. The geometry, constitutive equations, boundary conditions, and parameter values used here are identical. A brief description of the model is provided below, while a full overview is available in the appendix of the reference.

Here, the value of factors $fpas$ and $fact$vary over the LV geometry and allow for the variation of material properties within the myocardium. The fiber orientation was defined using a rule-based method in terms of a helix angle $αh$ and transverse angle $αt$ [21]. These represent the angle between the circumferential direction and the projection of the fiber vector on the circumferential–longitudinal and circumferential– transmural plane, respectively. $αh$ ranges from +70 deg at the endocardial surface, through +20 deg at midwall to −50 deg at the epicardial surface (Fig. 1(b)). Fiber activation was initiated simultaneously throughout the LV wall with a cycle time of 800 ms.

In the model, rigid body motion was suppressed using Dirichlet boundary conditions. For all nodes located in the basal plane, out-of-plane displacement was suppressed, and in-plane displacement was confined by restricting the solution of this subset of nodes to its nullspace. A uniform pressure $plv$ was applied to the endocardial surface of the geometry as a Neumann boundary condition. During the isovolumetric phases, $plv$ is determined by the mechanical equilibrium with the myocardial tissue at constant end-diastolic or end-systolic volume. During the filling and ejection phase, $plv$ is determined by the interaction of the LV with the circulation, represented by a 0D closed-loop lumped parameter model. The parameters used for the 0D model were kept identical for the infarct and patch simulations. A complete description of the 0D model, including used parameter values, can be found in the appendix of Ref. [14].

The infarct region was designed to mimic that resulting from a circumflex artery occlusion, represented by a circular area with a 2 cm radius and positioned approximately 1.5 cm below the LV equator. A border zone was included, separating healthy from infarct tissue as a gradual, linear transition in material properties with a width of 7.5 mm [22,23]. Both the infarct region and the border zone comprise 14 ml, equal to about 10% of the total LV wall volume. Considering the complete loss of contractility in the core infarct and an average 50% reduction in contractility within the border zone, this infarct was quantified as comprising 15% of the total LV wall volume. Myocardial infarction was modeled by eliminating active stress generation in the core infarct region, thus setting $fact$ to zero and increasing passive tissue stiffness by factor $fpas$⁠. In previous work [14], we assumed a tenfold increase of the passive tissue stiffness in the core infarct by setting $fpas$ equal to 10. As the goal of this study is to assess whether characteristics of the infarct region affect patch functionality, both tissue stiffness and wall thickness were varied. Passive tissue stiffness was varied between a value of 1, 5, and 10, based on in vivo and ex vivo tensile testing data from ovine, porcine, and murine models at strains of 15–20% [17–19]. Thinning of the ventricular wall was modeled by moving the endocardial surface in the infarct region outward by 60% and 80% while keeping the epicardial surface unchanged (Fig. 1(d)).

The cardiac patch was modeled as a rectangular strip of tissue, 6 cm long, 4 cm wide, and 2 mm thick (Fig. 1(c)). It was centered over the infarct area and modeled as fixed to the epicardial surface. The fibers within the patch were oriented along its length and activated simultaneously with the LV. The material properties of the patch were assumed to be equal to those of healthy myocardium, setting the factors $fpas$ and $fact$ to 1. In our previous study of cardiac patch mechanics, patch orientation was found an important determinant of patch functionality [14]. Aligning the patch roughly parallel to the epicardial fiber direction of the LV improved local tissue function most, both in the patch itself as well as the native myocardium neighboring the infarct region. In this study, we assumed this optimal orientation and set the angle of the cardiac patch with respect to the LV circumferential direction at 30 deg.

The model was implemented using the fenics open-source computing platform [24]. The mesh was divided into two sections corresponding to the LV and cardiac patch with elements conforming to the ellipsoidal surface boundary of the LV. Elements in the border zone and cardiac patch were refined using the fenics edge bisection algorithm. The average element size was 4.8 μl in the healthy myocardium and core infarct region and 0.6 μl in the patch and border zone. This ensured that the analytically defined boundaries between healthy tissue, border zone, and core infarct were approximated within 0.9 mm. The resulting mesh consisted of 69,299 quadratic tetrahedral elements with 302,493 degrees-of-freedom. Meshes with reduced wall thickness shared the same element count and topology. To prevent smoothing of properties within the elements, factors $fpas$ and $fact$ were defined in the elements' integration points based on the same analytic description used to subdivide the mesh.

where $ls$ and $ls, 0$ represent the actual and reference sarcomere length, respectively.

