胃电活动模型分析与胃电慢波和蠕动波三维模拟
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摘要
胃的电机械活动是胃完成其正常生理功能的基础。多年来对胃的电机械活动的研究、建模和仿真已经有很多结果,但是,我们还没有看到胃电机械活动传播的模型及其三维动态模拟的相关报道。本论文的主要工作是分析胃电活动模型,建立胃电活动传导和蠕动收缩传播的三维模型,进而对其进行三维动态模拟。
在阐述胃电机械活动的产生、特点及功能的基础上,本文首先用Matlab对离子机制的电活动模型进行分析和模拟,总结出不同类型细胞电活动的规律和特性,然后研究和模拟了电活动传导模型,最后建立了胃电机械活动关系和传播模型,并成功实现了用Matlab对胃的电机械活动的三维动态模拟。本文着重论述了逼近真实胃形态的三维胃模型和胃电机械活动耦合传播模型的建立及其Matlab模拟。
本文用Matlab对传统离子机制的电活动模型H-H模型和FHN模型进行数学分析,并用图象来展示其电活动规律,通过比较和分析,总结出ICC细胞和平滑肌细胞之间不同的电活动规律和特性。分析模拟的结果不仅增进了我们对ICC细胞和平滑肌细胞功能作用的理解和认识,而且证明了这些胃电模型的合理性。
本文对较成功的胃电活动传导的锥形体模型和柱导体模型进行研究,分析了电活动传导的规律。本文用这些模型建立的方法和原则建立了新的浆膜慢波传导模型,并用Matlab进行仿真。仿真结果反应了胃电活动传播规律,证实了传导模型的可靠性。
本文首次实现了用Matlab建立和模拟了接近真实胃形态的三维胃模型。为了实现三维胃模型尽可能接近真实胃形态,我们用多个变形锥形体(或者柱形体)组合逼近静态胃形态,从而建立了静态胃的三维模型。我们详细阐述了三维胃模型建立的方法、原则,给出了用Matlab对其实现仿真的程序和仿真结果。
本文首次对胃的电机械活动建立量化模型,并首次成功地实现了用Matlab对胃电机械活动的三维动态模拟。在所建立的三维胃模型基础上,根据实际胃生理,我们建立了胃电活动和蠕动收缩之间的量化关系模型,再由电机械耦合传导规律,进一步建立了胃电机械活动传导模型。最后用Matlab分别对静息胃的电活动传播和蠕动收缩胃的电机械活动的传播进行三维动态模拟,给出了相应的模拟结果。通过胃电机械活动的三维建模和三维动态模拟,形象地展现了胃电活动传播和胃蠕动收缩过程,为胃的电机械活动提供了三维动态模拟方法和新的认知途径。
总之,我们的研究工作不仅增进了对胃电生理和胃动力的理解,而且通过对胃电机械活动三维建模和动态模拟,形象展现了胃电活动传播、胃蠕动收缩波的传播过程,形象地揭示了胃电活动与胃动力之间的关系。特别是为胃电活动与胃动力的研究和模拟提供新的研究和认识途径,使其在胃动力疾病研究和诊断中发挥更大的作用。
Gastric electro-mechanical activity (GEMA) is foundation to complete its normal functions. Although it has been many results by studying, modeling and simulating for many years, there is still no relevant reports of quantitative relationship and three-dimensional dynamic simulation .The main work of this thesis is to analyze the model of gastric electrical activity (GEA), to establish its propagation model and peristalsis model in three-dimension, and then, to simulate it in dynamic three-dimension.
Based on the description of GEA and GEMA about its generation, characteristics and functions, this paper analyzes and simulates ion-mechanism model, summarizes the characteristics and laws of different cells at first. Secondly, it studies the propagation models about the GEA. Finally it models the electro-mechanical relationship and its propagation, and then succeeds in three-dimensional dynamic simulation. The thesis paid more attention to the model-building of three-dimensional stomach which is approximated to its true shape, and of GEMA, as well their simulations by Matlab.
This paper analyzes the traditional ion-mechanism models which are H-H and FHN models by Matlab. We use the images to show the laws of electrical activity about the different type cells. It makes a better understand of the difference between pacemaker cells and smooth muscle cells as well as their roles. It also proves that these models are reasonable.
