摘要：
The control problem in ultrasound therapy is to destroy the tumor tissue while not harming the intervening healthy tissue with a desired temperature elevation. The objective of this research is to present a robust and feasible method to control the temperature distribution and the temperature elevation in treatment region within the prescribed time, which can improve the curative effect and decrease the treatment time for heating large tumor (>= 2.0 cm in diameter). An adaptive self-tuning-regulator (STR) controller has been introduced into this control method by adding a time factor with a recursive algorithm, and the speed of sound and absorption coefficient of the medium is considered as a function of temperature during heating. The presented control method is tested for a self-focused concave spherical transducer (0.5 MHz, 9 cm aperture, 8.0 cm focal length) through numerical simulations with three control temperatures of 43 degrees C, 50 degrees C and 55 degrees C. The results suggest that this control system has adaptive ability for variable parameters and has a rapid response to the temperature and acoustic power output in the prescribed time for the hyperthermia interest. There is no overshoot during temperature elevation and no oscillation after reaching the desired temperatures. It is found that the same results can be obtained for different frequencies and temperature elevations. This method can obtain an ellipsoid-shaped ablation region, which is meaningful for the treatment of large tumor. (C) 2012 Elsevier B.V. All rights reserved.
期刊：
Journal of Chemical Information and Computer Sciences,2002年42(3):529-533 ISSN：0095-2338
通讯作者：
Liu, YC
作者机构：
[Liu, YC] Nanhua Univ, Inst Engn & Technol, Dept Math & Phys Sci, Hengyang 421001, Hunan, Peoples R China.;Xinjiang Univ, Inst Math & Phys, Urumqi 830046, Xinjiang, Peoples R China.;Huazhong Univ Sci & Technol, Dept Control Sci & Engn, Wuhan 430074, Hubei, Peoples R China.
通讯机构：
[Liu, YC] Nanhua Univ, Inst Engn & Technol, Dept Math & Phys Sci, Hengyang 421001, Hunan, Peoples R China.
摘要：
Some 2-D and 3-D graphical representations of DNA sequences have been given by Nandy, Leong and Mogenthaler, and Randic et al., which give visual characterizations of DNA sequences. In this paper, we presented a novel graphical representation of DNA sequences by taking four special vectors in 2-D Cartesian coordinate system to represent the four nucleic acid bases in DNA sequences, so that a DNA sequence is denoted on a plane by a directed walk. It is shown that the new graphical representation of DNA sequences has lower or nondegeneracy.
期刊：
Mathematical Medicine and Biology: A Journal of the IMA,2008年25(2):99-112 ISSN：1477-8599
通讯作者：
Zhu, HY
作者机构：
[Zhu, Huiyan] Nanhua Univ, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.;[Zou, Xingfu] Univ Western Ontario, Dept Appl Math, London, ON N6A 5B7, Canada.
通讯机构：
[Zhu, HY ] Nanhua Univ, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.;Nanhua Univ, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.
关键词：
HIV-1;cells;virus;delays;stability
摘要：
Analysed is a mathematical model for HIV-1 infection with two delays accounting, respectively, for (i) a latent period between the time target cells are contacted by the virus particles and the time the virions enter the cells and (ii) a virus production period for new virions to be produced within and released from the infected cells. For this model, the basic reproduction number
<tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{R}_{0}$</tex>
is identified and its threshold property is discussed: the uninfected steady state is proved to be globally asymptotically stable if
<tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{R}_{0}< 1$</tex>
and unstable if
<tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{R}_{0}>1$</tex>
. In the latter case, an infected steady state occurs and is proved to be locally asymptotically stable. The formula for shows that increasing either of the two delays will decrease
<tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{R}_{0}$</tex>
. This may suggest a new direction for new drugs—drugs that can prolong the latent period and/or slow down the virus production process.
