乙型肝炎免疫模型与仿真
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摘要
乙型肝炎病毒(HBV)感染诱发的乙型肝炎是一种世界性的疾病,世界1/3的人口曾经感染乙肝病毒,约有3.5亿人为HBV携带者,其中25%的人会发展成肝硬化甚至肝癌。中国是世界上乙肝患者最多的国家,为预防和治疗HBV感染,国家采取了众多措施,每年投入的经费高达数百亿人民币,如何预防和治疗乙肝一直是社会关注的焦点和重要的医学课题。
动物试验和分子生物学手段适于研究单一过程或单独的细胞,对于研究病毒的致病机理具有极其重要的作用,但对于分析有许多因素相互作用而无法分割的复杂系统如免疫系统则存在很大局限性。而数学方法可以突破实验手段的局限,综合已有的知识,根据可能的机理,依据不同的假设建立数学模型,通过检验仿真结果与实验和临床数据的符合程度来选择最适合的模型和参数用于解释医学现象、指导下一步医学实验或辅助治疗方案的确定。
目前感染医学中应用最为广泛的是Nowak建立的描述HIV在感染人体后艾滋病慢性发作过程的数学模型,该模型还用于评估药物抑制病毒感染的疗效。但由于HBV感染有急性、慢性等多种后果,Nowak模型还无法仿真,不能应用于HBV感染过程。
本文依据从简单到复杂的原则,先抓住最本质的因素构建最简单的模型,在简单模型能够表达HBV感染的多种后果,定性分析结果符合临床结论的基础上,逐步考虑更多的因素,构建复杂的模型反映更多的信息,并且保证复杂模型的分析结论可以概括简单模型的分析结论。复杂模型仿真时尽量利用简单模型仿真中使用的参数以减少搜寻参数的工作量。在缺乏临床数据检验仿真结果准确性的条件限制下,以被验证的简单模型的仿真结果为标准来判断复杂模型仿真结果的正确性,努力使各个模型的仿真结果一致。
本文首先基于Nowak模型,建立了HBV感染的细胞免疫模型,使用Nowak估计参数对初始模型进行仿真的结果表明模型可以反映人体被HBV感染的各种可能后果。鉴于模型的定性分析结果复杂,无法提供有价值的信息,对模型进行了改进,使模型的定性分析结果简洁明了,并与医学结论相符。根据近年来发现的细胞免疫的非杀伤效应机理,对模型进行了相应修正,定性分析结果可以包括前面的分析结论。
因为使用临床数据对模型进行仿真时发现肝细胞总是全部死亡,分析原因后重新设置了肝细胞增殖函数,同时将肝细胞受损程度与临床检验指标丙氨酸转氨酶(ALT)联系起来建立方程,形成了新的模型。应用该模型解释了慢性乙肝患者再感染甲肝后肝炎彻底消除,但同时易于发生暴发性肝炎的临床现象。模型定性分析的结果与前面的结果一致,模型可以仿真出人体被HBV感染后可能出现的各种后果,且仿真结果的潜伏期、转氨酶水平以及HBV DNA浓度均在临床范围内。
在前面模型的基础上构建了包含细胞免疫和体液免疫功能的HBV感染免疫模型。模型的定性分析结果可以涵盖前面的结论,并且可以体现体液免疫在抗感染中的作用。应用前面模型的仿真参数并添加新参数后的仿真结果可以表达人体被HBV感染的各种可能后果,并且仿真图形与世界卫生组织发布的HBV感染趋势图一致。
鉴于抗原提呈细胞在HBV感染免疫中的重要作用,在前面模型的基础上构建了包括抗原提呈细胞(APC)、辅助T细胞(Th1,Th2)、细胞毒性T细胞(CTL)和抗体分泌细胞(B细胞)以及抗体(Ab)等变量的HBV感染免疫模型。模型的定性分析结果与前面完全一致。仿真结果表明模型可以表现人体被HBV感染的各种可能后果。选择一种位于最严重后果和彻底痊愈之间的中间状态——急性转慢性感染过程的模型,且其方程的主要动力学参数变动10倍或为原来1/10时可遍历各种感染后果,通过研究表现不同后果的参数情况来分析各种因素对感染后果的影响。通过假设药物能将对免疫反应有利的参数扩大为原来2倍,对病毒有利的参数缩小为原来1/2,确定各种感染状态下最有效的治疗措施。仿真结果发现状态不同,治疗目标不同,最有效的措施也不相同。但一般而言降低病毒感染率和抑制病毒复制都是最有效的措施。
More than a third of the world’s population has been infected with hepatitis B virus (HBV) and it is estimated conservatively that there are 350 million persistent carriers of HBV worldwide, 25% of whom have chronic liver disease and cirrhosis, which could progress to hepatocellular carcinoma. Chinese government expends about ten billions of yuan per annum and takes many measures to prevent and treat HB as China has the highest number of sufferers. The prevention and treatment of this infection is the present focus of the society and is the most important task in the medical fields.
