Abstract
摘要:(1) 高強度聚焦超音波燒灼肝腫瘤的研究
(參與人員:許文翰、張恆華、M. Thiriet、O. Pironneau、何承懋醫師、梁柏欣醫師)
本研究主題志在建立一個整合三場的數學模型,以期更了解具非線性超音波傳輸,非線性血液動力及
因 HIFU 治療所引致的肝內溫升行為。發展一能有效求解此一 acoustics-hydrodynamics-thermal 耦合方程
組的計算方法是本計劃重要的工作之ㄧ。外籍學者 M. Thiriet 將參與數學模型的改善,O. Pironneau 將協
助把吾人所開發的計算方法融入他所主導開發的 FreeFEM++有限元程式集。張恆華、何承懋、梁柏欣則
擔負提供高品質 CT 肝影像,以及將其轉置成 CAD 模型。本計劃團隊將舉辦如下的國際研討會
TIMS-LJLL Symposium for Scientific Computing on Medicine ; October 2014 ; Abroad participants
(around 10) ; Domestic participants (around 30)。
(2) 探討細胞表面離子通道內的複雜動力行為
(參與人員: 林太家、Marc Thiriet、林慶龍 )
細胞膜內有成百上千種蛋白離子通道,具有許多重要功能,在生理和病理學中非常重要。通道控制跨
越細胞膜之陰、 陽離子的移動,藉由隨機打開和關閉通道來回應所有電性能和特定刺激的細胞和組織。
這種隨機打開和關閉通道的機制,尚有許多不解之謎。例如,通道的門控(gating)過程控制跨越細胞膜
的總電荷。成千上萬的類型的通道有不同類型的門控和不同類型的回應信號。許多生物學家正在關注此
問題,但關於此問題的基本性質仍有爭議。偏微分方程可解釋的離子通道機制,並提供重要的數學模型
來研究離子通道。Poisson-Nernst-Planck(PNP)方程式是描述離子通道的傳統模型,雖然可用來解決一些
問題,但卻無法解釋通道內的一些重要機制如 gating 和 selectivity 。本計劃將發展修正的 PNP 方程式,
用來研究 gating 和 selectivity 等離子通道的一些重要機制。
(3) 呼吸方式對氧於肺中分佈之研究
(參與人員: 許文翰、張恆華、林慶龍、T. Yamaguchi、A. Quarteroni)
呼吸的方式將影響氧氣在氣管內的濃度的分佈,它將更進一步地影響身體內各器官氧的獲得量。本計
劃將探討印度瑜珈、東方練氣者及吾人一般的呼吸方式,以了解它在氣管中所進行的對流及擴散行為。
外籍學者林慶龍、T. Yamaguchi 及 A. Quarteroni 將協助建置不同的 3D-1D 模型,吾人並將探討及評估這
三種模型的有效性。張恆華將協助建置高品質的氣管 CT 模型,本計劃將於 2013 年舉辦國際研討會
Computational Biofluid and its Medical ( Clinical ) Applications ; March 2013 ; Abroad participants
(around 10) ; Domestic participants (around 20)。
Abstract: (1) High-intensity focal ultrasound therapy for ablating liver tumor.
We are aimed to construct an integrated mathematical model for getting a better understanding of the nonlinear acoustic ultrasound wave propagation, nonlinear hemodynamics for blood flow, and energy equation for the temperature elevation in the liver due to HIFU therapy. Efficient scheme developed for solving this acoustics-hydrodynamics-thermal coupling mathematical equations is another key of this topic. M. Thiriet
involves refinement of the mathematical model. O. Pironneau helps to implement our developed numerical scheme to his FreeFEM++ freeware. H. H. Zhang、C. H. Ho、P. H. Liang are responsible to provide excellent liver CT images and transform them to the liver vessel CAD model
(2) Investigation into the complex dynamical behavior in the cell ion channel
Ion channels are proteins with a hole down the middle embedded in cell membranes which may contain hundreds or thousands of types of channels. Several crucial functions of ion channels may play important roles in physiology and pathology. Channels control the movement of anions and cations across cell membranes by opening and closing stochastically in response to all the electrical properties and specific stimuli of cells and tissues by mechanisms that are not yet understood. For example, the gating process of channels controls the total charge movement across the membrane. Each of the thousands of types of channels has different types of
gates that respond to different types of signals. Many biologists are working on gating, but agreement on even the structural basis of gating is not yet at hand. Partial differential equations may explain the ionic mechanisms and provide important mathematical models to study ion channels. The main goal of this project is to find suitable partial differential equations to study the ionic mechanisms underlying cell membranes. Although the Poisson-Nernst-Planck(PNP)equation is useful to investigate some problems of ion channels, it still cannot
explain the mechanisms of ion channels like gating and selectivity. In this project, we propose to find modified PNP equations which may study gating and selectivity efficiently.
(3) Assessment of breathing maneuvers on oxygen transport.
Breathing maneuver can greatly affect the oxygen distribution in the human airway. It can further alter the oxygen level in human organs. This study aims to assess the Yoga, Chi-practioner and normal breathing maneuvers. As a result, we can gain some knowledge about the convection-diffusion mode during a breathing phase. Foreign colaborators Ching-Long Lin、T. Yamaguchi and A. Quarteroni help us to construct three different 3D-1D models. We will then assess these models’ effectiveness. H. H. Zhang are responsible to
provide an excellent airway CAD model.
Keyword(s)
Navier-Stokes 方程
聚焦超音波
肝腫瘤
離子通道
Poisson-Nernst-Planck 方程
呼 吸方式
Navier-Stokes equations
focused ultrasound
liver tumor
ion channels
Poisson-Nernst-Planck equation
breathing maneuvers