Multiscale insights into postnatal aortic development.

Despite its vital importance for establishing proper cardiovascular function, the process through which the vasculature develops and matures postnatally remains poorly understood. From a clinical perspective, an ability to mechanistically model the developmental time course in arteries and veins, as well as to predict how various pathologies and therapeutic interventions alter the affected vessels, promises to improve treatment strategies and long-term clinical outcomes, particularly in pediatric patients suffering from congenital heart defects. In the present study, we conducted a multiscale investigation into the postnatal development of the murine thoracic aorta, examining key allometric relations as well as relationships between in vivo mechanical stresses, collagen and elastin expression, and the gradual accumulation of load-bearing constituents within the aortic wall. Our findings suggest that the production of fibrillar collagens in the developing aorta associates strongly with the ratio of circumferential stresses between systole and diastole, hence emphasizing the importance of a pulsatile mechanobiological stimulus. Moreover, rates of collagen turnover and elastic fiber compaction can be inferred directly by synthesizing transcriptional data and quantitative histological measurements of evolving collagen and elastin content. Consistent with previous studies, we also observed that wall shear stresses acting on the aorta are similar at birth and in maturity, supporting the hypothesis that at least some stress targets are established early in development and maintained thereafter, thus providing a possible homeostatic basis to guide future experiments and inform future predictive modeling.

Tissue formation and host remodeling of an elastomeric biodegradable scaffold in an ovine pulmonary leaflet replacement model.

In pursuit of a suitable scaffold material for cardiac valve tissue engineering applications, an acellular, electrospun, biodegradable polyester carbonate urethane urea (PECUU) scaffold was evaluated as a pulmonary valve leaflet replacement in vivo. In sheep (n = 8), a single pulmonary valve leaflet was replaced with a PECUU leaflet and followed for 1, 6, and 12 weeks. Implanted leaflet function was assessed in vivo by echocardiography. Explanted samples were studied for gross pathology, microscopic changes in the extracellular matrix, host cellular re-population, and immune responses, and for biomechanical properties. PECUU leaflets showed normal leaflet motion at implant, but decreased leaflet motion and dimensions at 6 weeks. The leaflets accumulated α-SMA and CD45 positive cells, with surfaces covered with endothelial cells (CD31+). New collagen formation occurred (Picrosirius Red). Accumulated tissue thickness correlated with the decrease in leaflet motion. The PECUU scaffolds had histologic evidence of scaffold degradation and an accumulation of pro-inflammatory/M1 and anti-inflammatory/M2 macrophages over time in vivo. The extent of inflammatory cell accumulation correlated with tissue formation and polymer degradation but was also associated with leaflet thickening and decreased leaflet motion. Future studies should explore pre-implant seeding of polymer scaffolds, more advanced polymer fabrication methods able to more closely approximate native tissue structure and function, and other techniques to control and balance the degradation of biomaterials and new tissue formation by modulation of the host immune response.

A Fast, Robust Method for Quantitative Assessment of Collagen Fibril Architecture from Transmission Electron Micrographs.

Collagen is the most abundant protein in mammals; it exhibits a hierarchical organization and provides structural support to a wide range of soft tissues, including blood vessels. The architecture of collagen fibrils dictates vascular stiffness and strength, and changes therein can contribute to disease progression. While transmission electron microscopy (TEM) is routinely used to examine collagen fibrils under normal and pathological conditions, computational tools that enable fast and minimally subjective quantitative assessment remain lacking. In the present study, we describe a novel semi-automated image processing and statistical modeling pipeline for segmenting individual collagen fibrils from TEM images and quantifying key metrics of interest, including fibril cross-sectional area and aspect ratio. For validation, we show first-of-their-kind illustrative results for adventitial collagen in the thoracic aorta from three different mouse models.

Effects of Age, Sex, and Extracellular Matrix Integrity on Aortic Dilatation and Rupture in a Mouse Model of Marfan Syndrome.