This paper studies the cone and column propagation model of GEA, and analyzes the laws of it, models and simulates the propagation of slow-wave by model-building methods and principles using Matlab. The results reveal its propagation law and confirm the reliability of conduction models.
It is the first to realize the modeling and simulating the three-dimensional complex stomach that is close to its true shape using Matlab. In order to approximate to the true shape, this paper uses a number of deformed cones (or columns) to combine for simulating the static stomach, it gets a static three-dimensional model of the stomach. It describes the modeling methods and principles in detail, gives the corresponding program and simulative results.
Based on its laws, it is the first to establish a model of the quantitative relationship of GEA and peristaltic contraction, and a three-dimensional dynamic model of its propagation. It is the first to achieve three-dimensional dynamic simulation successfully using Matlab. According to the actual gastric physiology and the established model , it establishes quantitative relationship model between GEA and peristalsis, and further establishes a propagation model of GEMA by conduction laws.Finally,it simulates the propagation of GEA for the resting gastric and of GEMA for peristalsis gastric separately in dynamic three-dimension.It gives the corresponding simulated results.By modeling and simulating, it vividly demonstrates the spreading process of GEA and gastric peristalsis contraction, and provides some simulative methods and cognitive means for GEMA.
In a word, our study has not only enhanced understands to electrophysiology and gastric motility, but also vividly showed the spread of GEA and mechanical activity as well as the relationship of them. In particular, it has provided new study and cognize approach for precise quantitative relationship between GEA and gastric motility, which can have it play a greater role in diagnosis and studies for gastric diseases.
在阐述胃电机械活动的产生、特点及功能的基础上,本文首先用Matlab对离子机制的电活动模型进行分析和模拟,总结出不同类型细胞电活动的规律和特性,然后研究和模拟了电活动传导模型,最后建立了胃电机械活动关系和传播模型,并成功实现了用Matlab对胃的电机械活动的三维动态模拟。本文着重论述了逼近真实胃形态的三维胃模型和胃电机械活动耦合传播模型的建立及其Matlab模拟。
本文用Matlab对传统离子机制的电活动模型H-H模型和FHN模型进行数学分析,并用图象来展示其电活动规律,通过比较和分析,总结出ICC细胞和平滑肌细胞之间不同的电活动规律和特性。分析模拟的结果不仅增进了我们对ICC细胞和平滑肌细胞功能作用的理解和认识,而且证明了这些胃电模型的合理性。
本文对较成功的胃电活动传导的锥形体模型和柱导体模型进行研究,分析了电活动传导的规律。本文用这些模型建立的方法和原则建立了新的浆膜慢波传导模型,并用Matlab进行仿真。仿真结果反应了胃电活动传播规律,证实了传导模型的可靠性。
本文首次实现了用Matlab建立和模拟了接近真实胃形态的三维胃模型。为了实现三维胃模型尽可能接近真实胃形态,我们用多个变形锥形体(或者柱形体)组合逼近静态胃形态,从而建立了静态胃的三维模型。我们详细阐述了三维胃模型建立的方法、原则,给出了用Matlab对其实现仿真的程序和仿真结果。
本文首次对胃的电机械活动建立量化模型,并首次成功地实现了用Matlab对胃电机械活动的三维动态模拟。在所建立的三维胃模型基础上,根据实际胃生理,我们建立了胃电活动和蠕动收缩之间的量化关系模型,再由电机械耦合传导规律,进一步建立了胃电机械活动传导模型。最后用Matlab分别对静息胃的电活动传播和蠕动收缩胃的电机械活动的传播进行三维动态模拟,给出了相应的模拟结果。通过胃电机械活动的三维建模和三维动态模拟,形象地展现了胃电活动传播和胃蠕动收缩过程,为胃的电机械活动提供了三维动态模拟方法和新的认知途径。
总之,我们的研究工作不仅增进了对胃电生理和胃动力的理解,而且通过对胃电机械活动三维建模和动态模拟,形象展现了胃电活动传播、胃蠕动收缩波的传播过程,形象地揭示了胃电活动与胃动力之间的关系。特别是为胃电活动与胃动力的研究和模拟提供新的研究和认识途径,使其在胃动力疾病研究和诊断中发挥更大的作用。
Gastric electro-mechanical activity (GEMA) is foundation to complete its normal functions. Although it has been many results by studying, modeling and simulating for many years, there is still no relevant reports of quantitative relationship and three-dimensional dynamic simulation .The main work of this thesis is to analyze the model of gastric electrical activity (GEA), to establish its propagation model and peristalsis model in three-dimension, and then, to simulate it in dynamic three-dimension.
