The stakes are considerable. Scoliosis affects roughly two to three percent of the pre-adult population, but a particularly vulnerable subset of children develop spinal deformity before the age of ten, before most of their skeletal growth has occurred. These cases, driven by congenital, neuromuscular, or acquired conditions, do far more than impair posture and height. Early onset spine deformity contributes to genuine morbidity and mortality, in part because a distorted spine and rib cage restrict the space available for the lungs to develop, sometimes culminating in a life-threatening condition known as thoracic insufficiency syndrome.

Modern surgical philosophy has shifted away from fusing a child’s spine with metal rods, an approach that corrects the curve but stunts thoracic growth and compromises pulmonary function. Instead, surgeons increasingly favor growth-preserving devices that exploit a century-old biological principle known as the Hueter-Volkmann law: compression across a growth plate inhibits bone elongation, while tension stimulates it. By applying asymmetric forces to a still-growing spine, implants such as posterior tethers can theoretically slow growth on one side of the vertebral column while the other side continues to lengthen, gradually straightening the deformity from within the child’s own biology.

The problem is that no instrument can measure the tissue-level stresses inside a living vertebra. That is where finite element models come in. These computational structures divide a spine into thousands of small elements and calculate how forces distribute through bone, discs, and ligaments. Yet most existing models of the porcine spine either used generic parametric geometry, which sacrifices anatomical detail, or modeled only single motion segments without any growth at all. The new study, led by Christian R. D’Andrea and Sriram Balasubramanian of Drexel University together with collaborators at the University of Pennsylvania, Thomas Jefferson University, the University of Delaware, and Boston Children’s Hospital, closes that gap.

The experimental foundation came from three skeletally immature female Yorkshire pigs, aged eight to twelve weeks, in which surgeons implanted a spring-loaded posterolateral cable tether spanning the lower thoracic and lower lumbar spine. The 1.7-millimeter cobalt-chromium cable attached to pedicle screws via lateral offset connectors, and tensioning it to approximately 30 newtons produced a left lateral bending moment across the intercalated segments. Over the following sixteen weeks, each pig developed a clinically significant convex right kyphoscoliosis, with Cobb angles reaching between 49 and 61 degrees. Serial CT scans captured the deformity’s progression from before surgery through the full growth period.

Building the digital counterpart required considerable ingenuity. Rather than meshing each spine from scratch, the team adapted a published dual-kriging morphing technique to warp a validated human spine mesh onto porcine anatomy defined by fifteen landmark points per vertebra. The resulting hexahedral mesh matched the CT-derived surface geometry with a mean symmetric error of just 1.48 millimeters, and roughly 94 percent of elements met recommended quality criteria. The researchers then recreated the implant hardware in software, modeled costovertebral joints as spherical articulations, represented ligaments and intercostal membranes with tension-only springs, and simulated vertebral growth using a thermal expansion trick that allowed each of four quadrants per vertebral body to elongate independently.

The heart of the model is a linear growth-modulation equation in which each vertebral quadrant’s growth rate depends on a baseline growth rate, a stress sensitivity coefficient, and the difference between the local intervertebral disc stress and the average stress under normal loading. Because the exact values of these parameters were unknown, the team calibrated them against the real pigs’ CT-derived curve progression, using a 64-sample Gaussian sampling strategy and an objective function that weighted Cobb angle errors and three-dimensional landmark displacements equally. Calibration slashed the objective function value by 83 to 93 percent compared with literature-based parameters, with baseline growth rates landing between 0.33 and 0.35 millimeters per week and stress sensitivities between 0.61 and 0.80 per megapascal.

The calibrated simulations reproduced the dominant frontal-plane deformity with a mean absolute Cobb angle error of 4.6 to 8.5 degrees across the three pigs, and landmark correspondence errors of only 2.1 to 2.9 millimeters, well within the five-millimeter precision target. For one pig, agreement matched or exceeded a previously reported parametric model, with errors of 2.5 plus or minus 1.6 degrees versus roughly 2.0 plus or minus 2.4 degrees. Just as importantly, the models captured the mechanism: disc compression rose nearly fourfold over sixteen weeks, from about 0.5 to 1.9 megapascals on average, with apical discs showing a stark gradient from 3.8 megapascals on the concavity to 1.4 on the convexity. That gradient suppressed growth on the compressed concave side, and vertebral body wedging accounted for roughly 83 percent of the final simulated deformity, mirroring the biological sequence in which disc wedging appears first and bony wedging follows.

The model was less convincing in the sagittal and transverse planes, where kyphosis angle errors ranged from 10.6 to 22.6 degrees and apical axial rotation errors hovered around 11 degrees. The authors attribute this partly to variability in how pigs were positioned during CT imaging, and partly to deliberate simplifications: rigid, non-growing ribs, no modeled growth of posterior vertebral elements, a homogeneous disc without a distinct nucleus pulposus, and a lumped follower load standing in for muscles and gravity. Notably, the pre-tether disc stresses of about 0.43 to 0.46 megapascals closely match the 0.48 megapascal growth-plate stress previously reported for standing pigs under low muscle activation, lending credibility to the loading assumptions.

