Coarctation of the aorta, often abbreviated CoA, affects roughly one in several thousand live births and can remain clinically silent until hypertension or heart failure emerges in adulthood. Even after the narrowing is relieved by surgery or stenting, many patients continue to develop hypertension, diastolic dysfunction, and premature cardiovascular disease. Previous work by the same group and others has hinted that eliminating the trans-coarctation pressure gradient does not always normalize left ventricular function or aortic shear stress, suggesting that something beyond the pressure drop itself shapes long-term outcomes. The new study homes in on one candidate: post-stenotic energy dissipation, the irreversible loss of useful mechanical energy that occurs when high-velocity, disturbed flow exiting the narrowing collides with the complex three-dimensional anatomy of the descending aorta.

To dissect this phenomenon, the team analyzed a cohort of twenty patients with coarctation of the aorta. From computed tomography and magnetic resonance imaging, they extracted detailed anatomical features of the aorta, including the centerline topology—the curved path tracing the vessel’s midline—and the variation in cross-sectional area along the descending aorta. These geometric descriptors capture how sharply the aorta bends, how abruptly its caliber changes, and how the vessel’s axis deviates between the coarctation site and the segments immediately downstream. Rather than treating the aorta as a simple tube, the approach quantifies the actual anatomical landscape through which the jet of blood must travel after it exits the stenosis.

On top of the imaging analysis, the researchers built patient-specific multiscale computational simulations that couple three-dimensional aortic hemodynamics with models of cardiac function and systemic circulation. This framework allows the virtual blood flow to respond both to the local anatomy of each patient’s aorta and to the global behavior of the heart and arterial system. Using these simulations, the team quantified energy dissipation per unit volume in the descending aorta—a measure of how much of the blood’s mechanical energy is converted into heat and turbulence rather than forward motion. The multiscale design matters because energy loss in the aorta cannot be interpreted in isolation; it depends on the pressure and flow waveforms delivered by the left ventricle and on the resistance and compliance of the entire circulation.

The central finding is strikingly geometric. Energy dissipation per unit volume in the descending aorta correlates with the combined effect of two quantities: the kinetic energy available in the flow at the coarctation site, and the centerline tangent angle difference between the coarctation and the downstream descending aorta. In plain terms, it is not enough to know how fast the blood is moving as it leaves the narrowing; one must also know how much the vessel’s axis changes direction just downstream. A jet that exits the stenosis into a sharply angled or tortuous segment cannot follow the vessel wall smoothly, and the resulting flow separation, secondary motions, and turbulence dissipate far more energy than the same jet entering a well-aligned segment.

This angle-based insight reframes a familiar clinical observation. Post-stenotic dilatation—the widening of the aorta just beyond a narrowing—has long been recognized on imaging, and computational studies have linked it to the disturbed hemodynamics downstream of stenoses. The new results suggest that the same anatomical misalignment that promotes dilatation also acts as an energy sink, converting the kinetic energy generated by the ventricle into wasted, irreversible losses. Two patients with identical pressure gradients could therefore carry very different energetic burdens depending on the shape of their descending aortas, a distinction that the standard diagnostic metric is blind to.

Crucially, the study connects these downstream losses to the heart itself. The geometric and energetic parameters—the kinetic energy at the coarctation and the centerline angle difference—were found to significantly influence the left ventricular workload expended to compensate for post-stenotic energy loss. In other words, when the aorta’s geometry squanders the energy the heart delivers, the ventricle must do additional work to maintain adequate perfusion of the body. Over years, this chronic energetic penalty plausibly contributes to the left ventricular hypertrophy, diastolic dysfunction, and exercise intolerance documented in adults with repaired coarctation, outcomes that prior clinical studies have linked to abnormal arterial load indices even when resting blood pressure appears controlled.

The implications for clinical practice are substantial. Current guidelines from the American Heart Association and the European Society of Cardiology rely heavily on pressure gradients, imaging-derived indices of narrowing severity, and ventricular function to guide decisions about intervention. The new findings argue for incorporating anatomical and energetic metrics—centerline curvature, angle change, cross-sectional area variation, and computed energy dissipation—alongside pressure gradients when assessing disease severity and cardiac burden. Because the required inputs come from CT and MRI images that patients already undergo, the geometric analysis could in principle be folded into existing imaging workflows, and the computational framework builds on the group’s broader program of non-invasive, patient-specific diagnostic tools for valvular and vascular disease.

