《數(shù)學(xué)建模與醫(yī)學(xué)》ppt課件

1、1數(shù)學(xué)建模與醫(yī)學(xué)數(shù)學(xué)建模與醫(yī)學(xué)Mathematical Modeling and Medicine學(xué)科前沿論壇生物醫(yī)學(xué)工程與醫(yī)學(xué)影像學(xué)院生物醫(yī)學(xué)工程與醫(yī)學(xué)影像學(xué)院數(shù)學(xué)與生物數(shù)學(xué)教研室數(shù)學(xué)與生物數(shù)學(xué)教研室羅明奎羅明奎2提要提要二、數(shù)學(xué)建模與當(dāng)今醫(yī)學(xué)二、數(shù)學(xué)建模與當(dāng)今醫(yī)學(xué)一、醫(yī)學(xué)數(shù)學(xué)建模典型案例一、醫(yī)學(xué)數(shù)學(xué)建模典型案例三、我們的任務(wù)與困惑三、我們的任務(wù)與困惑3一、醫(yī)學(xué)數(shù)學(xué)建模典型案例一、醫(yī)學(xué)數(shù)學(xué)建模典型案例 Mathematical modeling in medicine41960s兩個(gè)醫(yī)學(xué)數(shù)學(xué)建模典型案例Hodgkin-Huxley模型、Alan Turing 模型Science 13 Apr

2、il 2021: Vol. 336 no. 6078 pp. 175-179 提示了數(shù)學(xué)建模在醫(yī)學(xué)研討中的突出和獨(dú)特作用經(jīng)典的醫(yī)學(xué)數(shù)學(xué)模型數(shù)學(xué)模型成為處理醫(yī)學(xué)問題的重要工具5H-H模型的醫(yī)學(xué)背景20世紀(jì)50年代研討闡明： 神經(jīng)元細(xì)胞遭到電刺激，細(xì)胞內(nèi)外的電位差也就是膜電位將發(fā)生動(dòng)搖，從而構(gòu)成動(dòng)作電位； 動(dòng)作電位導(dǎo)致離子的跨膜運(yùn)動(dòng)，致使神經(jīng)信息經(jīng)過軸突從一個(gè)神經(jīng)元向其它神經(jīng)元傳送。8電流表電流表電壓表電壓表膜片鉗膜片鉗NaKCl鉀鈉泵鉀鈉泵膜電容膜電容細(xì)胞膜外細(xì)胞膜外細(xì)胞膜內(nèi)細(xì)胞膜內(nèi)()()()mmKKClClNaNadVJCGVVGVVGVVdtH-H模型的物理學(xué)原理922(, )4DV xx

3、 tJRxH-H模型的數(shù)學(xué)原理與方法利用微積分的微元思想根據(jù)離子微元的膜內(nèi)流動(dòng)和跨膜流動(dòng)1022204Dd VRCdt()()()mKKClClNaNadVCGVVGVVGVVdt( , )( )(1( , )( ) ( , )nndn V tVn V tV n V tdt( , )( )(1( , )( ) ( , )( , )( )(1( , )( ) ( , )mmhhdm V tVm V tV m V tdtdhV tVhV tV hV tdtH-H模型的4個(gè)微分方程110.1(25)25exp() 110mVV4exp()18mV0.07exp()20hV130exp() 110hV

4、0.01(10)10exp() 110nVV0.125exp()80nVH-H模型的6個(gè)代數(shù)方程H-H模型的仿真1213 由于上述極具影響力的任務(wù)，英國著名神經(jīng)生物學(xué)家Hodgkin和Huxley 于1963年獲得諾貝爾生理與醫(yī)學(xué)獎(jiǎng)。Nobel Prize14Hodgkin-Huxley type modelling and parameter estimation of GnRH neurons Bio Systems (2021) Parameter estimation of the Hodgkin-Huxley model using metaheuristics: applicati