BACKGROUND: Transmural failure of the aorta is responsible for substantial morbidity and mortality; it occurs when mechanical stress exceeds strength. The aortic root and ascending aorta are susceptible to dissection and rupture in Marfan syndrome, a connective tissue disorder characterized by a progressive reduction in elastic fiber integrity. Whereas competent elastic fibers endow the aorta with compliance and resilience, cross-linked collagen fibers confer stiffness and strength. We hypothesized that postnatal reductions in matrix cross-linking increase aortopathy when turnover rates are high. METHODS: We combined ex vivo biaxial mechanical testing with multimodality histological examinations to quantify expected age- and sex-dependent structural vulnerability of the ascending aorta in Fbn1C1041G/+ Marfan versus wild-type mice without and with 4-week exposures to ß-aminopropionitrile, an inhibitor of lysyl oxidase-mediated cross-linking of newly synthesized elastic and collagen fibers. RESULTS: We found a strong ß-aminopropionitrile-associated sexual dimorphism in aortic dilatation in Marfan mice and aortic rupture in wild-type mice, with dilatation correlating with compromised elastic fiber integrity and rupture correlating with compromised collagen fibril organization. A lower incidence of rupture of ß-aminopropionitrile-exposed Marfan aortas associated with increased lysyl oxidase, suggesting a compensatory remodeling of collagen that slows disease progression in the otherwise compromised Fbn1C1041G/+ aorta. CONCLUSIONS: Collagen fiber structure and function in the Marfan aorta are augmented, in part, by increased lysyl oxidase in female and especially male mice, which improves structural integrity, particularly via fibrils in the adventitia. Preserving or promoting collagen cross-linking may represent a therapeutic target for an otherwise vulnerable aorta.

A fast, robust method for quantitative assessment of collagen fibril architecture from transmission electron micrographs.

Collagen is the most abundant protein in mammals; it exhibits a hierarchical organization and provides structural support to a wide range of soft tissues, including blood vessels. The architecture of collagen fibrils dictates vascular stiffness and strength, and changes therein can contribute to disease progression. While transmission electron microscopy (TEM) is routinely used to examine collagen fibrils under normal and pathological conditions, computational tools that enable fast and minimally subjective quantitative assessment remain lacking. In the present study, we describe a novel semi-automated image processing and statistical modeling pipeline for segmenting individual collagen fibrils from TEM images and quantifying key metrics of interest, including fibril cross-sectional area and aspect ratio. For validation, we show illustrative results for adventitial collagen in the thoracic aorta from three different mouse models.

Simulation of Mitral Valve Plasticity in Response to Myocardial Infarction.

Left ventricular myocardial infarction (MI) has broad and debilitating effects on cardiac function. In many cases, MI leads to ischemic mitral regurgitation (IMR), a condition characterized by incompetency of the mitral valve (MV). IMR has many deleterious effects as well as a high mortality rate. While various clinical treatments for IMR exist, success of these procedures remains limited, in large part because IMR dramatically alters the geometry and function of the MV in ways that are currently not well understood. Previous investigations of post-MI MV remodeling have elucidated that MV tissues have a significant ability to undergo a form of permanent inelastic deformations in the first phase of the post-MI period. These changes appear to be attributable to the altered loading and boundary conditions on the MV itself, as opposed to an independent pathophysiological process. Mechanistically, these results suggest that the MV mostly responds passively to MI during the first 8 weeks post-MI by undergoing a permanent deformation. In the present study, we developed the first computational model of this post-MI MV remodeling process, which we term "mitral valve plasticity." Integrating methodologies and insights from previous studies of in vivo ovine MV function, image-based patient-specific model development, and post-MI MV adaptation, we constructed a representative geometric model of a pre-MI MV. We then performed finite element simulations of the entire MV apparatus under time-dependent boundary conditions and accounting for changes to material properties equivalent to those observed 0-8 weeks post-MI. Our results suggest that during this initial period of adaptation, the MV response to MI can be accurately modeled using a soft tissue plasticity approach, similar to permanent set frameworks that have been applied previously in the context of exogenously crosslinked tissues.

In vivo assessment of mitral valve leaflet remodelling following myocardial infarction.

