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Hu S, Lan X, Zheng J, Bi Y, Ye Y, Si M, Fang Y, Wang J, Liu J, Chen Y, Chen Y, Xiang P, Niu T, Huang Y. The dose-related plateau effect of surviving fraction in normal tissue during the ultra-high-dose-rate radiotherapy. Phys Med Biol 2023; 68:185004. [PMID: 37586385 DOI: 10.1088/1361-6560/acf112] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2023] [Accepted: 08/16/2023] [Indexed: 08/18/2023]
Abstract
Objective.Ultra-high-dose-rate radiotherapy, referred to as FLASH therapy, has been demonstrated to reduce the damage of normal tissue as well as inhibiting tumor growth compared with conventional dose-rate radiotherapy. The transient hypoxia may be a vital explanation for sparing the normal tissue. The heterogeneity of oxygen distribution for different doses and dose rates in the different radiotherapy schemes are analyzed. With these results, the influence of doses and dose rates on cell survival are evaluated in this work.Approach.The two-dimensional reaction-diffusion equations are used to describe the heterogeneity of the oxygen distribution in capillaries and tissue. A modified linear quadratic model is employed to characterize the surviving fraction at different doses and dose rates.Main results.The reduction of the damage to the normal tissue can be observed if the doses exceeds a minimum dose threshold under the ultra-high-dose-rate radiation. Also, the surviving fraction exhibits the 'plateau effect' under the ultra-high dose rates radiation, which signifies that within a specific range of doses, the surviving fraction either exhibits minimal variation or increases with the dose. For a given dose, the surviving fraction increases with the dose rate until tending to a stable value, which means that the protection in normal tissue reaches saturation.Significance.The emergence of the 'plateau effect' allows delivering the higher doses while minimizing damage to normal tissue. It is necessary to develop appropriate program of doses and dose rates for different irradiated tissue to achieve more efficient protection.
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Affiliation(s)
- Shuai Hu
- School of Physics and Astronomy, China West Normal University, Nanchong 637009, People's Republic of China
- School of Science, Sun Yat-Sen University, Shenzhen 518107, People's Republic of China
| | - Xiaofei Lan
- School of Physics and Astronomy, China West Normal University, Nanchong 637009, People's Republic of China
| | - Jinfen Zheng
- Dermatology, Center for Chronic Disease Prevention of Shenzhen, Guangdong Shenzhen 518020, People's Republic of China
| | - Yuanjie Bi
- School of Science, Sun Yat-Sen University, Shenzhen 518107, People's Republic of China
| | - Yuanchun Ye
- Department of Hematology, Oncology and Cancer Immunology Campus Benjamin Franklin Charité-Universitätsmedizin Berlin Corporate member of Freie Universität Berlin and Humboldt-Universität zu Berlin Hindenburgdamm, 30,12203, Berlin Germany
| | - Meiyu Si
- School of Science, Sun Yat-Sen University, Shenzhen 518107, People's Republic of China
- Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, People's Republic of China
- University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China
| | - Yuhong Fang
- School of Science, Sun Yat-Sen University, Shenzhen 518107, People's Republic of China
| | - Jinghui Wang
- Varian Medical Systems, Palo Alto, CA 94304, United States of America
| | - Junyan Liu
- Department of Radiation Oncology, Stanford University School of Medicine, Stanford, CA 94304, United States of America
| | - Yuan Chen
- The Institute for Advanced Studies of Wuhan University, 299, Bayi Road, Wuhan, 430072, People's Republic of China
| | - Yuling Chen
- Department of Rheumatology and Immunology, The Seventh Affiliated Hospital Sun Yat-sen University, Shenzhen 518107, People's Republic of China
| | - Pai Xiang
- The Institute for Advanced Studies of Wuhan University, 299, Bayi Road, Wuhan, 430072, People's Republic of China
| | - Tianye Niu
- Shenzhen Bay Laboratory, Shenzhen 518107, People's Republic of China
| | - Yongsheng Huang
- School of Science, Sun Yat-Sen University, Shenzhen 518107, People's Republic of China
- Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, People's Republic of China
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Kori J, Pratibha. Effect of first order chemical reactions through tissue-blood interface on the partial pressure distribution of inhaled gas. Comput Methods Biomech Biomed Engin 2021; 25:84-96. [PMID: 34057371 DOI: 10.1080/10255842.2021.1932839] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Abstract