For all patch simulations, the change in mechanical work $ΔWmech,i$ was calculated as the change in $Wmech,i$ with respect to the infarct case. We report the relative increases in mechanical work, compared to the total amount of work, reported as $ΔWmech,i$/$Wmech,total$⁠. Local tissue function was evaluated using Cauchy stress and logarithmic strain in fiber direction over the course of the last cardiac cycle in four sectors adjacent to the border zone (Fig. 1(a)).

The healthy heart was simulated by prescribing a value of 1 for both $fpas$ and $fact$ throughout the LV and retaining the original wall thickness to serve as a reference simulation (NORM). Simulations in the infarcted and cardiac patch-supported heart are indicated by labels MI and CP, respectively. Superscripts in these labels refer to the relative wall thickness of the infarct. Subscripts refer to the multiplication factor $fpas$ for passive stiffness of the infarct tissue. Table 1 gives an overview of the combinations of thickness and stiffness that were evaluated.

Figure 2 shows the pressure–volume loops and bar charts for stroke work (⁠$Whemo$⁠), stroke volume (SV), ejection fraction (EF), and work increase due to patch implantation (⁠$ΔWmech,i$⁠). The results for simulation NORM fall within reported physiological ranges for both male and female adult hearts [25,26]. Here, cardiac function is quantified by a SV of 67.0 ml, EF of 59.9%, and $Whemo$ of 0.98 J.

Compared to NORM, infarct cases are characterized by a reduction in maximum LV pressure and stroke volume (Fig. 2(a)). With increasing tissue stiffness, the pV-loops shift leftward, and end-diastolic volume, stroke volume, and stroke work decrease, but ejection fraction increases (Fig. 2(b)). With the addition of the cardiac patch in $MI01100$⁠, end-diastolic volume remains constant but stroke volume, ejection fraction, and stroke work increase. The change in mechanical work (⁠$ΔWmech,i$⁠) is attributed to contributions from both the cardiac patch (⁠$ΔWmech,cp$⁠) and the native myocardium (⁠$ΔWmech,lv$⁠), with the cardiac patch accounting for 40% of the total change, while the remaining 60% originating from the native myocardium. All functional improvements that result from patch implantation decline with increasing tissue stiffness, with the relative contribution of the patch decreasing to 34% in $CP05100$ and 30% in $CP10100$⁠.

Figure 3(a) shows the fiber stress versus strain loops in the healthy tissue neighboring the infarct region and border zone. In the healthy heart (NORM), the stress–strain loops follow a similar pattern in all sectors. Fiber stress and strain increase toward the end of diastole (denoted by ○). During isovolumic contraction, fiber strain remains about constant, while fiber stress increases. Subsequently, both fiber stress and strain decrease toward the end of ejection (denoted by ♦). During isovolumic relaxation, fiber strain remains about constant, while stress decreases.

In $MI01100$⁠, sectors 1 and 3 show stress–strain loops that are skewed to the left. Compared to NORM, fibers shorten during isovolumic contraction, end-systolic strain decreases, and peak fiber stress is lower. These changes decrease with elevated infarct tissue stiffness in simulations $MI05100$ and $MI10100$⁠. Implantation of the cardiac patch reduces the early shortening of fibers and increases peak fiber stress in these sectors, causing the loops to move toward those of the NORM case. The patch-induced increase in tissue work density, represented by the area enclosed by the stress–strain loops, decreases with increasing infarct tissue stiffness. In sectors 2 and 4, changes are less prominent. In $MI01100$⁠, end-diastolic strain is equal to that in NORM, but peak fiber stress is slightly reduced and fibers shorten less during ejection. With increasing tissue stiffness, end-diastolic strain also decreases, and peak fiber stress and fiber shortening during injection decrease further. In these sectors, patch implantation did not induce any significant changes.