Each year, more than 40,000 people undergo mitral valve (MV) repair surgery domestically to treat regurgitation caused by myocardial infarction (MI). Although continual MV tissue remodelling following repair is believed to be a major contributor to regurgitation recurrence, the effects of the post-MI state on MV remodelling remain poorly understood. This lack of understanding limits our ability to predict the remodelling of the MV both post-MI and post-surgery to facilitate surgical planning. As a necessary first step, the present study was undertaken to noninvasively quantify the effects of MI on MV remodelling in terms of leaflet geometry and deformation. MI was induced in eight adult Dorset sheep, and real-time three-dimensional echocardiographic (rt-3DE) scans were collected pre-MI as well as at 0, 4, and 8 weeks post-MI. A previously validated image-based morphing pipeline was used to register corresponding open- and closed-state scans and extract local in-plane strains throughout the leaflet surface at systole. We determined that MI induced permanent changes in leaflet dimensions in the diastolic configuration, which increased with time to 4 weeks, then stabilised. MI substantially affected the systolic shape of the MV, and the range of stretch experienced by the MV leaflet at peak systole was substantially reduced when referred to the current time-point. Interestingly, when we referred the leaflet strains to the pre-MI configuration, the systolic strains remained very similar throughout the post-MI period. Overall, we observed that post-MI ventricular remodeling induced permanent changes in the MV leaflet shape. This predominantly affected the MV's diastolic configuration, leading in turn to a significant decrease in the range of stretch experienced by the leaflet when referenced to the current diastolic configuration. These findings are consistent with our previous work that demonstrated increased plastic (i.e. non-recoverable) leaflet deformations post-MI, that was completely accounted for by the associated changes in collagen fiber structure. Moreover, we demonstrated through noninvasive methods that the state of the MV leaflet can elucidate the progression and extent of MV adaptation following MI and is thus highly relevant to the design of current and novel patient specific minimally invasive surgical repair strategies.

Neural operator learning of heterogeneous mechanobiological insults contributing to aortic aneurysms.

Thoracic aortic aneurysm (TAA) is a localized dilatation of the aorta that can lead to life-threatening dissection or rupture. In vivo assessments of TAA progression are largely limited to measurements of aneurysm size and growth rate. There is promise, however, that computational modelling of the evolving biomechanics of the aorta could predict future geometry and properties from initiating mechanobiological insults. We present an integrated framework to train a deep operator network (DeepONet)-based surrogate model to identify TAA contributing factors using synthetic finite-element-based datasets. For training, we employ a constrained mixture model of aortic growth and remodelling to generate maps of local aortic dilatation and distensibility for multiple TAA risk factors. We evaluate the performance of the surrogate model for insult distributions varying from fusiform (analytically defined) to complex (randomly generated). We propose two frameworks, one trained on sparse information and one on full-field greyscale images, to gain insight into a preferred neural operator-based approach. We show that this continuous learning approach can predict the patient-specific insult profile associated with any given dilatation and distensibility map with high accuracy, particularly when based on full-field images. Our findings demonstrate the feasibility of applying DeepONet to support transfer learning of patient-specific inputs to predict TAA progression.

Simulating progressive intramural damage leading to aortic dissection using DeepONet: an operator-regression neural network.

Aortic dissection progresses mainly via delamination of the medial layer of the wall. Notwithstanding the complexity of this process, insight has been gleaned by studying in vitro and in silico the progression of dissection driven by quasi-static pressurization of the intramural space by fluid injection, which demonstrates that the differential propensity of dissection along the aorta can be affected by spatial distributions of structurally significant interlamellar struts that connect adjacent elastic lamellae. In particular, diverse histological microstructures may lead to differential mechanical behaviour during dissection, including the pressure-volume relationship of the injected fluid and the displacement field between adjacent lamellae. In this study, we develop a data-driven surrogate model of the delamination process for differential strut distributions using DeepONet, a new operator-regression neural network. This surrogate model is trained to predict the pressure-volume curve of the injected fluid and the damage progression within the wall given a spatial distribution of struts, with in silico data generated using a phase-field finite-element model. The results show that DeepONet can provide accurate predictions for diverse strut distributions, indicating that this composite branch-trunk neural network can effectively extract the underlying functional relationship between distinctive microstructures and their mechanical properties. More broadly, DeepONet can facilitate surrogate model-based analyses to quantify biological variability, improve inverse design and predict mechanical properties based on multi-modality experimental data.

Patient-Specific Quantification of Normal and Bicuspid Aortic Valve Leaflet Deformations from Clinically Derived Images.

