A Mathematical Model for Estimating Muscle Tension in vivo during Esophageal Bolus Transport

Nicosia, Mark A.; Brasseur, James G.

doi:10.1006/jtbi.2002.3118

Cited by 37 publications

(67 citation statements)

References 47 publications

(61 reference statements)

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“…Because this is a new model, the equations are summarized in the APPENDIX. The basic fluid flow mathematical model, however, has been used extensively in past model studies (4,18,27,28,38,40), so these are described only qualitatively here.…”

Section: The Physio-mechanical Modelmentioning

confidence: 99%

“…We apply this mathematical formalism to model the stress-strain properties of the muscularis propria. All muscle mechanics studies done in the human esophagus, except for two notable exceptions (16,38), have assumed the esophageal wall to be "thin". 1 This incorrect assumption, although leading to great simplification of the mathematics, has important implications to the accuracy of predictions, so we do not make it.…”

Section: The Physio-mechanical Modelmentioning

confidence: 99%

“…In contrast with the muscularis, the mucosal layer is very compliant and provides little resistance to deformation compared with the much higher stiffness of the circular and longitudinal muscle layers (19,55). We model the collagenous material surrounding the muscle fibers with a variant of what in the engineering literature is called the "Mooney-Rivlin" constitutive model (34,37,38). Our "neo-Hookean" variant is a linear mathematical relationship between the stress and strain-rate "tensors," with the proportionality constant being the material stiffness parameter.…”

Section: The Physio-mechanical Modelmentioning

confidence: 99%

“…At baseline, the modeled pressures within the stomach and esophageal lumen were set equal to the external pressures. The net active component of hoop stress in the GES was specified using an approximate force balance between stress and intraluminal pressure (38). Active stress (and its corresponding pressure) was modeled with a smooth curve that peaked at the center of the GES and was zero at the boundaries of the GES.…”

Section: The Computer Experimentsmentioning

confidence: 99%

“…Many of the features of the mathematical formulation are borrowed from Nicosia and Brasseur (37,38). However, whereas Nicosia and Brasseur modeled the esophageal wall in the static state, in our application the dominant term in the Newton's law expression for the sphincter muscle is the acceleration term, from which the space-time changes in wall radius are computed after two integrations in time.…”

Section: Appendix: Mathematical Model Developmentmentioning

confidence: 99%

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Liquid in the gastroesophageal segment promotes reflux, but compliance does not: a mathematical modeling study

Ghosh¹,

Kahrilas

Brasseur³

2008

American Journal of Physiology-Gastrointestinal and Liver Physi

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Ghosh SK, Kahrilas PJ, Brasseur JG. Liquid in the gastroesophageal segment promotes reflux, but compliance does not: a mathematical modeling study. Am J Physiol Gastrointest Liver Physiol 295: G920 -G933, 2008. First published August 21, 2008 doi:10.1152/ajpgi.90310.2008.-The mechanical force relationships that distinguish normal from chronic reflux at sphincter opening are poorly understood and difficult to measure in vivo. Our aim was to apply physics-based computer simulations to determine mechanical pathogenesis of gastroesophageal reflux. A mathematical model of the gastroesophageal segment (GES) was developed, incorporating the primary anatomical and physiomechanical elements that drive GES opening and reflux. In vivo data were used to quantify muscle stiffness, sphincter tone, and gastric pressure. The liquid lining the mucosa was modeled as an "effective liquid film" between the mucosa and a manometric catheter. Newton's second law was solved mathematically, and the space-time details of opening and reflux were predicted for systematic variations in gastric pressure increase, film thickness, muscle stiffness, and tone. "Reflux" was defined as "2 ml of refluxate entering the esophagus within 1 s." GES opening and reflux were different events. Both were sensitive to changes in gastric pressure and sphincter tone. Reflux initiation was extremely sensitive to the liquid film thickness; the protective function of the sphincter was destroyed with only 0.4 mm of liquid in the GES. Compliance had no effect on reflux initiation, but affected reflux volume. The presence of abnormal levels of liquid within the collapsed GES can greatly increase the probability for reflux, suggesting a mechanical mechanism that may differentiate normal reflux from gastroesophageal reflux disease. Compliance does not affect the probability for reflux, but affects reflux volume once it occurs. Opening without reflux suggests the existence of "gastroesophageal pooling" in the distal esophagus, with clinical implications. gastroesophageal reflux disease; lower esophageal sphincter; compliance; stiffness MUCH IS UNDERSTOOD ABOUT THE biomechanics underlying gastroesophageal reflux once refluxate flow into the esophagus has occurred, such as sphincter relaxation pressures (21), transsphincteric pressure gradient (46), hiatal distension (25), and the proximal extent of reflux (11). However, the mechanical differences that distinguish normal from chronic reflux are those that manifest at the time of opening and the initiation of reflux; these are less well understood. This lack of understanding of the initiation process is primarily because the initial opening process involves a level of mechanical subtlety in the balances among multiple forces and muscle deformations that are difficult to measure accurately in vivo due to rapid changes occurring over very short times with small changes in radial distention.The opening of the gastroesophageal segment (GES) and reflux result from dynamic adjustments in the subtle force balance that are initi...