Based on the description of GEA and GEMA about its generation, characteristics and functions, this paper analyzes and simulates ion-mechanism model, summarizes the characteristics and laws of different cells at first. Secondly, it studies the propagation models about the GEA. Finally it models the electro-mechanical relationship and its propagation, and then succeeds in three-dimensional dynamic simulation. The thesis paid more attention to the model-building of three-dimensional stomach which is approximated to its true shape, and of GEMA, as well their simulations by Matlab.
This paper analyzes the traditional ion-mechanism models which are H-H and FHN models by Matlab. We use the images to show the laws of electrical activity about the different type cells. It makes a better understand of the difference between pacemaker cells and smooth muscle cells as well as their roles. It also proves that these models are reasonable.
This paper studies the cone and column propagation model of GEA, and analyzes the laws of it, models and simulates the propagation of slow-wave by model-building methods and principles using Matlab. The results reveal its propagation law and confirm the reliability of conduction models.
It is the first to realize the modeling and simulating the three-dimensional complex stomach that is close to its true shape using Matlab. In order to approximate to the true shape, this paper uses a number of deformed cones (or columns) to combine for simulating the static stomach, it gets a static three-dimensional model of the stomach. It describes the modeling methods and principles in detail, gives the corresponding program and simulative results.
Based on its laws, it is the first to establish a model of the quantitative relationship of GEA and peristaltic contraction, and a three-dimensional dynamic model of its propagation. It is the first to achieve three-dimensional dynamic simulation successfully using Matlab. According to the actual gastric physiology and the established model , it establishes quantitative relationship model between GEA and peristalsis, and further establishes a propagation model of GEMA by conduction laws.Finally,it simulates the propagation of GEA for the resting gastric and of GEMA for peristalsis gastric separately in dynamic three-dimension.It gives the corresponding simulated results.By modeling and simulating, it vividly demonstrates the spreading process of GEA and gastric peristalsis contraction, and provides some simulative methods and cognitive means for GEMA.
In a word, our study has not only enhanced understands to electrophysiology and gastric motility, but also vividly showed the spread of GEA and mechanical activity as well as the relationship of them. In particular, it has provided new study and cognize approach for precise quantitative relationship between GEA and gastric motility, which can have it play a greater role in diagnosis and studies for gastric diseases.
引文
[1].FuadHassan,EmanAl-Enizi,AbdelhamidH.Elgazzar.DigestiveSystem1:GastrointestinalTract.Chapter16.pp395-416
[2]、A.Aki和H.H.Sun.Time-frequency methods for detecting spike activity of stomach. Medical & Biological Engineering & Computing 1999.Vol. 37.
[3]、高秀来,于恩华.人体解剖学。北京:北京大学医学出版社,2003.2,91-92.
[4]、周吕.柯美云等《胃肠动力学》中《胃运动的功能》.北京科学出版社。1999 .04.
[5]、Kenneth L.Koch, MD. Diabetic Gastropathy Gastric Neuromuscular Dysfunction in Diabetes Dysfunction in Diabetes Mellitus A Review of Symptoms, Pathophysiology, andTreatment.Digestive Diseases and Sciences.Vol.44.No.6 (June 1999).
[6]、Mintchev等的stomach网站。http://www2.enel.ucalgary.ca/mintchev/stomach.htm
[7]、M.L.Buist ,L.K.Cheng ,K.M.Sanders ,A.J.Pullan. Multiscale modelling of human gastric electric activity:can the electrogastrogram detect functionalelectrical uncoupling? .Exp Physiol 91.2 pp 383–390
[8]、Huizinga JD,Thuneberg L,,Kluppel M,Malysz J,…W/kit gene required for interstitial cell of Cajal and for interstinal pacemaker activity.Nature 1995;373:347-349
[9]、Lee JC, Thuneberg L,Berezin I, Huizinga JD.Generation property of interstitial cells of Cajal.Am J Physiol1999;277;G409-G423
[10]、张扬,韩燕飞,许文燮,胃肠道平滑肌起搏电流产生机制的研究进展。世界华人消化杂志。2007年9月28日第15卷第27期。
[11]、龚严冰,高上凯.北京生物医学工程2001年9月第20卷第3期.