The clinical benefit of patient-specific modeling of heart valve disease remains an unrealized goal, often a result of our limited understanding of the in vivo milieu. This is particularly true in assessing bicuspid aortic valve (BAV) disease, the most common cardiac congenital defect in humans, which leads to premature and severe aortic stenosis or insufficiency (AS/AI). However, assessment of BAV risk for AS/AI on a patient-specific basis is hampered by the substantial degree of anatomic and functional variations that remain largely unknown. The present study was undertaken to utilize a noninvasive computational pipeline ( https://doi.org/10.1002/cnm.3142 ) that directly yields local heart valve leaflet deformation information using patient-specific real-time three-dimensional echocardiographic imaging (rt-3DE) data. Imaging data was collected for patients with normal tricuspid aortic valve (TAV, [Formula: see text]) and those with BAV ([Formula: see text] with fused left and right coronary leaflets and [Formula: see text] with fused right and non-coronary leaflets), from which the medial surface of each leaflet was extracted. The resulting deformation analysis resulted in, for the first time, quantified differences between the in vivo functional deformations of the TAV and BAV leaflets. Our approach was able to capture the complex, heterogeneous surface deformation fields in both TAV and BAV leaflets. We were able to identify and quantify differences in stretch patterns between leaflet types, and found in particular that stretches experienced by BAV leaflets during closure differ from those of TAV leaflets in terms of both heterogeneity as well as overall magnitude. Deformation is a key parameter in the clinical assessment of valvular function, and serves as a direct means to determine regional variations in structure and function. This study is an essential step toward patient-specific assessment of BAV based on correlating leaflet deformation and AS/AI progression, as it provides a means for assessing patient-specific stretch patterns.

Roles of mTOR in thoracic aortopathy understood by complex intracellular signaling interactions.

Thoracic aortopathy-aneurysm, dissection, and rupture-is increasingly responsible for significant morbidity and mortality. Advances in medical genetics and imaging have improved diagnosis and thus enabled earlier prophylactic surgical intervention in many cases. There remains a pressing need, however, to understand better the underlying molecular and cellular mechanisms with the hope of finding robust pharmacotherapies. Diverse studies in patients and mouse models of aortopathy have revealed critical changes in multiple smooth muscle cell signaling pathways that associate with disease, yet integrating information across studies and models has remained challenging. We present a new quantitative network model that includes many of the key smooth muscle cell signaling pathways and validate the model using a detailed data set that focuses on hyperactivation of the mechanistic target of rapamycin (mTOR) pathway and its inhibition using rapamycin. We show that the model can be parameterized to capture the primary experimental findings both qualitatively and quantitatively. We further show that simulating a population of cells by varying receptor reaction weights leads to distinct proteomic clusters within the population, and that these clusters emerge due to a bistable switch driven by positive feedback in the PI3K/AKT/mTOR signaling pathway.

Uncertainty quantification in subject-specific estimation of local vessel mechanical properties.

Quantitative estimation of local mechanical properties remains critically important in the ongoing effort to elucidate how blood vessels establish, maintain, or lose mechanical homeostasis. Recent advances based on panoramic digital image correlation (pDIC) have made high-fidelity 3D reconstructions of small-animal (e.g., murine) vessels possible when imaged in a variety of quasi-statically loaded configurations. While we have previously developed and validated inverse modeling approaches to translate pDIC-measured surface deformations into biomechanical metrics of interest, our workflow did not heretofore include a methodology to quantify uncertainties associated with local point estimates of mechanical properties. This limitation has compromised our ability to infer biomechanical properties on a subject-specific basis, such as whether stiffness differs significantly between multiple material locations on the same vessel or whether stiffness differs significantly between multiple vessels at a corresponding material location. In the present study, we have integrated a novel uncertainty quantification and propagation pipeline within our inverse modeling approach, relying on empirical and analytic Bayesian techniques. To demonstrate the approach, we present illustrative results for the ascending thoracic aorta from three mouse models, quantifying uncertainties in constitutive model parameters as well as circumferential and axial tangent stiffness. Our extended workflow not only allows parameter uncertainties to be systematically reported, but also facilitates both subject-specific and group-level statistical analyses of the mechanics of the vessel wall.

Altered Responsiveness to TGFß and BMP and Increased CD45+ Cell Presence in Mitral Valves Are Unique Features of Ischemic Mitral Regurgitation.

[Figure: see text].

Pre-surgical Prediction of Ischemic Mitral Regurgitation Recurrence Using In Vivo Mitral Valve Leaflet Strains.