Animal tests and new techniques in molecular biology have been crucial in deepening our understanding of the pathogenetic mechanisms. Most of these new techniques have allowed the isolation of the process or cell under study so that the results can be readily interpretable. At the present time, however, there is an emerging need to understand the system in a whole, e.g. the immune system. Mathematical models can serve several distinct purposes. They can be used to analyze experimental results, to synthesize existing knowledge and provide a theoretical framework for the interpretation of existing paradigms so as to provide predictions and suggestions for follow-up experiments and treatment.
The most common mathematical model in infection is presented by Nowak to explain the dynamics of host immune response to HIV and the pathogenesis of Aids. It is widely used to evaluate the antiviral effectiveness of drug treatment for HIV. The model is even used in the assessment of the efficiency of antiviral therapy for HBV and HCV. But it fails to explain the various outcomes of HBV infection.
According to the principle of from simplicity to complexity, a simple model is established on the essential factors. When the model is proved to be able to simulate the various outcomes of HBV infection and the qualitative analysis results is in accordance with the clinical conclusion, more details are taken into account and more complex model is built the simpler model. The qualitative analysis results of the complex model should generalize the conclusion from the simple one. The values of the parameters in the simple model are used to reduce the workload of searching parameters for the complex model and the simulation results of the simple model is used as a criterion for judging the results of the complex one because of the absence of clinical data.
Aimed at the shortcomings of Nowak’s model, a modified cellular model is proposed. Using parameters evaluated by Nowak, the simulation results show that the new model can account for the wide variety of clinical manifestations of HBV infection. As the qualitative analysis result of this model is too complex to provide any useful information, the model is modified and the qualitative analysis result is simple and is in good agreement with the clinical results. As noncytolytic effects of CTL is found and proved to be more important than cytolytic effects in the clearance of infected cells, the model is rebuilt on this discovery and the qualitative analysis result is in accordance with the former result.
The validation result of using clinical data demonstrates that the hepatocytes always die out. After analyzing the causation, hepatocyte proliferation function is regulated, and the equation is found considering the correlation between the functional defect of hepatocyte and clinical laboratory standard. A new model is constructed based on these. The model agrees with the clinical phenomenon that CHB infected with HAV hepatitis will always be completely cured, but the co-infection is easy to course fulminate hepatitis. The model simulates various results that appeared after HBV infection, and the delitescence, the aminotransferase and the HBV DNA concentration are all in the clinical range.
On the basis of the former model, a new model of B-T cell co-operation including cellular immunity and humoral immunity is constructed. The results of qualitative analysis is in accordance with the conclusion above, and demonstrate the effect of humoral immunity in anti-infectious. The model using the former parameters and some new parameters could simulate various possible results after HBV infection. The simulated graphic is consistent with the trend graph promulgated by WHO.
As APC plays a critical role in the immune reaction, a model considering APC, Helping T cells (Th1 and Th2), CTL, B cell and Ab is built based on the former model. The qualitative analysis result is the same as the former. The simulation results show that it can account for the wide variety of clinical manifestations.