Figure 3(b) shows the average stress–strain loops in the infarcted area. Compared to NORM, the surface area enclosed by the stress–strain loop disappears for all infarct simulations. The maximum strain excursion over the cardiac cycle reduces with increasing infarct stiffness. The maximum fiber stress remains constant irrespective of the stiffness of the tissue. Implantation of the cardiac patch reduces the maximum strain excursion by about 40% for all cases.

Figure 3(c) shows the average stress–strain loops in the cardiac patch. Here, increased tissue stiffness leads to a reduction of end-diastolic fiber strain. Stretching of fibers during isovolumic contraction increases with increasing infarct stiffness. Peak fiber stress and end-systolic strain decrease with higher tissue stiffness. Patch tissue work density reduces strongly with increasing infarct tissue stiffness.

Figure 4 shows the pressure–volume loops and bar charts for SV, EF, $Whemo$⁠, and $ΔWmech,i$⁠. A decrease in wall thickness increases the cavity volume of the unloaded reference geometry by 4.7 ml and 10.8 ml in the 20% and 40% thinning cases, respectively, and induces a rightward shift of the pV-loops. This is a direct consequence of the way in which the reduction in wall thickness is modeled (Fig. 1(d)). The shift in end-diastolic volume is larger, approximately 9.1 ml following 20% wall thinning and 20.9 ml following 40% wall thinning. With a 20% reduction in wall thickness, SV and $Whemo$ remain about constant. With further thinning, SV and $Whemo$ decrease. EF generally decreases as a result of wall thinning. The addition of a cardiac patch in $CP10100$ increases cardiac function in terms of SV, EF, and $Whemo$⁠. A reduction in wall thickness increases this amount of functional restoration, although the individual contribution of the cardiac patch decreases. Of the total amount of mechanical work that is restored, respectively, 28% and 26% stem from a contribution of the patch in $CP01080$ and $MI01060$⁠.

Figure 5 shows the local mechanics of all simulations with reduced wall thickness. In sectors 1 and 3 (Fig. 5(a)), wall thinning leads to an increase in end-diastolic and end-systolic strain, shifting the stress–strain loop to the right. Peak fiber stress also increases with wall thinning. In these sectors, the addition of a cardiac patch reduces the isovolumic change in length of fibers and increases peak fiber stress. In sectors 2 and 4, wall thinning leads to an increase in end-diastolic and end-systolic strain as well, but fiber strain remains about equal during the isovolumic phases. This results in more upright stress–strain loops. In these sectors, the effect of adding the cardiac patch is minor.

In the infarct region (Fig. 5(b)), stress–strain loops remain closed, and reduction of wall thickness leads to a higher strain excursion and peak fiber stress. The stress–strain path remains unchanged. The addition of a cardiac patch reduces the strain excursion and fiber stress by about 40%.

In the cardiac patch itself (Fig. 5(c)), a small increase in end-diastolic strain is found with lower wall thickness. Fibers lengthen during isovolumic contraction, and a higher amount of stress is generated with lower wall thicknesses. Patch tissue work density changes less than 10% with a reduction in wall thickness.

In this study, we evaluated how variations in infarct tissue stiffness and wall thickness affect the restoration of cardiac pump function following the implantation of a contractile cardiac patch.

In terms of stroke work, cardiac patch implantation over the acutely infarcted heart (⁠$CP01100$⁠) restored 15% of the loss in cardiac function caused by MI (Fig. 2(b)). A fivefold increase in tissue stiffness reduced the amount of restored pump function to 9%; a further increase did not induce significant changes. With increasing tissue stiffness, the relative contribution of the patch to overall cardiac function becomes smaller, indicating that changes in tissue stiffness predominantly affect patch functionality rather than the mechanical interactions between infarct tissue and healthy myocardium in the LV.

The disproportional loss of cardiac pump function with respect to infarct size can be attributed to disadvantageous mechanical interactions between healthy and infarcted myocardium on top of the loss of contractile tissue [15]. These interactions depend on the arrangement of fibers with respect to the infarct region.