Gas exchange is an essential process to get fresh oxygenated air from the environment. In the human respiratory system, partial pressure is responsible for exchanging gas between tissue-blood capillary (inter capillary). However, the mechanisms of partial pressure distribution in the human respiratory system remain incompletely understood in terms of inter-capillary transmission with tissue porosity and reactive boundary conditions. In this paper, we worked on the spatial (radial) and temporal variations of inhaled gas partial pressure through inter capillary. We assumed that the tissue of alveoli is porous and the material of blood capillary is absorptive and reactive and gas could bear linear first-order kinetic reactions, one is reversible among the material of blood capillary and the other is irreversible into the surrounding tissue. Mathematical modeling is done by using diffusion equation; and the effect of various dimensionless parameters e.g. the Damkohler number (DA), phase partitioning number (α), dimensionless absorption number (Γ) are analyzed. Numerical simulation shows that an increment in porosity does not change convection speed but the diffusion of gas increases in alveolar tissue, resultantly, partial pressure gradient of the gas decreases in tissue and increases in blood capillary. However, by increasing the breathing rate, the partial pressure of the gas inside the blood first decreases, and after some time it increases gradually with the breathing rate. Additionally, the dispersion coefficient advanced toward its steady-state in a short time at absorption rate Γ≤ 0.1 and Damkohler number 1≤DA≤10, while long-time dispersion is achieved at porosity ϵ = 0.9, absorption rate Γ = 1, and phase exchange rate 10<DA≤100. Ultimately, the findings of this study can be helpful for a better understanding of dispersion through human lung affected by aging and various lung diseases.
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Affiliation(s)
- Jyoti Kori
- Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India
| | - Pratibha
- Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India
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ZHAO NING, IRAMINA KEIJI. A MATHEMATICAL COUPLED MODEL OF OXYGEN TRANSPORT IN THE MICROCIRCULATION: THE EFFECT OF CONVECTION–DIFFUSION ON OXYGEN TRANSPORT. J MECH MED BIOL 2015. [DOI: 10.1142/s0219519415500037] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
This paper is aimed at examining the effect of convection–diffusion on oxygen transport at the micro-level. A coupled model of the convection–diffusion and molecular diffusion of oxygen is developed, and the solid deformation resulting from capillary fluctuations and the seepage of tissue fluid are incorporated into this model. The results indicate that (1) the oxygen concentration calculated from this coupled model is higher than that given by molecular diffusion models, both within the capillaries and tissue (maximum difference of 16%); (2) convection–diffusion has the greatest effect in tissue surrounding the middle of the capillary, and enhances the amount of oxygen transported to cells far from the oxygen source; (3) larger permeability coefficients or smaller diffusion coefficients produce a more obvious convection–diffusion effect; (4) a counter-current flow occurs near the inlet and outlet ends of the capillary. This model also provides a foundation for the study of how oxygen affects tumor growth.
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Affiliation(s)
- NING ZHAO
- Graduate School of Systems Life Sciences, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan
| | - KEIJI IRAMINA
- Department of Informatics, Graduate School of Information, Science and Electrical Engineering, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan
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Abstract
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 (i.e., biochemical, structural, and 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. Multivessel models are discussed that 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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Affiliation(s)
- Daniel Goldman
- Department of Medical Biophysics, The University of Western Ontario, London, Ontario, Canada.
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Abstract
A new microscopic model is developed to describe the dermal capillary clearance process of skin permeants. The physiological structure is represented in terms of a doubly periodic array of absorbing capillaries. Convection-dominated transport in the blood flow within the capillaries is coupled with interstitial diffusion, the latter process being quantified via a slender-body-theory approach. Convection across the capillary wall and in the interstitial phase is treated as a perturbation which may be added to the diffusive transport. The model accounts for the finite permeability of the capillary wall as well as for the geometry of the capillary array, based on realistic values of physiological parameters. Calculated dermal concentration profiles for permeants having the size and lipophilicity of salicylic acid and glucose illustrate the power and general applicability of the model. Furthermore, validation of the model with published in vivo experimental results pertaining to human skin permeation of hydrocortisone is presented. The model offers the possibility for in-depth theoretical understanding and prediction of subsurface drug distribution in the human skin following topical application, as well as rates of capillary clearance into the systemic circulation. A simpler approach that treats the capillary bed as a homogeneously absorbing zone is also employed. The latter may be used in conjunction with the capillary exchange model to estimate measurable dermal transport and clearance parameters in a straightforward manner.
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Affiliation(s)
- Kosmas Kretsos
- University at Buffalo, State University of New York, Department of Chemical and Biological Engineering, Furnas Hall, Buffalo, NY 14260-4200, USA.
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