The parameters of a model that can simulate the outcome between the most serious one and recovery are enlarged to ten folds or zoom in 1/10 to show all the outcomes of HBV infection, and to analyze the influence of parameters on outcomes. The parameters favoring the immune system ate doubled and those favoring HBV are reduced to 1/2, so as it find out the most effective measures. The simulation results show that the most efficient measures change with different goals under different states. Treatment by blocking the denovo rate of infection or by reducing the production of visions is always the most efficient measure.
动物试验和分子生物学手段适于研究单一过程或单独的细胞,对于研究病毒的致病机理具有极其重要的作用,但对于分析有许多因素相互作用而无法分割的复杂系统如免疫系统则存在很大局限性。而数学方法可以突破实验手段的局限,综合已有的知识,根据可能的机理,依据不同的假设建立数学模型,通过检验仿真结果与实验和临床数据的符合程度来选择最适合的模型和参数用于解释医学现象、指导下一步医学实验或辅助治疗方案的确定。
目前感染医学中应用最为广泛的是Nowak建立的描述HIV在感染人体后艾滋病慢性发作过程的数学模型,该模型还用于评估药物抑制病毒感染的疗效。但由于HBV感染有急性、慢性等多种后果,Nowak模型还无法仿真,不能应用于HBV感染过程。
本文依据从简单到复杂的原则,先抓住最本质的因素构建最简单的模型,在简单模型能够表达HBV感染的多种后果,定性分析结果符合临床结论的基础上,逐步考虑更多的因素,构建复杂的模型反映更多的信息,并且保证复杂模型的分析结论可以概括简单模型的分析结论。复杂模型仿真时尽量利用简单模型仿真中使用的参数以减少搜寻参数的工作量。在缺乏临床数据检验仿真结果准确性的条件限制下,以被验证的简单模型的仿真结果为标准来判断复杂模型仿真结果的正确性,努力使各个模型的仿真结果一致。
本文首先基于Nowak模型,建立了HBV感染的细胞免疫模型,使用Nowak估计参数对初始模型进行仿真的结果表明模型可以反映人体被HBV感染的各种可能后果。鉴于模型的定性分析结果复杂,无法提供有价值的信息,对模型进行了改进,使模型的定性分析结果简洁明了,并与医学结论相符。根据近年来发现的细胞免疫的非杀伤效应机理,对模型进行了相应修正,定性分析结果可以包括前面的分析结论。
因为使用临床数据对模型进行仿真时发现肝细胞总是全部死亡,分析原因后重新设置了肝细胞增殖函数,同时将肝细胞受损程度与临床检验指标丙氨酸转氨酶(ALT)联系起来建立方程,形成了新的模型。应用该模型解释了慢性乙肝患者再感染甲肝后肝炎彻底消除,但同时易于发生暴发性肝炎的临床现象。模型定性分析的结果与前面的结果一致,模型可以仿真出人体被HBV感染后可能出现的各种后果,且仿真结果的潜伏期、转氨酶水平以及HBV DNA浓度均在临床范围内。
在前面模型的基础上构建了包含细胞免疫和体液免疫功能的HBV感染免疫模型。模型的定性分析结果可以涵盖前面的结论,并且可以体现体液免疫在抗感染中的作用。应用前面模型的仿真参数并添加新参数后的仿真结果可以表达人体被HBV感染的各种可能后果,并且仿真图形与世界卫生组织发布的HBV感染趋势图一致。
鉴于抗原提呈细胞在HBV感染免疫中的重要作用,在前面模型的基础上构建了包括抗原提呈细胞(APC)、辅助T细胞(Th1,Th2)、细胞毒性T细胞(CTL)和抗体分泌细胞(B细胞)以及抗体(Ab)等变量的HBV感染免疫模型。模型的定性分析结果与前面完全一致。仿真结果表明模型可以表现人体被HBV感染的各种可能后果。选择一种位于最严重后果和彻底痊愈之间的中间状态——急性转慢性感染过程的模型,且其方程的主要动力学参数变动10倍或为原来1/10时可遍历各种感染后果,通过研究表现不同后果的参数情况来分析各种因素对感染后果的影响。通过假设药物能将对免疫反应有利的参数扩大为原来2倍,对病毒有利的参数缩小为原来1/2,确定各种感染状态下最有效的治疗措施。仿真结果发现状态不同,治疗目标不同,最有效的措施也不相同。但一般而言降低病毒感染率和抑制病毒复制都是最有效的措施。
More than a third of the world’s population has been infected with hepatitis B virus (HBV) and it is estimated conservatively that there are 350 million persistent carriers of HBV worldwide, 25% of whom have chronic liver disease and cirrhosis, which could progress to hepatocellular carcinoma. Chinese government expends about ten billions of yuan per annum and takes many measures to prevent and treat HB as China has the highest number of sufferers. The prevention and treatment of this infection is the present focus of the society and is the most important task in the medical fields.