[12]、Yamazawa T,Iino M.Simultaneous imaging of Ca2+ signals in interstitial cells of Cajal and longitudinal smooth muscle cells during rhythmic activity in mouse ileum.J Physiol,2000,525:355.
[13]、Sanders KM. A case for interstitial cells of cajal as pacemaker and mediators of neurotransmission in the gastrointestinal tract . Gastroenterol , 1996 , 111 : 49
[14]、史洪涛.Cajal间质细胞的功能与基础.重庆医学2007.8.第36卷第5期
[15]、Hinder RA,Kelly KA.Human gastric pacemaker potential :Site of origin,spread,and response to gastric transaction and proximal gstric vagotomy .Am J Surg,1977 ,133:29_33
[16]、王伟.白萝卜粗提物作用于Cajal间质细胞.第四军医大学硕士学位论文.2008.5
[17]、Hinder RA,Kelly KA.Human gastric pacemaker potential :Site of origin,spread,and response to gastric transaction and proximal gstric vagotomy .Am J Surg,1977 ,133:29_33
[18]、张开光.胃电图及其在胃动力研究中的应用.国外医学消化系统疾病分册.1995.第15卷第2期
[19]、安鹏.胃电图在消化道疾病中的应用.云南医药2007年第28卷第5期
[20]、刘理,任惠茹.胃电图的记录、分析及其应用.生物医学工程学杂志.2003;20(3)
[21]、Kim TY, Han W T, Kim W K. Cont ract ion2related f requency , harmonics in human elect rogast rography . 18th A nnual International Conference of IEEE Engineering inM edicine and Biology Society. Am sterdam. 1996∶1917-1918
[22]、Patterson M,Rintala R,L loyd D,et al.Validation of elect rode placement in neonatal elect rogast rography.Digestive Diseases and Sciences, 2001;46(10)∶2245
[23]、Akin A and Sun H H. Time2 frequency methods for detecting spike activity of stomach. Med Biol Eng Comput , 1999 , 37 : 381
[24]、Chen JDZ , Lin ZY and McCallum RW. Noninvasive feature-based detection of delayed gastric emptying in humans using neural networks.IEEE Transactions on Biomedical Engineering , 2000 , 47 : 409。
[25]、Wang Zhishun , He Zhenya and Chen Jiande Z. Blind EGG separation using ICA neural networks. 19th Annual International Conference of the IEEE Engineering in Medicine and Biology Society , 1997 : 1351.
[26]、(美) Gerald Recktenwald著数值方法和MATLAB实现与应用。伍万国,万群等译,北京机械工业出版社.2004.
[27]、Hodgkin AL, Huxley AF. A quantitative discription of membrane current and its application to conduction and excitation in nerve. J Physiol(Lond),1952;117∶500.
[28]、FitzHugh R. .Impulses and Physiological states in theoretical models of nerve membrane·. BioPhys.J.1961(l):445一465. impulses and physiological states in theoretical models of nerve membrane.
[29]、Nagumo J S. , Arimoto S , Yoshizawa S.An active pulse transmission line simulating nerveaxon.Proe.IRE.1962(50):2061一2071.
[30]、Shuji Yoshizawa, Hiroyasu Osada, and Jin-ichi Nagumo.Pulse Sequences Generated by a Degenerate Analog Neuron Model.Biol. Cybern. 45, 23-33 (1982).
[31]、杨万利,王铁宁编著非线性动力学理论方法及应用.国防出版社。2007
[32]、原著Morris W.Hirsch,Stephen Smale,Rrt L.Devaney。甘少波译。微分方程、动力系统与混沌导论【第2版】人民邮电出版社2008
[33]、求是科技编著,MATLAB7.0从入门到精通,人民邮电出版社,2006.
