Computational model captures cardiac growth in hypertensive pregnancies and in the postpartum period

Abstract

Heart growth in the pregnant patient helps maintain cardiovascular function while supporting the growing fetus. However, in some cases, the cardiovascular demand of pregnancy can trigger life-threatening conditions, including hypertensive disorders of pregnancy and peripartum cardiomyopathy. The mechanisms that control heart growth throughout pregnancy are unclear, and treating these diseases remains elusive. We previously developed a computational model that accounts for hormonal and hemodynamic interactions throughout pregnancy and demonstrated its ability to capture realistic cardiac growth in normal rat pregnancy. In this study, we evaluated whether this model could capture heart growth beyond normal pregnancy. After further validation of our normal pregnancy predictions, we tested our model predictions of three rat studies of hypertensive pregnancies. We next simulated the postpartum period and examined the impact of lactation on cardiac growth in rats. We demonstrate that our multiscale model can capture cardiac growth associated with new-onset hypertension during pregnancy and lactation status in the postpartum period. We conclude by elaborating on the potential clinical utility of our model in the future.

NEW & NOTEWORTHY Our multiscale model predicts appropriate heart growth beyond normal pregnancy, including elevated heart weights in rats with induced hypertension during pregnancy and in lactating mice and decreased heart weight in nonlactating mice. Our model captures distinct mechanisms that result in similar organ-level growth, highlighting its potential to distinguish healthy from diseased pregnancy-induced growth.

INTRODUCTION

Throughout pregnancy, the pregnant body continuously adapts to accommodate the growing fetus. In a normal singleton pregnancy, the left ventricle (LV) grows ∼30% in mass and cavity volume to meet the increased demands on the cardiovascular system (1). After delivery, this growth reverses as the hemodynamic load is relieved. Although this hypertrophy is normally helpful, pregnancy can trigger maladaptive growth that can lead to cardiac dysfunction. For example, hypertension impacts 10% of pregnancies worldwide (2) and increases the risk of fetal growth restriction, placental abruption, fetal death, and maternal death, accounting for 10% of all pregnancy-related deaths after delivery (3). Pregnancy can also initiate a form of systolic heart failure at the end of pregnancy or postpartum, known as peripartum cardiomyopathy (PPCM), which impacts 1 in 1,000–4,000 deliveries in the United States (4). PPCM increases the risk of thromboembolic complications, cardiac arrest, and maternal death, accounting for another 15% of all pregnancy-related deaths after delivery (3). Together, cardiovascular complications are the leading cause of pregnancy-related mortality in the United States. Because the underlying mechanisms of heart growth during pregnancy are unclear, differentiating normal from abnormal pregnancy-induced hypertrophy remains an obstacle.

Cardiomyocytes grow in response to biological and mechanical stimuli (5), which change substantially throughout gestation. Circulating angiotensin II (ANG II), progesterone (P4), and estrogen (E2) levels significantly increase by term pregnancy (6, 7). Simultaneously, blood volume expands by 50% as systemic resistance falls over 30%, driven by a 36% increase in cardiac output (CO) and subtle changes in mean arterial pressure (MAP) (8, 9). Hormonal and hemodynamic changes are known to regulate cardiac growth individually, but their interactions remain unclear. Based on their significant changes, we hypothesize that hormonal and mechanical interactions are foundational for understanding pregnancy-induced hypertrophy.

Computational models are valuable tools for exploring cardiac growth mechanisms. Systems biology models predict cell-level hypertrophy through networks of intracellular signaling pathways (10), whereas biomechanical growth models predict organ-level growth due to mechanical overload (11). We previously combined these models into a multiscale framework to account for hormonal and hemodynamic interactions (5) and demonstrated its ability to predict LV mass changes throughout a normal rat pregnancy. This study aims to determine whether this model can predict heart growth in perturbed pregnancies and after delivery. Toward this objective, we simulated three rat models of hypertensive pregnancies and postpartum cardiac growth after delivery. We demonstrate our model can capture LV mass changes associated with new-onset hypertension during pregnancy and lactation in the postpartum period. Moreover, our model can differentiate between mechanisms that produce similar observable heart growth, highlighting its potential for clinical applications.