Ischemic mitral regurgitation (IMR) is a prevalent cardiac disease associated with substantial morbidity and mortality. Contemporary surgical treatments continue to have limited long-term success, in part due to the complex and multi-factorial nature of IMR. There is thus a need to better understand IMR etiology to guide optimal patient specific treatments. Herein, we applied our finite element-based shape-matching technique to non-invasively estimate peak systolic leaflet strains in human mitral valves (MVs) from in-vivo 3D echocardiographic images taken immediately prior to and post-annuloplasty repair. From a total of 21 MVs, we found statistically significant differences in pre-surgical MV size, shape, and deformation patterns between the with and without IMR recurrence patient groups at 6 months post-surgery. Recurrent MVs had significantly less compressive circumferential strains in the anterior commissure region compared to the recurrent MVs (p = 0.0223) and were significantly larger. A logistic regression analysis revealed that average pre-surgical circumferential leaflet strain in the Carpentier A1 region independently predicted 6-month recurrence of IMR (optimal cutoff value - 18%, p = 0.0362). Collectively, these results suggest greater disease progression in the recurrent group and underscore the highly patient-specific nature of IMR. Importantly, the ability to identify such factors pre-surgically could be used to guide optimal treatment methods to reduce post-surgical IMR recurrence.

Mitral valve leaflet response to ischaemic mitral regurgitation: from gene expression to tissue remodelling.

Ischaemic mitral regurgitation (IMR), a frequent complication following myocardial infarction (MI), leads to higher mortality and poor clinical prognosis if untreated. Accumulating evidence suggests that mitral valve (MV) leaflets actively remodel post MI, and this remodelling increases both the severity of IMR and the occurrence of MV repair failures. However, the mechanisms of extracellular matrix maintenance and modulation by MV interstitial cells (MVICs) and their impact on MV leaflet tissue integrity and repair failure remain largely unknown. Herein, we sought to elucidate the multiscale behaviour of IMR-induced MV remodelling using an established ovine model. Leaflet tissue at eight weeks post MI exhibited significant permanent plastic radial deformation, eliminating mechanical anisotropy, accompanied by altered leaflet composition. Interestingly, no changes in effective collagen fibre modulus were observed, with MVICs slightly rounder, at eight weeks post MI. RNA sequencing indicated that YAP-induced genes were elevated at four weeks post MI, indicating elevated mechanotransduction. Genes related to extracellular matrix organization were downregulated at four weeks post MI when IMR occurred. Transcriptomic changes returned to baseline by eight weeks post MI. This multiscale study suggests that IMR induces plastic deformation of the MV with no functional damage to the collagen fibres, providing crucial information for computational simulations of the MV in IMR.

Development of a Functionally Equivalent Model of the Mitral Valve Chordae Tendineae Through Topology Optimization.

Ischemic mitral regurgitation (IMR) is a currently prevalent disease in the US that is projected to become increasingly common as the aging population grows. In recent years, image-based simulations of mitral valve (MV) function have improved significantly, providing new tools to refine IMR treatment. However, clinical implementation of MV simulations has long been hindered as the in vivo MV chordae tendineae (MVCT) geometry cannot be captured with sufficient fidelity for computational modeling. In the current study, we addressed this challenge by developing a method to produce functionally equivalent MVCT models that can be built from the image-based MV leaflet geometry alone. We began our analysis using extant micron-resolution 3D imaging datasets to first build anatomically accurate MV models. We then systematically simplified the native MVCT structure to generate a series of synthetic models by consecutively removing key anatomic features, such as the thickness variations, branching patterns, and chordal origin distributions. In addition, through topology optimization, we identified the minimal structural complexity required to capture the native MVCT behavior. To assess the performance and predictive power of each synthetic model, we analyzed their performance by comparing the mismatch in simulated MV closed shape, as well as the strain and stress tensors, to ground-truth MV models. Interestingly, our results revealed a substantial redundancy in the anatomic structure of native chordal anatomy. We showed that the closing behavior of complete MV apparatus under normal, diseased, and surgically repaired scenarios can be faithfully replicated by a functionally equivalent MVCT model comprised of two representative papillary muscle heads, single strand chords, and a uniform insertion distribution with a density of 15 insertions/cm2. Hence, even though the complete sub-valvular structure is mostly missing in in vivo MV images, we believe our approach will allow for the development of patient-specific complete MV models for surgical repair planning.