[34]、D. Valenti , G. Augello, and B. Spagnolo.Dynamics of a FitzHugh-Nagumo system subjected to autocorrelated noise. Eur. Phys. J. B , 443–451 (2008).
[35]、Babajide O. Familoni, Thomas L.Abell .Driving GastricElectrical Activity with Electrical Stimulation. Annals ofBiomedical Engineering, Vol. 33, No. 3, March2005 ((C) 2005) pp. 356–364.
[36]、M.L.Buist ,L.K.Cheng ,K.M.Sanders andA.J.Pullan。Multiscale modelling of human gastric electric activity:can the electrogastrogram detect functional electrical uncoupling? Exp Physiol 91.2 pp 383–390. [ 37]. M L Buist , L K Cheng , R Yassi ,L A Bradshaw , W O Richards.An anatomical model of the gastric system for producing bioelectric and biomagnetic fields . Physiol. Meas. 25(2004)849–861.
[38]. William Richard Ievand and John P.Wikswo.A Simple Nonlinear Model of Electrical Activity in the Intestine。J. theor. Biol. (2000) 204.
[39]、Andrew Pullan, Leo Cheng, Rita Yassi, Martin Buist. Modelling gastrointestinal bioelectric activity. Progress in Biophysics & Molecular Biology 85 (2004) 523–550.
[40]、Babajide O. Familoni, Thomas L.Abell .Driving GastricElectrical Activity with Electrical Stimulation. Annals Of Biomedical Engineering, Vol. 33, No. 3, March2005 ((C) 2005) pp. 356–364.
[41]、Z.S. Wang and JDZ Chen. Mathematical Modeling of Nonlinear Coupling Mechanisms of Gastric Slow Wave Propagation and Its SIMULINK Simulation .for Investigating Gastric Dysrhythmia and Pacing. 2000 IEEE.
[42]、Mintchev等MODELING OF GASTRIC ELECTRICAL ACTIVITY.
[43]. M. P. Mintchev, K.L. Bowes. Conoidal dipole model of electrical field produced by the human stomach. Medical & Biological Engineering & Computing March 1995.
[44]. M. P. Mintchev , K.L. Bowes. Conoidal dipole model of electrical field produced by the human stomach. Medical & Biological Engineering & Computing March 1995
[45] MARTIN MINTCHEV and KENNETH BOWES. Computer Model of Gastric Electrical Stimulation. Annals of Biomedical Engineering, Vol. 25, pp. 726-730, 1997
[46] N.Mirizzi ,R.Srella.Amodel of extracellular waveshape of the gastric electrical activity .Medical & Biological Engineering & Computing January 1985.
[47]. Babajide 0. Familoni, Thomas L. Abell, and Kenneth L. Bowes . A Model of Gastric Electrical Activity in Health and Disease . IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 42, NO. 7, JULY.
[48]、JIE LIANG, MS and J.D.Z. CHEN, PhD. What Can Be Measured from Surface Electrogastrography Computer Simulations. Digestive Diseases and Sciences, Vol. 42, No. 7 (July 1997), pp. 1331-1343.
[49]、A.J.P.M. SMOUT, MD, E.J. VAN DER SCHEE, MSc, and J.L. GRASHUIS, PhD. What Is Measured in Electrogastrography? Digestive Diseases and Sciences, Vol. 25, No. 3 (March 1980).
[50]、张凯,姜熙君,陈磊。体表胃电图慢波提取方法的比较研究。北京生物医学工程。2006.4.
[51]、姜熙君。体表胃电图的检测、处理及胃电慢波传导的研究。硕士毕业论文。扬州大学,2007.6.
[2]、A.Aki和H.H.Sun.Time-frequency methods for detecting spike activity of stomach. Medical & Biological Engineering & Computing 1999.Vol. 37.
[3]、高秀来,于恩华.人体解剖学。北京:北京大学医学出版社,2003.2,91-92.
[4]、周吕.柯美云等《胃肠动力学》中《胃运动的功能》.北京科学出版社。1999 .04.
[5]、Kenneth L.Koch, MD. Diabetic Gastropathy Gastric Neuromuscular Dysfunction in Diabetes Dysfunction in Diabetes Mellitus A Review of Symptoms, Pathophysiology, andTreatment.Digestive Diseases and Sciences.Vol.44.No.6 (June 1999).