MATERIALS AND METHODS

Multiscale Model of Heart Growth

We previously developed a multiscale model of heart growth (freely available at https://doi.org/10.13020/gqsa-tn55) that predicts LV mass changes throughout normal pregnancy in rats (5). This model couples an intracellular signaling network model to a compartmental model of the rat heart and circulation to account for hormonal and hemodynamic interactions during pregnancy (Fig. 1). The intracellular network model (Fig. 1A) incorporates hormonal and mechanical inputs [progesterone (P4), estrogen (E2), angiotensin II (ANG II), and cardiomyocyte stretch (myoStretch)] to predict isotropic cardiomyocyte growth (CellArea). The network model solves a system of logic-based normalized Hill ordinary differential equations, informed from cardiomyocyte studies and generated through Netflux (https://github.com/saucermanlab/Netflux), to predict species activity. The compartmental model (Fig. 1B) predicts organ-level stretches in response to hemodynamic inputs [heart rate (HR), end-diastolic and end-systolic pressure-volume relationships, vascular resistances (R), vascular compliance (C), and stressed blood volume (SBV)] and LV growth informed by CellArea. This computationally efficient model (12) couples a lumped-parameter circuit model of the vasculature to thin-walled spheres, representing the ventricles that use time-varying elastance to simulate pressure and volume changes throughout the cardiac cycle, defining the combined vascular and ventricular compartmental volumes as the SBV. During model creation, a sensitivity analysis determined the uniqueness of the fitted baseline parameters (5). Default parameters for the intracellular signaling network and compartmental models are available in Supplemental Table S1 (https://doi.org/10.13020/gqsa-tn55).

Figure 1.

Multiscale model of heart growth couples. A: intracellular signaling network model that predicts cell-level growth in response to hormones and mechanics. B: compartmental model of the rat heart and circulation that predicts organ-level deformation in response to cell-level growth and hemodynamics. Figure created with a licensed version of BioRender.com.

The multiscale model connects the intracellular signaling network model and compartmental model using the kinematic growth framework (13), which calculates the total observable stretch (F_tot = F_e × F_g) as the product of its growth stretch (F_g) and elastic stretch (F_e). At each growth step, the CellArea predicted by the network model feeds into the compartmental model as F_g, updating the unloaded LV geometry while maintaining the intrinsic material properties of the myocardium. After applying growth, the compartmental model calculates F_tot and F_e throughout a steady-state heartbeat. The maximum elastic fiber stretch from F_e is mapped into the network model myoStretch using a linear equation, closing the loop between the models. Separate linear equations map circulating hormone concentrations to network model inputs. The baseline condition in our model represents a nonpregnant, ovariectomized female rat or an intact male rat, where P4, E2, and ANG II levels are low. We previously calibrated these linear equations to match reported LV growth in volume overload and P4, E2, and ANG II infusion experiments in nonpregnant, ovariectomized female rats and intact male rats and validated the model against E2-supplemented volume overload and ANG II infusion experiments (5).

In all simulations, we incorporated time-appropriate hormone concentrations and hemodynamic changes. We prescribed reported changes in heart rate and systemic resistance (R_as) based on reported mean arterial pressure (MAP) and cardiac output (CO) as R_as = MAP/CO. We simulated blood volume changes observed in pregnancy by adjusting SBV. However, because SBV is challenging to quantify noninvasively and SBV changes throughout gestation are unknown, we optimized SBV at each growth step to match reported hemodynamics during pregnancy as described in Normal Pregnancy and Prediction Sensitivity to SBV Optimization. We validated all model-predicted growth against reported data. We selected peer-reviewed studies that provided animals with standard housing, water, and diet. Furthermore, we prioritized studies that reported heart weights independent of body weight, as pregnancy is a confounding factor in animal weight measurements. We broadened our literature search to include data from multiple rat strains and some from mice when rat data were unavailable. We normalized all gestation lengths to 21 days to reflect an average rat pregnancy (12). Model-predicted growth and hemodynamics were compared against the percent change in reported metrics ± one relative standard deviation (RSD, ratio of standard deviation to experimental mean) from the available literature unless otherwise specified. All references for the experimental data used to validate all simulations are available in Supplemental Data S1 (https://doi.org/10.13020/gqsa-tn55).