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Section: The Physio-mechanical Modelmentioning

confidence: 99%

Section: The Physio-mechanical Modelmentioning

confidence: 99%

Section: The Physio-mechanical Modelmentioning

confidence: 99%

Section: The Computer Experimentsmentioning

confidence: 99%

Section: Appendix: Mathematical Model Developmentmentioning

confidence: 99%

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Liquid in the gastroesophageal segment promotes reflux, but compliance does not: a mathematical modeling study

Ghosh¹,

Kahrilas

Brasseur³

2008

American Journal of Physiology-Gastrointestinal and Liver Physi

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Resolving the three-dimensional myoarchitecture of bovine esophageal wall with diffusion spectrum imaging and tractography

et al. 2008

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In order to determine the three-dimensional (3D) resolved muscular anatomy of the mammalian esophagus, we have examined its myoarchitecture with diffusion spectrum magnetic resonance imaging (DSI) and tractography. DSI measures diffusion displacement as a function of magnetic gradients of varied direction and intensity and displays the displacement profile as a 3D contour per voxel. In tractography, the orientation vectors of maximum diffusion/voxel are identified, and intervoxel associations are constructed by a streamline algorithm based on angular similarity in order to generate mesoscale myofiber tracts. We demonstrate that the proximal body of the esophagus consists of helically aligned crossing fiber populations that overlap between layers in the form of a "zipper" region along the length of the tissue. With increasingly distal position along the length of the tissue, helix angle and skeletal muscle prevalence are reduced such that fibers align themselves in the most distal location into distinct inner circular and outer longitudinal smooth muscle layers. We conclude that esophageal myoanatomy consists of crossing myofibers exhibiting a decreasing degree of helicity as a function of axial position and propose that this unique geometric construct provides a mechanism to resist distension and promote aboral flow.

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Simulation studies of the role of esophageal mucosa in bolus transport

Kou¹,

Pandolfino²,

Kahrilas³

et al. 2017

Biomech Model Mechanobiol

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Based on a fully coupled computational model for esophageal transport, we analyzed the role of the mucosa (including the submucosa) in esophageal bolus transport and how bolus transport is affected by mucosal stiffness. Two groups of studies were conducted using a computational model. In the first group, a base case that represents normal esophageal transport and two hypothetical cases were simulated: 1) esophageal mucosa replaced by muscle and 2) esophagus without mucosa. For the base case, the geometric configuration of the esophageal wall was examined and the mechanical role of mucosa was analyzed. For the hypothetical cases, the pressure field and transport features were examined. In the second group of studies, cases with mucosa of varying stiffness were simulated. Overall transport characteristics were examined and both pressure and geometry were analyzed. Results show that a compliant mucosa helped accommodate the incoming bolus and lubricate the moving bolus. Bolus transport was marginally achieved without mucosa or with mucosa replaced by muscle. A stiff mucosa greatly impaired bolus transport due to lowered esophageal distensibility and increased luminal pressure. We conclude that mucosa is essential for normal esophageal transport function. Mechanically stiffened mucosa reduces the distensibility of the esophagus by obstructing luminal opening and bolus transport. Mucosal stiffening may be relevant in diseases characterized by reduced esophageal distensibility, elevated intra-bolus pressure, and/or hypertensive muscle contraction such as eosinophilic esophagitis and jackhammer esophagus.

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A Mathematical Model for Estimating Muscle Tension in vivo during Esophageal Bolus Transport

Cited by 37 publications

References 47 publications

Liquid in the gastroesophageal segment promotes reflux, but compliance does not: a mathematical modeling study

Liquid in the gastroesophageal segment promotes reflux, but compliance does not: a mathematical modeling study

Resolving the three-dimensional myoarchitecture of bovine esophageal wall with diffusion spectrum imaging and tractography

Simulation studies of the role of esophageal mucosa in bolus transport

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