《數(shù)學(xué)建模與醫(yī)學(xué)》課件

1、1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)院數(shù)學(xué)與生物數(shù)學(xué)教研室羅明奎2提要二、數(shù)學(xué)建模與當(dāng)今醫(yī)學(xué)一、醫(yī)學(xué)數(shù)學(xué)建模典型案例三、我們的工作與困惑3一、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 April 2012: Vol. 336 no. 6078 pp. 175-179 揭示了數(shù)學(xué)建模在醫(yī)學(xué)研究中的突出和獨(dú)特作用經(jīng)典的醫(yī)學(xué)數(shù)學(xué)模型數(shù)學(xué)模型成為解決醫(yī)學(xué)問

2、題的重要工具9xxDxxDH-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)10H-H模型的4個(gè)微分方程11H-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工作，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 (2010) Parameter estimation of the Hodgkin-Huxley model

3、 using metaheuristics: application to neuromimetic analog integrated circuits Biomedical Circuits (2009) H-H模型仍然是研究熱點(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)，到現(xiàn)在依然是研究的熱點(diǎn)。16Bioinformatics 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)空間結(jié)構(gòu)預(yù)測(cè)DNA雙螺旋結(jié)構(gòu)DNA序列的對(duì)稱性基因分類17Systems biology and mathematics圖論統(tǒng)

4、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)新理論數(shù)學(xué)模型的實(shí)踐檢驗(yàn)結(jié)構(gòu)改變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)的重復(fù)修正系統(tǒng)的結(jié)構(gòu)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19Protrusion modelCurrent Opinion in Cell Biology 2006, 18:323920Contraction modelBiophys.J.2009，96（3）：1189-120921Adhesion modelAdhesion is perhaps the hottest subfi

5、eld of the cell motility these days, with tens ofbiological papers published on this topic every month.Math. Biol. (2009) 22數(shù)學(xué)建模對(duì)醫(yī)學(xué)的作用making easier access to simulations of complex systems An important element for this success is the precise continuous samplings of new clinical data have generated e

6、xperiments.Another important element is the attempts to focus on precise definitions of physiological concepts in order to avoid confusion, misunderstandings and waste of efforts. Furthermore, it is shown, that mathematics may also provide a tool to structure thoughts, an area which have gained an i

7、ncreasing attention lately.23三、我們的工作與困惑Our work and confusion 24 主持國家自然科學(xué)基金2項(xiàng)傳染病模型構(gòu)建 SCI返修論文數(shù)據(jù)分析年均20余篇 數(shù)學(xué)建模與數(shù)據(jù)分析年均100余人次Our work 嫌疑犯身高預(yù)測(cè)模型（與重慶市刑警總隊(duì)合作） 呼吸機(jī)療效評(píng)價(jià)模型（與深圳安?？萍加邢薰竞献鳎?眼科手術(shù)療效評(píng)價(jià)模型（與西南醫(yī)院眼科合作）26 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(cè) 眼科病床的合理安排 Our work27traditional experimental biological methodsMathematical and computational modelingConfusion！lack of standard modeling methods！ difficulties