The team is candid that this is a proof of principle. Three animals, one of which yielded only eight weeks of data due to tether failure, cannot establish a generalizable porcine stress-growth law, and because the same pigs served for both calibration and assessment, the reported agreement reflects in-sample fit rather than true validation on unseen cases. Still, the framework scales: larger cohorts, standardized imaging, posture-specific loading, and validation on animals excluded from calibration could turn these models into virtual testing grounds where implant designs and surgical configurations are screened computationally before any animal or child is involved. In an era when digital twins are transforming cardiovascular devices and orthopedic implants alike, a spine that grows inside a computer may soon be the first patient every new scoliosis treatment meets.

Subject of Research: Finite element modeling of stress-modulated vertebral growth in a porcine model of mechanically induced scoliosis

Article Title: Scoliosis Induction in the Porcine Spine Using a Growth-Modulating Posterior Tether: Finite Element Model Development and Calibration

Article References: D’Andrea, C. R., Orbach, M. R., Fusco, A., Vresilovic, E. J., Snyder, B. D., Schaer, T. P., Cahill, P. J., & Balasubramanian, S. (2026). Scoliosis Induction in the Porcine Spine Using a Growth-Modulating Posterior Tether: Finite Element Model Development and Calibration. Annals of Biomedical Engineering. https://doi.org/10.1007/s10439-026-04403-3

Image Credits: AI Generated

DOI: 10.1007/s10439-026-04403-3

Keywords: scoliosis, finite element model, porcine spine, growth modulation, posterior tether, Hueter-Volkmann law, early onset scoliosis, spine biomechanics, intervertebral disc stress, vertebral growth, implant design, computational biomechanics

Researchers led by Janez Urevc of the University of Ljubljana, working with colleagues at the Medical University of Graz and supported by the European Space Agency, have built what they call a force–area digital twin of the internal jugular vein. The idea is to record, simultaneously and quantitatively, the force the probe exerts on the neck and the cross-sectional area of the vein visible in the B-mode ultrasound image. The resulting force–area curve is not merely a picture of collapse; it is a mechanical fingerprint of the vein–tissue system, one whose slope and shape change systematically depending on what is inside the vessel. By pairing real measurements with a physics-based computational model, the team has shown, in silico, that healthy veins, partially obstructed veins and fully occluded veins each leave distinct signatures in this curve.

The experimental half of the work relied on a custom-built force-sensing attachment mounted on a standard linear ultrasound transducer. Three load cells inside a rigid housing stream force data at roughly 100 hertz while the Philips CX50 system acquires images at 30 frames per second. Nine healthy adults underwent supine imaging of the internal jugular vein, with an experienced cardiovascular physician performing three slow compressions per recording, from minimal contact through full lumen closure and back. After rigorous quality control, which excluded six of seventeen recordings due to load-cell artefacts, alignment failures or unusable cycles, the team retained 34 compression cycles from eight subjects. Manual segmentation of the vein lumen in every frame, smoothed with a Savitzky–Golay filter, yielded the area trace that was paired with the force signal.

The measured response had a characteristic concave shape: at large vein areas the probe force stayed low, but as the vein approached collapse the force rose steeply. Fitting a straight line over the active compression regime, defined as forces above 0.2 newtons, gave a cohort reference slope of 0.148 plus or minus 0.113 newtons per square millimetre. That large spread, with a standard deviation equal to 76 percent of the mean, underscores how much inter-subject variability even healthy necks contain, and it foreshadows one of the study’s central challenges: how to compare a single representative computer model against a scattered population of real anatomies.

The digital twin itself is a finite-element model built in Abaqus, representing the principal load-bearing structures between the probe and the vertebral body: the internal jugular vein and carotid artery as thin pressurised shells, the sternocleidomastoid muscle and surrounding connective tissue as continuum blocks, and the probe as a rigid body pressing from above. Geometry came from cohort mean anatomical landmarks, including wall depths, vein diameter and the artery–vein centre distance, while the stress-free collapsed reference configuration was extrapolated from head-up tilt recordings in which progressively reducing venous pressure drives the vein toward collapse. Three unknown material parameters, the vein wall modulus and the effective stiffnesses of muscle and subvenous tissue, were identified by an inverse procedure that jointly matched the cohort mean closure force, indentation depth and anatomical landmarks, reproducing every target within roughly fifteen percent.