Normal Pregnancy and Prediction Sensitivity to SBV Optimization

We first determined whether the hemodynamic parameter used to optimize SBV affects our normal pregnancy growth predictions. Previously, we optimized SBV to match reported changes in end-diastolic diameter (EDD). To test the sensitivity of our model predictions to this choice, we optimized SBV to match reported changes in CO and MAP from days 0–21 of normal rat pregnancy and compared the mean squared error (MSE) between predicted and experimental LV mass for the three optimization schemes. Relevant experimental data are detailed in Supplemental Table S2 (https://doi.org/10.13020/gqsa-tn55). Based on this analysis, we optimized SBV to match reported changes in MAP in the remaining simulations.

Simulation of Hypertensive Pregnancies

We next tested our model’s response to perturbations by simulating hypertensive pregnancies. Given the diversity of etiologies, various rat models of hypertensive pregnancy exist. We tested our model against three independent studies, each inducing different means of hypertension during pregnancy. We selected peer-reviewed studies based on hemodynamic and growth data availability. In each case, we simulated normal pregnancy until the average date of experimental perturbation, when we increased R_as to fit the case-dependent changes in MAP and appropriate ANG II changes. Supplemental Table S3 (https://doi.org/10.13020/gqsa-tn55) details all relevant experimental data.

First, we simulated an ANG II implantation introduced between day 8.5 and day 9.5 (pregnancy + ANG II) (14). Since plasma ANG II levels are not reported after pump implantation in the pregnant rats, we based the relative change in circulating ANG II levels on a study that reported plasma ANG II concentrations in weight-matched male rats with similar ANG II treatment (15). We imposed this stepwise increase in ANG II at day 9 and linearly increased R_as to impose a reported rise in MAP in the ANG II-supplemented pregnant rats (14). We compared pregnancy + ANG II growth predictions against reported LV weights at day 19.5 to reflect the experimental end point (14). Second, we simulated transverse aortic constriction induced between day 5.5 and day 8.5 (pregnancy + TAC) (16). Although TAC is not a standard model of hypertensive pregnancy, we simulated this study since it allowed us to test whether our model could capture cardiac growth in response to a hemodynamic perturbation during pregnancy. We increased R_as to impose an acute MAP increase at day 6.4 along with an ANG II increase to reflect post-constriction changes in ANG II (17). Appropriate ANG II changes were determined by fitting ANG II to produce LV growth in nonpregnant TAC animals from the same study (16). We compared pregnancy + TAC growth predictions against reported LV weights at day 20.5 to reflect the experimental end point (16). Finally, we simulated reduced uterine perfusion pressure (RUPP) that constricts the subrenal abdominal aorta and uterine arteries on day 14 (pregnancy + RUPP) (18). We adjusted R_as at day 14 to impose a stepwise increase in MAP after constriction (19), keeping ANG II constant as RUPP is not mediated by the renin-angiotensin system (20). We compared pregnancy + RUPP growth predictions against reported LV growth at day 19 based on the experimental end point (18). For all simulations, we compared the percent change between hypertensive and normal pregnancy simulations at each end point to the reported heart weight and LV mass changes.

Simulation of Postpartum Heart Growth after Delivery

We next evaluated whether the model could predict postpartum LV changes after delivery. Since lactation affects postpartum hormones (21) and hemodynamics (22) in rats, we simulated 28 days of hormonal and hemodynamic changes in rats allowed to nurse a large litter of pups (lactating) and in rats removed from their pups immediately after delivery (nonlactating). In the lactating simulation, we implemented reported P4 and E2 changes and decreased R_as based on observed increases in CO (21, 22). In the nonlactating simulation, we assumed P4 and E2 returned to prepregnant levels after delivery and increased R_as based on observed decreases in CO (22). Since reported blood pressure is similar between lactating and nonpregnant rats (23), we assumed lactation did not influence MAP (24), optimizing SBV to match the same reported MAP changes for lactating and nonlactating simulations. We compared the percent change in predicted LV mass from the end of pregnancy to postpartum against experimental heart weights (25). We compared our model predictions against peer-reviewed studies that reported lactation status and included prepregnant or virgin measurements as an experimental control, prioritizing studies that adjusted litter sizes to maintain a large litter (>8 pups) during lactation. Because of limited data availability, especially regarding lactation status, we included data from mice. Supplemental Table S4 lists the relevant data from postpartum experimental studies (https://doi.org/10.13020/gqsa-tn55).