The healthy fibers in sectors 1 and 3 are positioned in a series arrangement with the infarct region (Fig. 1). Upon activation, they will pull onto, and stretch, the relatively compliant tissue in the case of $MI01100$⁠. As a result, they shorten during isovolumic contraction, generate less stress following the Frank–Starling principle, and have reduced work density (Fig. 3(a)). This isovolumic shortening is reduced by increasing infarct stiffness, leading to an increase in tissue work density. The patch provides extra stiffness for these series-arranged fibers, leading to a further reduction of isovolumic shortening and a further increase in work density. This extra effect of the patch is greatest when the stiffness of the infarct tissue is lowest.

The healthy fibers in sectors 2 and 4 are positioned in a parallel arrangement with the infarct. With increased tissue stiffness in the infarct region, end-diastolic strain in these fibers is limited through mechanical tethering (Fig. 3(a)). Consequently, the stress–strain loop is narrower, and stress generation during systole is reduced following the Frank–Starling principle. In these parallel-arranged fibers, the addition of a cardiac patch has little impact on local tissue function except for a minor decrease in peak fiber stress.

In the infarct region, the absence of active stress development means only the passive stress–strain relation is visible (Fig. 3(b)). The slope of this relation increases with increasing tissue stiffness. As peak fiber stress remains constant to balance the cavity pressure, increases in infarct tissue stiffness lead to a decrease in the maximum strain excursion over the cardiac cycle. Although the addition of a cardiac patch does not change this stress–strain relation, it does reduce the maximum strain excursion and fiber stress in the infarct region.

In the cardiac patch, increased tissue stiffness in the underlying infarct restricts end-diastolic strain similar to parallel-arranged fibers in the native myocardium (Fig. 3(c)). This suggests that mechanical tethering can also limit the functionality of the cardiac patch. However, even when this effect is absent in $CP01100$⁠, the work density remains lower compared to healthy tissue. This is also reflected in the restoration of global cardiac function: while 25% of contractile tissue was introduced via the patch, only 15% of the loss in cardiac function was restored, suggesting that factors beyond fiber orientation and infarct properties influence the outcome.

These findings suggest that implantation of a cardiac patch at the time-point at which tissue stiffness is lowest is most beneficial in terms of cardiac support. At this time, mechanical tethering does not restrict the functionality of native parallel fibers nor the cardiac patch, and the function of fibers in a series arrangement is optimally restored.

A reduction in wall thickness induces an almost identical shift in both end-diastolic and end-systolic volumes (Fig. 2). As a result, SV and $Whemo$ remain constant within 5%. The relative decrease in EF is about 20%, indicating that it does not correlate well with $Whemo$⁠. The shift in end-diastolic volume is larger than the increase in unloaded cavity volume. This difference arises because thinner walls result in greater compliance of the infarct area, allowing it to deform more under the same filling pressure. This increased compliance leads to a disproportionate rise in end-diastolic volume, beyond what would be expected from geometric changes alone. The total amount of work restored due to patch implantation increases with lower wall thickness, although the relative contribution of the cardiac patch decreases (Fig. 4(b)). This suggests that changes in wall thickness primarily affect the mechanical interactions between infarct tissue and healthy myocardium in the LV itself.

In the series-arranged fibers in sectors 1 and 3, the reduction in wall thickness shifts the stress–strain loops to the right (Fig. 5(a)). While this shift does not directly impact work density, the increased end-diastolic strain leads to higher stress generation through the Frank–Starling principle, which does increase work density. Similar to the effects observed with variations in tissue stiffness, the cardiac patch adds extra stiffness to the series-arranged fibers, reducing their isovolumic shortening and consequently increasing their work density. The extent of this effect appears independent of wall thickness.

In the parallel-arranged fibers in sectors 2 and 4, a reduction in wall thickness diminishes the mechanical tethering effect, increasing end-diastolic and end-systolic strain, and increasing peak fiber stress and work density. In this respect, the effect is similar to a reduction in tissue stiffness, except that there is no isovolumic shortening present (Fig. 3(a)). The effects of adding a cardiac patch are again minor, except for a slight decrease in peak fiber stress.