With the healthy model validated against experiment, the team turned to the question that motivates the whole framework: what does a thrombus do to the compression curve? Clots were modelled as isotropic linear-elastic bodies inserted into the already pressurised vein, ensuring that all simulated cases started from an identical pre-stressed baseline so that differences arose purely from the thrombus itself. Fully occlusive configurations spanned three lengths of two, four and eight centimetres and three stiffness levels of five, thirty and one hundred kilopascals, reflecting the reported mechanical range of venous thrombi. Partial, non-occlusive clots occupying about ten or fifty percent of the lumen were attached to either the lateral or the inferior wall, yielding seventeen thrombotic configurations in total.

The results were striking. Fully occlusive thrombi produced force–area slopes between roughly 2.5 and 14.7 times steeper than the healthy reference of 0.038 newtons per square millimetre, with thrombus stiffness, not length, acting as the dominant driver. Partial occlusions produced intermediate responses, with fifty percent obstructions approaching the fully thrombotic regime and ten percent obstructions shifting measurably toward greater mechanical resistance even though such veins would still appear compressible under conventional binary assessment. Crucially, the dimensionless version of the slope, which normalises both force and area and thereby removes the influence of anatomy and absolute scale, agreed closely between simulation and experiment: minus 0.81 for the model versus minus 0.86 plus or minus 0.33 for the cohort. That agreement indicates the digital twin captures the underlying shape of the compression response, even though the dimensional slope differed by a factor of about four, a gap the authors attribute to population variability, model simplifications and the intrinsically nonlinear experimental data.

The study also introduced a second, complementary indicator derived from the geometry of collapse. By computing the eigenvalues of the covariance matrix of the vein contour at each simulation step, the researchers defined an aspect ratio change that quantifies how strongly the lumen departs from its initial shape toward a flattened, slit-like geometry. Healthy veins produced large aspect ratio changes as they collapsed, while fully occlusive thrombi confined the response to a narrow low-deformation regime. Partial thrombi generated intermediate and asymmetric patterns, and, notably, the simulations distinguished between clots attached to the inferior wall and those on the lateral wall, information the slope alone could not provide. In one soft, small lateral configuration the slope stayed near the healthy value while the deformation trajectory remained clearly distinct, demonstrating exactly why the two indicators work best together: the slope measures how strongly the vein resists compression, the aspect ratio change measures how the lumen deforms as it yields.

The authors are careful to frame the work as a mechanistic proof of concept rather than a validated diagnostic tool. No patients with confirmed thrombosis were scanned, the reported indicator values are configuration-specific rather than diagnostic thresholds, and the thrombus model, while appropriate for quasi-static loading given published loss tangents of only 0.02 to 0.1, deliberately ignores viscoelasticity and nonlinear behaviour that emerges at strains near seventy percent. Intraluminal pressure was prescribed rather than measured, force and ultrasound streams were synchronised post hoc, and the cohort of nine subjects cannot establish population-level reference distributions. Clinical translation, the team writes, will require tissue-mimicking phantom studies followed by prospective trials in patients, ideally exploiting the natural within-subject control offered by unilateral jugular thrombosis.

Even so, the implications reach well beyond the laboratory. In space medicine, where microgravity distends the internal jugular vein, promotes blood stasis and has already produced one confirmed in-flight thrombosis in 2019, autonomous and objective diagnostics are essential because real-time teleguidance is unavailable on deep-space missions. A sensorised probe that reports continuous biomechanical indicators, potentially accelerated by reduced-order surrogates of the digital twin for near-real-time inference, could flag abnormal compression behaviour before complete occlusion develops. The framework is also not vein-specific: adapting it to the femoral or popliteal veins for standard deep vein thrombosis screening would require site-specific geometry and tissue representation but no change to the underlying method. By transforming a subjective visual judgement into a physics-informed biomechanical measurement, this work moves quantitative compression ultrasound from empirical observation toward a genuinely mechanistic biomarker, one in which learned image features can eventually be constrained by known biomechanics rather than treated as opaque outputs of a black box.

Subject of Research: Quantitative compression ultrasound using a force–area digital twin to assess venous thrombosis biomechanics

Article Title: Quantitative Compression Ultrasound via a Force–Area Digital Twin for Mechanistic Assessment of Venous Thrombosis

Article References: Urevc, J., Kovšca, D., Maček, A., Halilovič, M., Goswami, N., & Bergauer, A. (2026). Quantitative Compression Ultrasound via a Force–Area Digital Twin for Mechanistic Assessment of Venous Thrombosis. Annals of Biomedical Engineering. https://doi.org/10.1007/s10439-026-04362-9

Image Credits: AI Generated

DOI: 10.1007/s10439-026-04362-9

Keywords: compression ultrasound, venous thrombosis, internal jugular vein, digital twin, finite-element modelling, biomechanics, deep vein thrombosis, force sensing, space medicine, computational biomechanics, ultrasonography, biomedical engineering