Arterial Mechanical Models are Extremely Sensitive to Uncertainties in Input Geometrical Measurements

Nir Emuna 1 David Durban 1 Shmuel Osovski 2
1Technion—Israel Institute of Technology, Israel
2Technion—Israel Institute of Technology, Israel

Background: Despite major advances made in vascular biomechanics, the predictive power of constitutive models is still limited by uncertainty of input data. Specifically, key experimental measurements, like the geometry of stress-free (SF) state, involve a definite, sometimes non-negligible, degree of uncertainty. These uncertainties induce errors in the calibrated model parameters, and propagate to the model outputs, e.g. global mechanics of arteries, arterial wall stresses and deformation.

Methods: We introduce a new, deterministic, approach for sensitivity analysis of vascular hyperelastic constitutive models to uncertainty in SF measurements. As a practical illustration we consider two prevalent vascular hyperelastic models: the phenomenological Fung model and the structure-motivated Holzapfel–Gasser–Ogden (HGO) model. We apply our procedure to experimental data of human thoracic and abdominal aorta, common carotid, subclavian, renal, and common iliac arteries.

Results: Relatively small (10%), experimentally plausible, error measurements may lead to large errors in calibrated constitutive parameters (more than 160%). Associated relative errors in the mechanical outputs are higher than 30% in the luminal pressure, 36% in the axial force, and over 200% in the stress predictions.

Conclusion: The propagation of uncertainties into the predictions of biophysical parameters, e.g., force, luminal pressure, and wall stresses, is of clinical significance in the design and execution of clinical devices and interventions. Upshot is that the ability to quantify such sensitives is imperative in studies that employ constitutive parameters to reveal the underlying microstructure of vascular tissues, their biophysical processes (e.g. growth and remodeling), aging and disease states.

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