In the infarct region, the reduction in wall thickness means that higher stress is required in order to obtain mechanical equilibrium with the cavity pressure. This stress can only be obtained by additional stretching of the tissue. Since the curve of the stress–strain relation is not affected by changes in wall thickness, both peak fiber stress and the maximum strain excursion increase as a result of wall thinning (Fig. 5(b)).

In the cardiac patch, mechanical tethering to the underlying infarct limits end-diastolic strain, similar to cases of higher tissue stiffness, thereby restricting the amount of work performed over the cardiac cycle (Fig. 5(c)).

Previously, we reported that changes in wall thickness have a similar effect on local tissue function as a decrease in tissue stiffness [15]. This conclusion still holds for local tissue function in fibers surrounding the infarct region in the current study. However, this observation does not apply to the infarct region and the cardiac patch. The curve of the stress–strain relation in the infarct region is not affected by a reduction in wall thickness, as infarct tissue properties were kept identical. However, it becomes increasingly flatter with decreasing tissue stiffness. Therefore, with a thinner wall, the strain excursion over the cardiac cycle is comparatively lower, but peak fiber stress is higher. In the cardiac patch, decreased tissue stiffness enhances functionality, while decreased wall thickness has no significant impact. This is likely due to a combination of low end-diastolic strain and increased systolic fiber stress in the infarct tissue. Low end-diastolic stress already reduces the maximum amount of stress that can be generated via the Frank–Starling mechanism, and more stress is required before the cardiac patch can shorten and perform work. As a result, the amount of shortening is decreased and reduced work performed by the patch.

Experimental studies show that cardiac patches can restore pump function and attenuate adverse ventricular remodeling in acute MI [6–10], but not chronic MI [11–13]. Our results indicate that elevated wall stress and high strain levels in the infarct region and border zone in acute MI (⁠$MI01100$⁠) can be significantly reduced by the cardiac patch (Figs. 3(b) and 5(b)).

This reduction could contribute to the attenuation of LV remodeling and prevent the decline of cardiac function over time. Our findings may also help explain why experimental studies report a lack of improvement in pump function in models of chronic MI. The increase in tissue stiffness associated with the transition from acute MI to a chronically remodeled state reduces both the functionality of the patch, due to mechanical tethering, and the effectiveness with which mechanical interactions between healthy myocardium and infarcted tissue are counteracted.

In this study, we investigated how variations in infarct tissue stiffness and wall thickness, reflecting the progression from acute MI to a chronically remodeled state, impact the ability of a contractile cardiac patch to restore cardiac function. We chose to model MI through an absence of active stress development, an increase in passive tissue stiffness, and a reduction in wall thickness. While these changes agree with observations in literature, adverse ventricular remodeling encompasses more facets than those we took into consideration in this study, such as hypertrophy, infarct expansion, and fiber reorientation [17–19,27–29]. These aspects were intentionally omitted to limit the number of variations in the current study and keep the analysis tractable. Although these changes in LV geometry may shift the pressure–volume loops, the trends observed in local tissue function would likely remain consistent. Notably, previous computational studies have shown that alterations in fiber orientation or tissue anisotropy within the infarct region have minimal effect on local stress and strain patterns compared to changes in tissue stiffness or wall thickness in our model [14,15].

The change in passive tissue stiffness was modeled as an isotropic increase, assuming equal stiffening in all directions. While this assumption was based on in vivo and ex vivo experimental data from ovine, porcine, and murine models at strains of 15–20%, post-MI ventricular remodeling has also been reported to induce changes in anisotropy and fiber orientation of infarcted tissue. In particular, experimental studies have shown a larger stiffness increase along the fiber direction compared to the cross-fiber direction [17–19,30,31]. Our previous study showed that changes in anisotropy affect the degree of isovolumic shortening and the strain excursion of infarcted tissue, proportional to stiffness in fiber direction [14]. This also influences cardiac patch mechanics, although these are relatively small compared to the changes induced by variations in tissue stiffness or wall thickness.

