A computer model of oxygen dynamics in human colon mucosa: Implications in normal physiology and early tumor development

Guebel, Daniel V.; Torres, Néstor V.

doi:10.1016/j.jtbi.2007.09.035

Cited by 15 publications

(29 citation statements)

References 85 publications

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“…More precisely, we consider the surface of the colon epithelium as a 2D periodic structure, since the domain εP , representing the "crypt and the small region surrounding its orifice", is replicated in all the domain Ω, as depicted in Figure 3, left. We also emphasize that this periodic structure is observed in conventional colonoscopy images, that give a top view of the colon wall at the tissue level, as exemplified in Figure 1, as well as in histological images [1,32], were an hexagonal-like periodicity can be perceived, as displayed in Figure 3, right.…”

Section: Heterogeneous Periodic Modelmentioning

confidence: 58%

“…The two following lemmas assure the existence and uniqueness of solutions of the parabolic and elliptic equations (32), separately. These results will be used in the next section for proving the existence of solution of the homogenized system (32).…”

Section: Partial Existence Resultsmentioning

confidence: 99%

“…Each crypt has a test-tube shaped structure, closed at the bottom and open at the top. According to [32,33], the average dimensions for a human colonic crypt are 433 µm (1µm = 10 −6 m), from the bottom to the top, and 16 µm for the diameter of the top orifice excluding the epithelium, with a cell depth of 15.1µm. In this work, we approximate the geometry of a single crypt with a flat-bottomed cylinder S ⊂ R 3 , as done in other works (see e.g.…”

Section: Crypt Geometry (3d and 2d)mentioning

confidence: 99%

“…This is a macroscopic model that represents the evolution of ACF at the surface of the colon, by using the information of the cell dynamics in the crypts. This information is transmitted to the homogenization model through the physiologic parameters that in (32) are averaged (they are represented by the same letters as before with a tilde over them).…”

Section: Two-scale Asymptotic Expansionsmentioning

confidence: 99%

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Homogenization Model for Aberrant Crypt Foci

Figueiredo¹,

Leal²,

Romanazzi³

et al. 2016

SIAM J. Appl. Math.

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Several explanations can be found in the literature about the origin of colorectal cancer. There is however some agreement on the fact that the carcinogenic process is a result of several genetic mutations of normal cells. The colon epithelium is characterized by millions of invaginations, very small cavities, called crypts, where most of the cellular activity occurs. It is consensual in the medical community, that a potential first manifestation of the carcinogenic process, observed in conventional colonoscopy images, is the appearance of Aberrant Crypt Foci (ACF). These are clusters of abnormal crypts, morphologically characterized by an atypical behavior of the cells that populate the crypts. In this work an homogenization model is proposed, for representing the cellular dynamics in the colon epithelium. The goal is to simulate and predict, in silico, the spread and evolution of ACF, as it can be observed in colonoscopy images. By assuming that the colon is an heterogeneous media, exhibiting a periodic distribution of crypts, we start this work by describing a periodic model, that represents the ACF cell-dynamics in a two-dimensional setting. Then, homogenization techniques are applied to this periodic model, to find a simpler model, whose solution symbolizes the averaged behavior of ACF at the tissue level. Some theoretical results concerning the existence of solution of the homogenized model are proven, applying a fixed point theorem. Numerical results showing the convergence of the periodic model to the homogenized model are presented.

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Section: Heterogeneous Periodic Modelmentioning

confidence: 58%

Section: Partial Existence Resultsmentioning

confidence: 99%

Section: Crypt Geometry (3d and 2d)mentioning

confidence: 99%

Section: Two-scale Asymptotic Expansionsmentioning

confidence: 99%

See 2 more Smart Citations

Homogenization Model for Aberrant Crypt Foci

Figueiredo¹,

Leal²,

Romanazzi³

et al. 2016

SIAM J. Appl. Math.

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show abstract

“…Luminal oxygen is an unlikely source for epithelial consumption, since intraluminal P O 2 is lower than mucosal P O 2 [12]. In the intact colon in vivo , oxygen reaches the epithelial cells through their basolateral membranes by diffusion from the capillary network which surrounds the crypts[8,13]. …”

Section: Introductionmentioning

confidence: 99%

Rectification of oxygen transfer through the rat colonic epithelium

Saraví

Carra

Matus

et al. 2017

WJGP

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AIMTo assess whether higher sensitivity of colonic epithelium to hypoxia at the serosal side is associated with oxygen transfer asymmetry.METHODSRats were fed either with normal chow or a low-sodium diet. Tissues were mounted as flat sheets in a modified, airtight Ussing chamber with oxygen meters in each hemichamber. Mucosal samples from normal diet animals were studied under control conditions, in low-chloride solution and after adding chloride secretion inhibitors and chloride secretagogues. Samples from sodium-deprived rats were studied before and after ouabain addition. In separate experiments, the correlation between short-circuit current and oxygen consumption was analyzed. Finally, hypoxia was induced in one hemichamber to assess the relationship between its oxygen content and the oxygen pressure difference between both hemichambers.RESULTSIn all studied conditions, oxygen consumption was larger in the serosal hemichamber than in the mucosal one (P = 0.0025 to P < 0.0001). Short-circuit current showed significant correlation with both total oxygen consumption (r = 0.765; P = 0.009) in normoxia and oxygen consumption in the serosal hemichamber (r = 0.754; P = 0.011) during mucosal hypoxia, but not with oxygen consumption in the mucosal hemichamber. When hypoxia was induced in the mucosal hemichamber, an oxygen pressure difference of 13 kPa with the serosal hemichamber was enough to keep its oxygen content constant. However, when hypoxia was induced in the serosal hemichamber, the oxygen pressure difference with the mucosal hemichamber necessary to keep its oxygen content constant was 40 kPa (P < 0.0001).CONCLUSIONSerosal oxygen supply is more readily available to support short-circuit current. This may be partly due to a rectifying behavior of transepithelial oxygen transfer.

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The Small Intestine as a Target for Radiation

Smirnova¹

2010

Environmental Radiation Effects on Mammals

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A computer model of oxygen dynamics in human colon mucosa: Implications in normal physiology and early tumor development

Cited by 15 publications

References 85 publications

Homogenization Model for Aberrant Crypt Foci

Homogenization Model for Aberrant Crypt Foci

Rectification of oxygen transfer through the rat colonic epithelium

The Small Intestine as a Target for Radiation

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