RESULTS

Model Predicts Consistent Growth with Varied SBV Optimization

We previously demonstrated that our model can capture LV mass changes in a normal rat pregnancy when SBV is optimized to match EDD (5). Since EDD measurements are not readily available, we examined more common hemodynamic parameters, CO and MAP, for SBV optimization. In all simulations, the model predicted a similar increase in LV mass throughout pregnancy, growing by 21, 23, and 27% when matching MAP, CO, and EDD by term, respectively (Fig. 2). Similarly, our model predicted comparable changes in EDD, posterior wall thickness (WT), and in our network model’s main signaling pathways in all simulations (Supplemental Figs. S1 and S2, https://doi.org/10.13020/gqsa-tn55). All predictions agreed with experimental organ-level growth (MSE < 0.02) and captured known intracellular-level trends (Supplemental Fig. S2), suggesting that all SBV optimization schemes are appropriate. For the rest of the study, we optimized SBV to match MAP, given its accessibility and clinical relevance.

Figure 2.

Heart growth predictions during normal pregnancy. Model-predicted changes in left ventricular (LV) mass compared against experimental measurements. Lines: model predictions when stressed blood volume (SBV) is optimized to match changes in end-diastolic diameter (EDD; maroon) (26), cardiac output (CO; gold) (27), or mean arterial pressure (MAP; black) (27). Symbols: experimental data as percent changes in means ± 1 relative standard deviation (RSD), with each representing 1 study (see Supplemental Table S2, https://doi.org/10.13020/gqsa-tn55). *P ≤ 0.05, reported significant growth from nonpregnant. MSE, mean squared error between predicted and experimental LV mass.

Model Captures Additional Heart Growth in Hypertensive Pregnancies

We next examined LV growth predictions in three distinct experiments of hypertensive pregnancies. In all three cases, our model correctly predicted further growth in addition to normal pregnancy, beginning immediately after perturbation. By the experimental end points, our model predicted LV mass increases of 25, 22, and 4% for pregnancy + ANG II, pregnancy + TAC, and pregnancy + RUPP, respectively (Fig. 3A), which were quantitatively consistent with the reported experimental heart weight data (Fig. 3B) (14, 16, 18). Although our predictions for pregnancy + ANG II and pregnancy + TAC agreed with reported changes in reported echo-based LV mass, the model underpredicted LV mass in pregnancy + RUPP. Although our model assumed isotropic cardiomyocyte growth and did not predict wall thickening due to pressure overloading, our predictions were consistent with reported WT in pregnancy + TAC and pregnancy + RUPP. However, this prediction disagreed with pregnancy + ANG II, where a significant increase in the relative wall thickness was reported. In total, our model can capture additional LV mass associated with hypertensive pregnancies within reported experimental ranges.

Figure 3.

Model predicts additional growth in hypertensive pregnancies. A: predicted left ventricular (LV) mass changes in pregnant rats with hypertension induced by angiotensin II infusion (pregnancy + ANG II; maroon), transverse aortic constriction (pregnancy + TAC; orange), and reduced uterine perfusion pressure (pregnancy + RUPP; gold). Solid lines represent model predictions as percent changes from day 0. B: model-predicted changes in LV mass between normal and hypertensive pregnancies compared against experimental heart weights and echo-based LV mass (14, 16, 18). Light bars represent percent mean changes from normal pregnancy at the experimental end point ± 1 relative standard deviation (RSD) (see Supplemental Table S3, https://doi.org/10.13020/gqsa-tn55). Solid bars represent model predictions at the corresponding experimental end point. *P ≤ 0.05, reported significant growth from pregnant control. C: network model predictions differentiate cues driving growth in hypertensive pregnancy simulations.

