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For a given class of materials, universal deformations are those deformations that can be maintained in the absence of body forces and by applying solely boundary tractions. For inhomogeneous bodies, in addition to the universality constraints that determine the universal deformations, there are extra constraints on the form of the material inhomogeneities—universal inhomogeneity constraints. Those inhomogeneities compatible with the universal inhomogeneity constraints are called universal inhomogeneities. In a Cauchy elastic solid, stress at a given point and at an instance of time is a function of strain at that point and that exact moment in time, without any dependence on prior history. A Cauchy elastic solid does not necessarily have an energy function, i.e. Cauchy elastic solids are, in general, non-hyperelastic (or non-Green elastic). In this paper, we characterize universal deformations in both compressible and incompressible inhomogeneous isotropic Cauchy elasticity. As Cauchy elasticity includes hyperelasticity, one expects the universal deformations of Cauchy elasticity to be a subset of those of hyperelasticity both in compressible and incompressible cases. It is also expected that the universal inhomogeneity constraints to be more stringent than those of hyperelasticity, and hence, the set of universal inhomogeneities to be smaller than that of hyperelasticity. We prove the somewhat unexpected result that the sets of universal deformations of isotropic Cauchy elasticity and isotropic hyperelasticity are identical, in both the compressible and incompressible cases. We also prove that their corresponding universal inhomogeneities are identical as well.
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Physiowise: A Physics-aware Approach to Dicrotic Notch Identification
Dicrotic Notch (DN), one of the most significant and indicative features of the arterial blood pressure (ABP) waveform, becomes less pronounced and thus harder to identify as a matter of aging and pathological vascular stiffness. Generalizable and automatic DN identification for such edge cases is even more challenging in the presence of unexpected ABP waveform deformations that happen due to internal and external noise sources or pathological conditions that cause hemodynamic instability. We propose a physics-aware approach, named Physiowise (PW), that first employs a cardiovascular model to augment the original ABP waveform and reduce unexpected deformations, then apply a set of predefined rules on the augmented signal to find DN locations. We have tested the proposed method on in-vivo data gathered from 14 pigs under hemorrhage and sepsis study. Our result indicates 52% overall mean error improvement with 16% higher detection accuracy within the lowest permitted error range of 30 ms. An additional hybrid methodology is also proposed to allow combining augmentation with any application-specific user-defined rule set.
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- PAR ID:
- 10486045
- Publisher / Repository:
- ACM
- Date Published:
- Journal Name:
- ACM Transactions on Computing for Healthcare
- Volume:
- 4
- Issue:
- 2
- ISSN:
- 2691-1957
- Page Range / eLocation ID:
- 1 to 17
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1145/3578556
