An implicit discontinuous Galerkin method for modeling acute edema and resuscitation in the small intestine

Abstract

Edema, also termed oedema, is a generalized medical condition associated with an abnormal aggregation of fluid in a tissue matrix. In the intestine, excessive edema can lead to serious health complications associated with reduced motility. A $7.5\%$ solution of hypertonic saline (HS) has been hypothesized as an effective means to reduce the effects of edema following surgery or injury. However, detailed clinical edema experiments can be difficult to implement, or costly, in practice. In this manuscript we introduce an implicit in time discontinuous Galerkin method with novel adaptations for modeling edema in the 3D layered physiology of the intestine. The model improves over early work via inclusion of the tissue intrinsic storage coefficient, and the effects of Starling overestimation for high venous pressures. Validation against a recent clinical experiment in HS resuscitation of acute edema is presented; the results support the clinical hypothesis that 7.5% HS solution may be effective in the resuscitation of acute edema formation. New results include an improved view into the effects of resuscitation on the hydrostatic pressure profile of edematous rats, effects on lumenal volume attenuation, relative fluid gain and an estimation of the impacts of both acute edema and resuscitation on intestinal motility.

Fluid–structure interaction for highly complex, statistically defined, biological media: Homogenisation and a 3D multi-compartmental poroelastic model for brain biomechanics

“…In the literature, several works have utilised a poroelastic approach in modelling parenchymal tissue within the realm of hydrocephalus and oedema formation in the brain and small intestine (Tully and Ventikos, 2011;Vardakis et al, 2013b;Guo et al, 2018;Vardakis et al, 2017Vardakis et al, , 2016Chou et al, 2016;Chou, 2016;Vardakis et al, 2013a;Kaczmarek et al, 1997;Levine, 1999Levine, , 2000Smillie et al, 2005;Sobey and Wirth, 2006;Shahim et al, 2012;Aldea et al, 2019;Thompson et al, 2019). The poroelastic modelling of parenchymal tissue for the purpose of investigating AD yields a narrower selection of relevant work (Guo et al, 2018;Thompson et al, 2019). Recently, Aldea and colleagues (Aldea et al, 2019) utilise poroelastic theory in a multiscale model of arteries in order to test the hypothesis that cerebrovascular smooth muscle cells drive intramural periarterial drainage.…”

Accurate discretization of poroelasticity without Darcy stability

“…This view can either be interpreted literally or as having divided (1.1a-1.1c) through by α to obtain rescaled material parameters. Moreover, one need not look far [12,13,17,25,27,33,34] to find applications where κ is small, and the storage coefficient c 0 varies over a wide range of values in the presence of only modest choices of λ. For instance, the literature contains examples of low hydraulic conductivities where both λ and c 0 are approximately unity [17]; in various soft-tissues, λ ≈ 10 2 and c 0 ≈ 10 −5 have been used [12,13], in addition to λ ≈ 10 1 or λ ≈ 10 3 with c 0 ≈ 10 −10 [25,33], and even c 0 = 0 [27,34].…”

“…Moreover, one need not look far [12,13,17,25,27,33,34] to find applications where κ is small, and the storage coefficient c 0 varies over a wide range of values in the presence of only modest choices of λ. For instance, the literature contains examples of low hydraulic conductivities where both λ and c 0 are approximately unity [17]; in various soft-tissues, λ ≈ 10 2 and c 0 ≈ 10 −5 have been used [12,13], in addition to λ ≈ 10 1 or λ ≈ 10 3 with c 0 ≈ 10 −10 [25,33], and even c 0 = 0 [27,34]. This wide variation in c 0 , while λ remains modest, can be due to several reasons: an ad-hoc modeling assumption; to simplify numerical methods when storage coefficients are near the limits of computing precision; or due to the fact that, especially in biological applications, measurements for certain parameters may be unavailable and values are often estimated, chosen, or substituted from those, of similar biological regime, for which reasonable parameter estimates are available.…”

Highly integrated workflows for exploring cardiovascular conditions: Exemplars of precision medicine in Alzheimer's disease and aortic dissection

“…Microvascular permeability and overall cerebral compliance can be linked within the numerical template, thus providing insight (via remodelling processes which account for white matter alterations associated with AD) into the influence of lifestyle and environmental factors, and age-dependent vascular compliance (through a more detailed understanding of cerebral hypoperfusion [28]) [55]. The generic MPET model for perfused parenchymal tissue can be used to provide insight into the underlying mechanisms of the NVU in different regions of the brain on similar-sized subject cohorts [55], to account for aqueductal stenosis during hydrocephalus [43], provide insight into oedema formation within parenchymal tissue [56,57], offer personalised management of surgical procedures that affect the cerebroventricular system (such as endoscopic third and fourth ventriculostomy) [57,58] and may also be applied to the study of other organs [59].…”