Interestingly, pregnancy + ANG II and pregnancy + TAC simulations led to comparable LV growth, driven by distinct intracellular mechanisms in our model. In pregnancy + ANG II, an acute rise in ANG II after implantation triggered growth (Fig. 3C), keeping myoStretch low. In the following growth steps, myoStretch gradually increased alongside the ANG II-induced increase in MAP. In contrast, pregnancy + TAC triggered an acute increase in myoStretch because of increased cardiac afterload. This stretch signal and the modest increase in circulating ANG II triggered LV growth, resulting in a gradual decrease in myoStretch (Fig. 3C). These results demonstrate that our model can differentiate between distinct mechanisms that produce similar, observable, organ-level growth.

Model Predicts Continued Heart Growth in Lactating, but Reversal in Nonlactating Animals

Finally, we simulated the postpartum period, incorporating 28 days of hormonal and hemodynamic changes in rats allowed to nurse a litter of pups (lactating) and in rats removed from their pups immediately after delivery (nonlactating). Although these changes included P4 and E2 (21), the primary difference between the simulations was the lactation-induced changes in CO (Fig. 4A) (22).

Figure 4.

Model predicts postpartum heart growth continues in lactating animals and reverses in nonlactating animals. A: prescribed changes in cardiac output (CO) vs. experimental measurements in pregnancy (27) and postpartum (22) in lactating (maroon) and nonlactating (gold) rats. B: left ventricular (LV) mass predictions compared against excised heart weights during pregnancy (gray, same data and simulation as Fig. 2), during postpartum with lactation, without lactation, and with unspecified lactation status (orange). Symbols represent percent changes in experimental means ± 1 relative standard deviation (RSD) (see Supplemental Table S4, https://doi.org/10.13020/gqsa-tn55). Solid lines represent model predictions.

Our model predicted an additional 9% increase in LV mass in the lactating simulation, growing 31% more compared with day 0 (Fig. 4B). The nonlactating simulation predicted a rapid 9% decrease in LV mass by postpartum day 7, driven by the drop in hormones and CO after delivery. The predicted mass was maintained, remaining 6% above day 0 at postpartum day 28. Although we could not find studies that directly compared heart growth between lactating versus nonlactating rats, our predictions agreed with heart weight changes from term pregnancy to postpartum from studies where lactation status was reported (Fig. 4B) (25). The difference in growth predictions was primarily driven by postpartum CO, which caused myoStretch signals to diverge between lactating and nonlactating simulations. Additional experiments are needed to validate this result, as most postpartum measurements did not disclose the animals’ lactation status (Fig. 4B).

DISCUSSION

In this study, we demonstrate the breadth of our previously developed computational model (5) through its ability to predict heart growth in hypertensive pregnancies and postpartum. Our simulations of three experimental models of hypertensive pregnancies resulted in additional growth beyond normal pregnancy-induced hypertrophy, which was quantitatively consistent with the literature (14, 16, 18). When we extended our simulations to the postpartum period, our model predicted continued heart growth in nursing but reversal in nonnursing rats, aligning with reported differences in mice (25).

Our pregnancy + ANG II and pregnancy + TAC predictions showed distinct intracellular interactions culminating in similar organ-level growth. Furthermore, our pregnancy + ANG II simulation predicted additional growth (39% increase in LV mass from the time of pump implantation) when compared with our previous simulation of ANG II + E2 (10% increase over the same length of time) (5), suggesting that our model can differentiate between pathological stimuli in pregnant and nonpregnant animals. These findings underscore a key advantage of our multiscale model framework—its ability to discern and capture physiological and pathological LV growth. This feature is important for clinical applications, where challenges include contrasting complicated versus normal pregnancy solely based on observable cardiac growth. For example, we can expand the signaling model to incorporate biomarkers, including brain natriuretic peptide, which is elevated in patients with PPCM (4) and already included in related network models (10, 28), or use the multiscale framework to computationally screen potential drug treatments without the risk of impacting maternal or fetal health.