[6]、Mintchev等的stomach网站。http://www2.enel.ucalgary.ca/mintchev/stomach.htm
[7]、M.L.Buist ,L.K.Cheng ,K.M.Sanders ,A.J.Pullan. Multiscale modelling of human gastric electric activity:can the electrogastrogram detect functionalelectrical uncoupling? .Exp Physiol 91.2 pp 383–390
[8]、Huizinga JD,Thuneberg L,,Kluppel M,Malysz J,…W/kit gene required for interstitial cell of Cajal and for interstinal pacemaker activity.Nature 1995;373:347-349
[9]、Lee JC, Thuneberg L,Berezin I, Huizinga JD.Generation property of interstitial cells of Cajal.Am J Physiol1999;277;G409-G423
[10]、张扬,韩燕飞,许文燮,胃肠道平滑肌起搏电流产生机制的研究进展。世界华人消化杂志。2007年9月28日第15卷第27期。
[11]、龚严冰,高上凯.北京生物医学工程2001年9月第20卷第3期.
[12]、Yamazawa T,Iino M.Simultaneous imaging of Ca2+ signals in interstitial cells of Cajal and longitudinal smooth muscle cells during rhythmic activity in mouse ileum.J Physiol,2000,525:355.
[13]、Sanders KM. A case for interstitial cells of cajal as pacemaker and mediators of neurotransmission in the gastrointestinal tract . Gastroenterol , 1996 , 111 : 49
[14]、史洪涛.Cajal间质细胞的功能与基础.重庆医学2007.8.第36卷第5期
[15]、Hinder RA,Kelly KA.Human gastric pacemaker potential :Site of origin,spread,and response to gastric transaction and proximal gstric vagotomy .Am J Surg,1977 ,133:29_33
[16]、王伟.白萝卜粗提物作用于Cajal间质细胞.第四军医大学硕士学位论文.2008.5
[17]、Hinder RA,Kelly KA.Human gastric pacemaker potential :Site of origin,spread,and response to gastric transaction and proximal gstric vagotomy .Am J Surg,1977 ,133:29_33
[18]、张开光.胃电图及其在胃动力研究中的应用.国外医学消化系统疾病分册.1995.第15卷第2期
[19]、安鹏.胃电图在消化道疾病中的应用.云南医药2007年第28卷第5期
[20]、刘理,任惠茹.胃电图的记录、分析及其应用.生物医学工程学杂志.2003;20(3)
[21]、Kim TY, Han W T, Kim W K. Cont ract ion2related f requency , harmonics in human elect rogast rography . 18th A nnual International Conference of IEEE Engineering inM edicine and Biology Society. Am sterdam. 1996∶1917-1918
[22]、Patterson M,Rintala R,L loyd D,et al.Validation of elect rode placement in neonatal elect rogast rography.Digestive Diseases and Sciences, 2001;46(10)∶2245
[23]、Akin A and Sun H H. Time2 frequency methods for detecting spike activity of stomach. Med Biol Eng Comput , 1999 , 37 : 381
[24]、Chen JDZ , Lin ZY and McCallum RW. Noninvasive feature-based detection of delayed gastric emptying in humans using neural networks.IEEE Transactions on Biomedical Engineering , 2000 , 47 : 409。
[25]、Wang Zhishun , He Zhenya and Chen Jiande Z. Blind EGG separation using ICA neural networks. 19th Annual International Conference of the IEEE Engineering in Medicine and Biology Society , 1997 : 1351.
[26]、(美) Gerald Recktenwald著数值方法和MATLAB实现与应用。伍万国,万群等译,北京机械工业出版社.2004.
[27]、Hodgkin AL, Huxley AF. A quantitative discription of membrane current and its application to conduction and excitation in nerve. J Physiol(Lond),1952;117∶500.
[28]、FitzHugh R. .Impulses and Physiological states in theoretical models of nerve membrane·. BioPhys.J.1961(l):445一465. impulses and physiological states in theoretical models of nerve membrane.
[29]、Nagumo J S. , Arimoto S , Yoshizawa S.An active pulse transmission line simulating nerveaxon.Proe.IRE.1962(50):2061一2071.