A noninvasive method for the determination of in vivo mitral valve leaflet strains.

Assessment of mitral valve (MV) function is important in many diagnostic, prognostic, and surgical planning applications for treatment of MV disease. Yet, to date, there are no accepted noninvasive methods for determination of MV leaflet deformation, which is a critical metric of MV function. In this study, we present a novel, completely noninvasive computational method to estimate MV leaflet in-plane strains from clinical-quality real-time three-dimensional echocardiography (rt-3DE) images. The images were first segmented to produce meshed medial-surface leaflet geometries of the open and closed states. To establish material point correspondence between the two states, an image-based morphing pipeline was implemented within a finite element (FE) modeling framework in which MV closure was simulated by pressurizing the open-state geometry, and local corrective loads were applied to enforce the actual MV closed shape. This resulted in a complete map of local systolic leaflet membrane strains, obtained from the final FE mesh configuration. To validate the method, we utilized an extant in vitro database of fiducially labeled MVs, imaged in conditions mimicking both the healthy and diseased states. Our method estimated local anisotropic in vivo strains with less than 10% error and proved to be robust to changes in boundary conditions similar to those observed in ischemic MV disease. Next, we applied our methodology to ovine MVs imaged in vivo with rt-3DE and compared our results to previously published findings of in vivo MV strains in the same type of animal as measured using surgically sutured fiducial marker arrays. In regions encompassed by fiducial markers, we found no significant differences in circumferential(P = 0.240) or radial (P = 0.808) strain estimates between the marker-based measurements and our novel noninvasive method. This method can thus be used for model validation as well as for studies of MV disease and repair.

A functionally graded material model for the transmural stress distribution of the aortic valve leaflet.

Heterogeneities in structure and stress within heart valve leaflets are of significant concern to their functional physiology, as they affect how the tissue constituents remodel in response to pathological and non-pathological (e.g. exercise, pregnancy) alterations in cardiac function. Indeed, valve interstitial cells (VICs) are known to synthesize and degrade leaflet extracellular matrix (ECM) components in a manner specific to their local micromechanical environment. Quantifying local variations in ECM structure and stress is thus necessary to understand homeostatic valve maintenance as well as to develop predictive models of disease progression and post-surgical outcomes. In the aortic valve (AV), transmural variations in stress have previously been investigated by modeling the leaflet as a composite of contiguous but mechanically distinct layers. Based on previous findings about the bonded nature of these layers (Buchanan and Sacks, BMMB, 2014), we developed a more generalized structural constitutive model by treating the leaflet as a functionally graded material (FGM), whose properties vary continuously over the thickness. We informed the FGM model using high-resolution morphological measurements, which demonstrated that the composition and fiber structure change gradually over the thickness of the AV leaflet. For validation, we fit the model against an extensive database of whole-leaflet and individual-layer mechanical responses. The FGM model predicted large stress variations both between and within the leaflet layers at end-diastole, with low-collagen regions bearing significant radial stress. These novel results suggest that the continually varying structure of the AV leaflet has an important purpose with regard to valve function and tissue homeostasis.

Mitral valve leaflet remodelling during pregnancy: insights into cell-mediated recovery of tissue homeostasis.

Little is known about how valvular tissues grow and remodel in response to altered loading. In this work, we used the pregnancy state to represent a non-pathological cardiac volume overload that distends the mitral valve (MV), using both extant and new experimental data and a modified form of our MV structural constitutive model. We determined that there was an initial period of permanent set-like deformation where no remodelling occurs, followed by a remodelling phase that resulted in near-complete restoration of homeostatic tissue-level behaviour. In addition, we observed that changes in the underlying MV interstitial cell (MVIC) geometry closely paralleled the tissue-level remodelling events, undergoing an initial passive perturbation followed by a gradual recovery to the pre-pregnant state. Collectively, these results suggest that valvular remodelling is actively mediated by average MVIC deformations (i.e. not cycle to cycle, but over a period of weeks). Moreover, tissue-level remodelling is likely to be accomplished by serial and parallel additions of fibrillar material to restore the mean homeostatic fibre stress and MVIC geometries. This finding has significant implications in efforts to understand and predict MV growth and remodelling following such events as myocardial infarction and surgical repair, which also place the valve under altered loading conditions.