The difference in predicted postpartum LV growth between lactating and nonlactating groups was mechanically driven by myoStretch, mirroring lactation-induced differences in CO (22). Conversely, LV growth during pregnancy in our model was driven by an early rise in progesterone (5), suggesting different physiological stimuli drive growth during and after pregnancy. We anticipate that similar cues differentiate pregnancy and postpartum-induced growth clinically, as circulating estrogen and progesterone concentrations decline sharply after delivery (29), whereas hemodynamics remain elevated postpartum (30). However, no significant differences in hemodynamics or LV mass have been reported between breastfeeding and bottle-feeding patients (30). This distinction between rodents and humans could be attributed to the larger average number of rodent pups than human infants per pregnancy, particularly as postpartum CO correlates with the number of suckling pups (22). Other noteworthy postpartum hormones currently not included in our model, including prolactin and oxytocin, respond to factors including sucking frequency and intensity (31) and affect cardiomyocyte hypertrophy (32, 33), which could contribute to postpartum cardiac remodeling. With too few studies reporting LV mass in lactating animals, more rigorous experimental data coupled with computational modeling are needed to confirm if our model can accurately capture heart growth and remodeling after delivery. Together, our predictions highlight the importance of lactation in postpartum-related cardiovascular research and the need to define clinically appropriate animal models.

Although we have demonstrated our model’s breadth, there are limitations in its current iteration. Although our model can predict overall changes in LV mass because of hypertension, it assumes isotropic cardiomyocyte growth and cannot predict concentric wall thickening. As the signaling pathways for directional cardiomyocyte growth are better defined (34), the next iteration of our network model can incorporate anisotropic growth. We also acknowledge that our simplified signaling network model does not capture other critical pathways involved in cardiomyocyte growth. As signaling pathways implicated in normal and pathological heart during pregnancy become clearer, we can update the signaling model to address this shortcoming. Our model also assumes LV growth is solely due to cardiomyocyte hypertrophy, neglecting nonmyocyte contributions and the extracellular matrix. This assumption may suffice for normal pregnancy, in which growth occurs without fibrosis or changes in myocardial vessel density (14), but may not be appropriate for pathological remodeling. Moreover, we assume that ventricular and vascular material properties do not change throughout gestation. Future models could incorporate these effects as changes throughout pregnancy are uncovered. Another limitation is our model’s representation of the female rat anatomy and physiology, while we used experimental data from mice and male rats. We emphasize that we used mouse or male rat data only when appropriate female rat data were unavailable. We also highlight the need for more research on cardiac growth in female animals and during pregnancy. Our analysis of available data suggests similar growth and hormonal trends (35) in rats and mice during pregnancy. Thus, we do not anticipate significant differences in our results but plan to recalibrate our model to mice, as they provide more opportunities to test our model, including genetic perturbations and PPCM.

In summary, we demonstrate that our model has the breadth to capture heart growth in normal and hypertensive pregnancies and after delivery. We conclude that our modeling framework holds promise for clinical applications to explore potential screening and treatments and inform personalized patient care by accounting for patient-specific biology, physiology, and anatomy.

DATA AVAILABILITY

The multiscale model code and plain text files defining the experimental data used to simulate and analyze model predictions are freely available in the data repository for the Univ. of Minnesota at https://doi.org/10.13020/gqsa-tn55.

SUPPLEMENTAL DATA

Supplemental Tables S1–S4, Supplemental Figs. S1 and S2, and Supplemental Data S1: https://doi.org/10.13020/gqsa-tn55.

GRANTS

We acknowledge support from National Heart, Lung, and Blood Institute Grant T32-HL139431 (to M.S.K.) and American Heart Association Grant 23CDA1048434 (to K.Y.).

DISCLAIMERS

OpenAI, ChatGPT-3.5 was used to check grammar and syntax while writing this manuscript. The tool was used in a manner that does not conflict with APS ethical policies and the authors take full responsibility for the content.

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the authors.

AUTHOR CONTRIBUTIONS

M.S.K. and K.Y. conceived and designed research; M.S.K. analyzed data; M.S.K. and K.Y. interpreted results of experiments; M.S.K. prepared figures; M.S.K. drafted manuscript; M.S.K. and K.Y. edited and revised manuscript; M.S.K. and K.Y. approved final version of manuscript.