[30]、Shuji Yoshizawa, Hiroyasu Osada, and Jin-ichi Nagumo.Pulse Sequences Generated by a Degenerate Analog Neuron Model.Biol. Cybern. 45, 23-33 (1982).
[31]、杨万利,王铁宁编著非线性动力学理论方法及应用.国防出版社。2007
[32]、原著Morris W.Hirsch,Stephen Smale,Rrt L.Devaney。甘少波译。微分方程、动力系统与混沌导论【第2版】人民邮电出版社2008
[33]、求是科技编著,MATLAB7.0从入门到精通,人民邮电出版社,2006.
[34]、D. Valenti , G. Augello, and B. Spagnolo.Dynamics of a FitzHugh-Nagumo system subjected to autocorrelated noise. Eur. Phys. J. B , 443–451 (2008).
[35]、Babajide O. Familoni, Thomas L.Abell .Driving GastricElectrical Activity with Electrical Stimulation. Annals ofBiomedical Engineering, Vol. 33, No. 3, March2005 ((C) 2005) pp. 356–364.
[36]、M.L.Buist ,L.K.Cheng ,K.M.Sanders andA.J.Pullan。Multiscale modelling of human gastric electric activity:can the electrogastrogram detect functional electrical uncoupling? Exp Physiol 91.2 pp 383–390. [ 37]. M L Buist , L K Cheng , R Yassi ,L A Bradshaw , W O Richards.An anatomical model of the gastric system for producing bioelectric and biomagnetic fields . Physiol. Meas. 25(2004)849–861.
[38]. William Richard Ievand and John P.Wikswo.A Simple Nonlinear Model of Electrical Activity in the Intestine。J. theor. Biol. (2000) 204.
[39]、Andrew Pullan, Leo Cheng, Rita Yassi, Martin Buist. Modelling gastrointestinal bioelectric activity. Progress in Biophysics & Molecular Biology 85 (2004) 523–550.
[40]、Babajide O. Familoni, Thomas L.Abell .Driving GastricElectrical Activity with Electrical Stimulation. Annals Of Biomedical Engineering, Vol. 33, No. 3, March2005 ((C) 2005) pp. 356–364.
[41]、Z.S. Wang and JDZ Chen. Mathematical Modeling of Nonlinear Coupling Mechanisms of Gastric Slow Wave Propagation and Its SIMULINK Simulation .for Investigating Gastric Dysrhythmia and Pacing. 2000 IEEE.
[42]、Mintchev等MODELING OF GASTRIC ELECTRICAL ACTIVITY.
[43]. M. P. Mintchev, K.L. Bowes. Conoidal dipole model of electrical field produced by the human stomach. Medical & Biological Engineering & Computing March 1995.
[44]. M. P. Mintchev , K.L. Bowes. Conoidal dipole model of electrical field produced by the human stomach. Medical & Biological Engineering & Computing March 1995
[45] MARTIN MINTCHEV and KENNETH BOWES. Computer Model of Gastric Electrical Stimulation. Annals of Biomedical Engineering, Vol. 25, pp. 726-730, 1997
[46] N.Mirizzi ,R.Srella.Amodel of extracellular waveshape of the gastric electrical activity .Medical & Biological Engineering & Computing January 1985.
[47]. Babajide 0. Familoni, Thomas L. Abell, and Kenneth L. Bowes . A Model of Gastric Electrical Activity in Health and Disease . IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 42, NO. 7, JULY.
[48]、JIE LIANG, MS and J.D.Z. CHEN, PhD. What Can Be Measured from Surface Electrogastrography Computer Simulations. Digestive Diseases and Sciences, Vol. 42, No. 7 (July 1997), pp. 1331-1343.
[49]、A.J.P.M. SMOUT, MD, E.J. VAN DER SCHEE, MSc, and J.L. GRASHUIS, PhD. What Is Measured in Electrogastrography? Digestive Diseases and Sciences, Vol. 25, No. 3 (March 1980).
[50]、张凯,姜熙君,陈磊。体表胃电图慢波提取方法的比较研究。北京生物医学工程。2006.4.
[51]、姜熙君。体表胃电图的检测、处理及胃电慢波传导的研究。硕士毕业论文。扬州大学,2007.6.