Engineered cardiac patches often differ from native myocardium in both passive and active mechanical behavior. Passive properties depend on scaffold composition and collagen formation, while contractile function is typically limited by reduced force generation of the embedded cells [32]. Our model does not capture the full complexity of these tissue-engineered constructs but instead assumes idealized patch properties that mimic those of native myocardium, reflecting the logical aim of designing biomimetic patches. As a result, the functional improvements observed in our simulations may represent an upper bound of what can actually be achieved in practice experimentally. The patch was also assumed to be bonded to the epicardial surface. This assumption was motivated by preliminary experimental observations within our consortium, suggesting that fibrosis anchors the patch within the first weeks postimplantation.

We also simplified the LV geometry to a rotationally symmetric truncated ellipsoid, making the analysis more tractable. In contrast, realistic cardiac geometries contain spatial inhomogeneities in wall thickness and curvature, which can influence stress and strain distributions throughout the cardiac cycle. These distributions may also be expected to change when including the right ventricle or replacing the zero pressure condition on the epicardium with a more detailed model of the effect of the pericardium. However, we expect that the mechanism through which local changes in tissue function in the infarcted and patch-supported heart depend on the orientation of the fibers with respect to the infarct (serial or parallel) will remain important in more realistic geometries with more realistic boundary conditions as well. Further research should investigate whether this expectation is valid.

Overall, we have captured the effects of MI and patch implantation in a number of discrete cases. However, ventricular remodeling is characterized by a variable and dynamic progression over time. A transient model, capable of describing the evolution of adverse ventricular remodeling, provides a more complete view on the impact of patch implantation on heart failure progression and treatment efficacy. Recent work has demonstrated the value of such approaches in elucidating temporal changes in ventricular mechanics and structure following MI [33]. However, we expect that the trends observed in this study will remain valuable in understanding the complex behavior of the combination of the infarcted heart supported by a cardiac patch.

As detailed in Sec. 4.1, our results suggest that cardiac patch therapy may yield the best restoration of pump function when implantation at a specific time-point in the remodeling process. While it might seem logical to advocate for early implantation, before adverse ventricular remodeling has compromised patient health, this poses practical challenges in the clinic. About 13% of MI patients develop HF following discharge and may then be eligible for cardiac patch treatment to limit further progression of HF [34]. Early and accurate screening would be required to assess a patient's risk of developing HF post-MI. While the importance of screening is recognized, HF prediction and prognostication after MI is lacking [35].

In this computational study, we investigate how infarct tissue stiffness and wall thickness influence the ability of a contractile cardiac patch to restore cardiac function. Cardiac function was evaluated in terms of both global pump metrics and local myocardial mechanics. A decrease in infarct stiffness, resulting from either a reduction in tissue stiffness or wall thickness, leads to a higher amount of restoration in pump function due to cardiac patch implantation. This is also reflected in local tissue function of both the native LV and cardiac patch. With lower infarct stiffness, fibers in parallel arrangement are not restricted by mechanical tethering to the infarct tissue, while the cardiac patch ensures that functionality in serial fibers is retained. These observations are in line with the aforementioned experimental observations of patch implantation in acute MI [6–10] and chronic MI [12,13]. The results of this study show that mechanical tethering of both native myocardium as well as the cardiac patch itself to relatively stiff infarct tissue can reduce the restoration of pump function and local tissue function.

• European Research Council (ERC) under the European Union's Horizon 2020 research innovation programme (BRAV) (Grant Agreement No. 874827; Funder ID: 10.13039/501100000781).

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

EF =

ejection fraction, %

$f$ =

spatial multiplication factor, %

$ls$ =

sarcomere length, μm

$ls,0$ =

reference sarcomere length, μm

$plv$ =

left ventricular cavity pressure, Pa

SV =

stroke volume, ml

$Vcavity$ =

left ventricular cavity volume, ml

$Whemo$ =

stroke work, J

$Wmech, cp$ =

mechanical work in the cardiac patch, J

$Wmech, lv$ =

mechanical work in the myocardium, J

$αh$ =

helix angle, deg

$αt$ =

transverse angle, deg

$ε$ =

logarithmic strain

$σ$ =

Cauchy stress, kPa

act =

active

$f$ =

in fiber direction

pas =

passive

HF =

heart failure

LV =

left ventricle

MI =

myocardial infarction