5、on to neuromimetic analog integrated circuits Biomedical Circuits (2021) H-H模型依然是研討熱點(diǎn) 由于H-H模型由一系列微分方程構(gòu)成、并涉及諸多參數(shù)，如何尋求參數(shù)的合理估計(jì)依然是數(shù)學(xué)和醫(yī)學(xué)的難點(diǎn)，到如今依然是研討的熱點(diǎn)。15二、數(shù)學(xué)建模與當(dāng)今醫(yī)學(xué)二、數(shù)學(xué)建模與當(dāng)今醫(yī)學(xué)Mathematical modeling and up-to-date medicine16Bioinformatics and Mathematics概率論與隨機(jī)過程運(yùn)籌學(xué)最優(yōu)化拓?fù)鋵W(xué)群論序列比對(duì)蛋白質(zhì)空間構(gòu)造預(yù)測DNA雙螺旋構(gòu)造DNA序列的對(duì)稱性基因分

6、類17Systems biology and mathematics圖論統(tǒng)計(jì)神經(jīng)網(wǎng)絡(luò)生物數(shù)學(xué)數(shù)學(xué)規(guī)劃模糊數(shù)學(xué)生物動(dòng)力學(xué)最優(yōu)化方法、數(shù)學(xué)新實(shí)際數(shù)學(xué)模型的實(shí)際檢驗(yàn)構(gòu)造改動(dòng)下的信息整合初始模型的實(shí)驗(yàn)數(shù)據(jù)修正實(shí)驗(yàn)數(shù)據(jù)的反復(fù)修正系統(tǒng)的構(gòu)造基因作用網(wǎng)絡(luò)代謝途徑細(xì)胞內(nèi)與細(xì)胞間作用機(jī)理基因突變下基因表達(dá)蛋白質(zhì)表達(dá)及代謝的變化模型的建立參數(shù)校正作用機(jī)理致病機(jī)理Cell motility and mathematics1675,Leeuwenhoek discoveredCell motilityProtrusionContractionAdhesion1819Protrusion modelCurrent Op

7、inion in Cell Biology 2006, 18:323920Contraction modelBiophys.J.2021，963：1189-120921Adhesion modelAdhesion is perhaps the hottest subfield of the cell motility these days, with tens ofbiological papers published on this topic every month.Math. Biol. (2021) 22數(shù)學(xué)建模對(duì)醫(yī)學(xué)的作用making easier access to simulat

8、ions of complex systems An important element for this success is the precise continuous samplings of new clinical data have generated experiments.Another important element is the attempts to focus on precise definitions of physiological concepts in order to avoid confusion, misunderstandings and was

9、te of efforts. Furthermore, it is shown, that mathematics may also provide a tool to structure thoughts, an area which have gained an increasing attention lately.23三、我們的任務(wù)與困惑三、我們的任務(wù)與困惑Our work and confusion 24u 主持國家自然科學(xué)基金2項(xiàng)傳染病模型構(gòu)建u SCI返修論文數(shù)據(jù)分析年均20余篇u 數(shù)學(xué)建模與數(shù)據(jù)分析年均100余人次Our worku 嫌疑犯身高預(yù)測模型與重慶市刑警總隊(duì)協(xié)作u 呼

10、吸機(jī)療效評(píng)價(jià)模型與深圳安?？萍紖f(xié)作u 眼科手術(shù)療效評(píng)價(jià)模型與西南醫(yī)院眼科協(xié)作25Our work從從19921992年的年的314314隊(duì)開展到隊(duì)開展到20212021年的年的1949019490隊(duì)隊(duì)我校：獲得我校：獲得Matlab創(chuàng)新獎(jiǎng)創(chuàng)新獎(jiǎng)1項(xiàng)獲獎(jiǎng)率項(xiàng)獲獎(jiǎng)率1/10000指點(diǎn)本科生發(fā)表論文指點(diǎn)本科生發(fā)表論文30余篇余篇獲得全國一等獎(jiǎng)獲得全國一等獎(jiǎng)15項(xiàng)獲獎(jiǎng)率項(xiàng)獲獎(jiǎng)率1/10026 DNA 序列分類 血管的三維重建 SARS的傳播 艾滋病療法的評(píng)價(jià)及療效的預(yù)測 眼科病床的合理安排 Our work27traditional experimental biological methodsMathematical and computational modelingConfusion！lack of standard modeling methods！