Modeling Oxygen Transport: Development of Methods and Current State

Bruley, Duane F.

doi:10.1007/978-1-4615-2468-7_5

Cited by 6 publications

(4 citation statements)

References 12 publications

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“…-DV2P + j.iP = S(x,y, z,t) (1) where x, y, z is the spatial location in x, y, z direction (cm), respectively, t is the time (ps), and S (x, y, z, t) is a source term. C is the speed of the light in the media.…”

Section: Theorymentioning

confidence: 99%

<title>Breast tumor characterization using near-infrared spectroscopy</title>

et al. 1993

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INTRODUCFIONNIR time resolved spectroscopy (TRS) is one of the most feasible methods which can be used for the characterization of biological systems, due to its non-invasive nature and safety features in measurement. Breast cancer is the leading cause of death in women ages 40-44 and accounts for 32 % of all cancer diagnosis in women. The occurrence rate is as high as one out of nine women in the USA. Breast cancer is the most common form of cancer and the second leading cause of cancer death in North America4. Therefore, it is natural for researchers in the field of NIR spectroscopy to have strong interest in optical properties of normal and abnormal breast tissue. One of the main interest of NIR spectroscopy in breast cancer is the localization of the tumor. Another important feature is to characterize an anomaly non-invasively since more than 75 % ofmammographycal anomalies are found to be benign. This could reduce the anxiety that the patients would have, as well as lower the clinical expense for the biopsy and operation (approximately $4,000 per a case).Compared to other types of tissue, breast tissue has a lower absorption coefficient due to high fatty tissue content and a low number of blood vessels (Chance, unpublished data). During the tumor's growth vasculature development occurs at a denser level than the surrounding tissue7. Therefore, it was expected that tumors with a dense vasculature in breasts would be more easily detected than in other tissue with high absorption. (HUP) have a joint research program on the characterization of optical properties of normal breasts and breasts with anomalies, by using TRS. Appropriate protocols for the measurements of the observable absorption and the scattering coefficients were designed for normal subjects and patients. Measurements for normal subjects were performed to see the optical properties of breast (4 African-Americans and 6 Caucasians) from different locations. Breast anomalies from 51 patients were characterized by measuring the observable absorption and the scattering coefficients. Non-parametric and parametric analyses were performed with the collected data.It should be noted that the absorption coefficient in the text is presented in log10 scale (not in loge). THEORYThe photon transport in a highly scattering medium can be analogous to the dye molecule transport in a liquid containing bleach. Photons are diffused in a scattering medium at a certain diffusion rate, at the same time consumed by the media. Therefore, the governing equation for the photon energy density, P (x, y, z, t), in an isotropic scattering medium can be expressed as a simple diffusion equation with a constant consumption rate, Ja6.-DV2P + j.iP = S(x,y, z,t)(1) where x, y, z is the spatial location in x, y, z direction (cm), respectively, t is the time (ps), and S (x, y, z, t) is a source term. C is the speed of the light in the media. D is the diffusion coefficient, which is 0-8194-11 15-91931$6.O() SPIE Vol. 1888 /487 Downloaded From: http://proceedings.spiedigitallibrary.org/ o...

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Section: Theorymentioning

confidence: 99%

<title>Breast tumor characterization using near-infrared spectroscopy</title>

et al. 1993

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“…The governing equation for the photon energy density (number of photons/cm3), P(x, y, z, t), in an isotropic scauering medium can be expressed as a simple diffusion equation with constant absorption rate, -;:--D V2P + LaP S(x,y,z,t) (1) where C is the light velocity in the medium (c/n, where c is the light velocity in vacuum and n is refrative index). x, y, z is the spatial location in x, y, z direction, respectively.…”

Section: Homogeneous System Without Boundarymentioning

confidence: 99%

<title>Application of near-field interference of phase-modulated spectroscopy for detection of absorbers: theoretical prediction of phase shift with respect to the location of the absorber by using a probabilistic-numerical technique, the B-W-K method</title>

et al. 1993

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“…By supplementing the above model with a crosssectionally averaged model of capillary O 2 transport, it is possible to predict the PO 2 in a capillary and its surrounding tissue. Neglecting O 2 dissolved in the plasma, intracapillary transport can be described by the following convection problem for capillary SO 2 (S), given capillary entrance SO 2 (S a ), as shown in Equation 8: :…”

Section: Standard Krogh Modelmentioning

confidence: 99%

“…Another approach that has been used in parallel array models of O 2 transport, and which could also be applied to capillary networks, is the Williford-Bruley (W-B) ''probabilistic deterministic'' numerical method [8,45]. This technique uses time-dependent probability density functions in three spatial dimensions to evolve tissue O 2 distributions on a grid.…”

Section: Parallel Capillary Modelsmentioning

confidence: 99%

Theoretical Models of Microvascular Oxygen Transport to Tissue

Goldman¹

2008

Microcirculation

165

176

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To improve understanding of microvascular O 2 transport, theoretical modeling has been pursued for many years. The large number of studies in this area attests to the complexities (biochemical, structural, hemodynamic) involved. This article focuses on theoretical studies from the last two decades and, in particular, on models of O 2 transport to tissue by discrete microvessels. A brief discussion of intravascular O 2 transport is first given, highlighting the physiological importance of intravascular resistance to blood-tissue O 2 transfer. This is followed by a description of the Krogh tissue cylinder model of O 2 transport by a single capillary, which is shown to remain relevant in modified forms that relax many of the original biophysical assumptions. However, there are many geometric and hemodynamic complexities that require the consideration of microvascular arrays and networks. Multi-vessel models are discussed which have shown the physiological importance of heterogeneities in vessel spacing, O 2 supply, red blood cell flow path, as well as interactions between capillaries and arterioles. These realistic models require sophisticated methods for solving the governing partial differential equations, and a range of solution techniques are described. Finally, the issue of experimental validation of microvascular O 2 delivery models is discussed, and new directions in O 2 transport modeling are outlined.

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Modeling Oxygen Transport: Development of Methods and Current State

Cited by 6 publications

References 12 publications

<title>Breast tumor characterization using near-infrared spectroscopy</title>

<title>Breast tumor characterization using near-infrared spectroscopy</title>

<title>Application of near-field interference of phase-modulated spectroscopy for detection of absorbers: theoretical prediction of phase shift with respect to the location of the absorber by using a probabilistic-numerical technique, the B-W-K method</title>

Theoretical Models of Microvascular Oxygen Transport to Tissue

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