The work also resonates with a growing body of literature on cardiovascular energetics. Four-dimensional flow magnetic resonance imaging has been used to measure turbulent kinetic energy in aortic stenosis and coarctation, and studies of hypertrophic cardiomyopathy have shown that individualized computational modeling can reveal energetic inefficiencies invisible to conventional metrics. By identifying a simple, image-derived geometric predictor of energy loss, the McMaster team offers a bridge between high-fidelity simulation and practical clinical assessment. The method’s reliance on centerline morphology—something extractable from standard angiographic and tomographic data—makes it more translatable than approaches requiring specialized flow-sensitive sequences.

Limitations and next steps remain. The cohort comprised twenty patients, and the study, supported by NSERC Discovery and Alliance grants and computational resources from the Digital Research Alliance of Canada, will need validation in larger and more diverse populations, including patients before and after intervention. Longitudinal studies will be required to test whether geometrically driven energy dissipation predicts ventricular remodeling, hypertension, or clinical events over time. Still, the message is clear and potentially practice-changing: in coarctation of the aorta, the pressure drop across the narrowing is only the opening chapter of the story. The shape of the vessel that receives the jet—the bends, the angles, the tapering of the descending aorta—determines how much of the heart’s energy survives the journey, and how hard the ventricle must work to make up the difference. Reading the aorta’s centerline, the study suggests, may be as important as measuring its pressures.

Subject of Research: Geometric determinants of post-stenotic flow energy loss and left ventricular workload in coarctation of the aorta

Article Title: Geometric Determinants of Post-stenotic Energetics in Coarctation of Aorta: Linking Centerline Morphology to Downstream Energy Loss

Article References: Daeian, M., Karbassi, A., Ganame, J., Smith, S., & Keshavarz-Motamed, Z. (2026). Geometric Determinants of Post-stenotic Energetics in Coarctation of Aorta: Linking Centerline Morphology to Downstream Energy Loss. Annals of Biomedical Engineering. https://doi.org/10.1007/s10439-026-04351-y

Image Credits: AI Generated

DOI: 10.1007/s10439-026-04351-y

Keywords: aortic coarctation, hemodynamics, energy dissipation, centerline morphology, left ventricular workload, computational fluid dynamics, descending aorta, pressure gradient, patient-specific modeling, cardiac function, viscous dissipation, medical imaging

The innovation at the heart of the work is a novel geometric model built on a unit-step-function formulation. Unlike classical stenosis models that impose a single cosine, Gaussian, or parabolic profile on a symmetric narrowing, the new framework allows the upper and lower arterial walls to be prescribed independently, capturing true bilateral asymmetry. Surface irregularities, the micro-undulations and protrusions that pathological specimens display, are encoded through independently tunable parameters for each wall. Crucially, phase parameters control the relative axial alignment of the opposing irregularities, permitting systematic exploration of in-phase configurations, where wall peaks align with peaks, and out-of-phase configurations, where a peak on one wall faces a trough on the other. The model also enforces first-order differentiability at the junctions between diseased and healthy lumen, eliminating artificial slope discontinuities that would destabilize analytical and numerical solutions.

Blood itself is treated in an unusually sophisticated way. In vessels 80 to 500 micrometers in diameter, the size of red blood cells, averaging about 7.65 micrometers, becomes comparable to the vessel dimension, and the fluid’s microstructure cannot be ignored. The study therefore models blood as a couple-stress fluid, a formulation first proposed by V.K. Stokes in 1966 that incorporates higher-order stresses associated with particle rotation. This captures the micro-rotation of blood cells and their interaction with surrounding structures, effects that conventional shear-thinning or viscoelastic models miss entirely. The couple-stress parameter, defined as the ratio of vessel radius to an intrinsic microstructural length scale, falls physiologically between roughly 5 and 30 for small arteries, and the analysis employs representative values of 5, 8, and 20.

The flow problem is solved under lubrication and low-Reynolds-number approximations, appropriate because lesion lengths in coronary imaging are several times the local lumen width and because inertial effects are negligible at these scales. The governing equations reduce to a fourth-order differential equation in the transverse direction, and the closed-form solution yields an explicit expression for the pressure gradient as a function of local lumen width and the couple-stress parameter. In the Newtonian limit, as the couple-stress effect vanishes, the solution gracefully recovers the classical plane Poiseuille relation, a rigorous check on the mathematics. The resulting formulas reveal that effective resistance exceeds the classical Newtonian value, particularly in regions where the lumen is most constricted.

The model’s most striking results concern the phase relationship between opposing lesions. When irregular lesions overlap in-phase, with a 47.37 percent axial overlap and mild roughness, the pressure gradient plunges to roughly negative 12 at the throat for the strongest couple-stress case, producing a single broad trough and a predictable bell-shaped rise in wall shear stress. But simply shifting the upper wall by half a unit, inverting the central region to out-of-phase alignment and increasing overlap to 55.55 percent, nearly doubles the peak adverse pressure gradient to negative 24.38, a 99 percent increase relative to the comparable in-phase case. The tortuous channel forces blood through successive accelerations and decelerations, generating sharp, deep spikes in the pressure gradient that dominate the flow field.

Quantitative tables reinforce the message that lesion extent alone is a poor predictor of hemodynamic burden. In one comparison, an out-of-phase configuration with 80 percent overlap and 63.5 percent throat occlusion produced a maximum adverse pressure gradient approximately 231 percent higher and a total pressure drop about 51.8 percent higher than an in-phase baseline, despite having a shorter overlap interval than a rival in-phase case with 89.47 percent overlap. The authors conclude that out-of-phase alignment combined with greater throat occlusion amplifies resistance more strongly than overlap extent alone, helping explain why anatomically similar plaques can impose markedly different functional consequences in patients.

Wall shear stress tells an equally consequential story. In an in-phase configuration with 68.42 percent overlap, shear stress forms a broad bell-shaped peak, reaching a maximum of 9.37 at the throat. In the out-of-phase counterpart with 60 percent overlap, peak shear stress jumps to 12.61, about 34.7 percent higher, while the spatially averaged shear stress remains nearly identical. This divergence means out-of-phase geometries concentrate extreme mechanical loads at discrete micro-constrictions rather than distributing them evenly, imposing localized endothelial injury disproportionate to what aggregate flow indices would suggest. Chronic exposure to such abnormal shear promotes a pro-inflammatory endothelial phenotype, stimulating production of enzymes that degrade elastin and collagen, weakening the arterial wall, and potentially fostering microaneurysm formation with attendant rupture risk.

The downstream clinical cascade modeled by the study is sobering. The marked pressure drop across an irregular stenosis represents irreversible energy loss through viscous dissipation, leaving downstream blood at a permanent pressure deficit even after the gradient normalizes. This weakened driving pressure threatens perfusion of metabolically active organs such as the brain, kidneys, and myocardium, potentially triggering compensatory flow redistribution or vascular steal phenomena. To compensate, the heart must generate higher pressures, a chronic strain linked to cardiac hypertrophy and heightened susceptibility to heart failure. Meanwhile, low and oscillatory shear in the pre- and post-stenotic zones creates athero-prone environments that promote inflammatory cell adhesion and LDL cholesterol infiltration, seeding new lesions or enlarging existing ones in a self-reinforcing cycle of vascular decline.

Context matters here: cardiovascular diseases account for roughly 31 percent of global deaths according to the World Health Organization, and while large-artery atherosclerosis is well studied, small penetrating artery disease remains comparatively neglected. Recent reviews have highlighted persistent challenges in defining, classifying, and treating cerebral small vessel disease, and neuropathological assessment of brain arteriolosclerosis still relies on semi-quantitative scales with only moderate reliability. By providing a mechanistic analytical tool that reflects realistic lesion morphology, the new model could complement imaging-based assessment and contribute to improved risk stratification in atherosclerotic disease, particularly if geometric parameters can one day be extracted from high-resolution clinical imaging.

The study’s broader warning is that smooth-wall simulations may systematically underestimate hemodynamic variations linked to endothelial dysfunction and atherogenesis. Surface irregularities, though modest in amplitude, add remarkable fluctuations to pressure and shear patterns and amplify the damage potential of disturbed flow. Conversely, the couple-stress effect proves nearly negligible in wide, laminar regions but acts as a powerful amplifier wherever geometry concentrates velocity gradients, underscoring the intimate coupling between blood rheology and lesion topology. As a first-order mechanistic foundation for functional lesion assessment, this work marks a significant step toward understanding why the smallest vessels in the body, when diseased, can exert some of the largest influences on human health.

Subject of Research: Mathematical modeling of blood flow in stenosed small arteries with irregular luminal surfaces

Article Title: A novel geometric model of blood flow in stenosed small arteries with luminal surface irregularities

Article References: Elogail, M. (2026). A novel geometric model of blood flow in stenosed small arteries with luminal surface irregularities. Results in Physics, Article 108751. https://doi.org/10.1016/j.rinp.2026.108751

Image Credits: AI Generated

DOI: 10.1016/j.rinp.2026.108751

Keywords: small arteries, stenosis, couple-stress fluid, hemodynamics, wall shear stress, pressure gradient, arteriolosclerosis, cerebral small vessel disease, lubrication approximation, non-Newtonian blood flow, atherosclerosis, mathematical modeling