Animal tests and new techniques in molecular biology have been crucial in deepening our understanding of the pathogenetic mechanisms. Most of these new techniques have allowed the isolation of the process or cell under study so that the results can be readily interpretable. At the present time, however, there is an emerging need to understand the system in a whole, e.g. the immune system. Mathematical models can serve several distinct purposes. They can be used to analyze experimental results, to synthesize existing knowledge and provide a theoretical framework for the interpretation of existing paradigms so as to provide predictions and suggestions for follow-up experiments and treatment.
The most common mathematical model in infection is presented by Nowak to explain the dynamics of host immune response to HIV and the pathogenesis of Aids. It is widely used to evaluate the antiviral effectiveness of drug treatment for HIV. The model is even used in the assessment of the efficiency of antiviral therapy for HBV and HCV. But it fails to explain the various outcomes of HBV infection.
According to the principle of from simplicity to complexity, a simple model is established on the essential factors. When the model is proved to be able to simulate the various outcomes of HBV infection and the qualitative analysis results is in accordance with the clinical conclusion, more details are taken into account and more complex model is built the simpler model. The qualitative analysis results of the complex model should generalize the conclusion from the simple one. The values of the parameters in the simple model are used to reduce the workload of searching parameters for the complex model and the simulation results of the simple model is used as a criterion for judging the results of the complex one because of the absence of clinical data.
Aimed at the shortcomings of Nowak’s model, a modified cellular model is proposed. Using parameters evaluated by Nowak, the simulation results show that the new model can account for the wide variety of clinical manifestations of HBV infection. As the qualitative analysis result of this model is too complex to provide any useful information, the model is modified and the qualitative analysis result is simple and is in good agreement with the clinical results. As noncytolytic effects of CTL is found and proved to be more important than cytolytic effects in the clearance of infected cells, the model is rebuilt on this discovery and the qualitative analysis result is in accordance with the former result.
The validation result of using clinical data demonstrates that the hepatocytes always die out. After analyzing the causation, hepatocyte proliferation function is regulated, and the equation is found considering the correlation between the functional defect of hepatocyte and clinical laboratory standard. A new model is constructed based on these. The model agrees with the clinical phenomenon that CHB infected with HAV hepatitis will always be completely cured, but the co-infection is easy to course fulminate hepatitis. The model simulates various results that appeared after HBV infection, and the delitescence, the aminotransferase and the HBV DNA concentration are all in the clinical range.
On the basis of the former model, a new model of B-T cell co-operation including cellular immunity and humoral immunity is constructed. The results of qualitative analysis is in accordance with the conclusion above, and demonstrate the effect of humoral immunity in anti-infectious. The model using the former parameters and some new parameters could simulate various possible results after HBV infection. The simulated graphic is consistent with the trend graph promulgated by WHO.
As APC plays a critical role in the immune reaction, a model considering APC, Helping T cells (Th1 and Th2), CTL, B cell and Ab is built based on the former model. The qualitative analysis result is the same as the former. The simulation results show that it can account for the wide variety of clinical manifestations.
The parameters of a model that can simulate the outcome between the most serious one and recovery are enlarged to ten folds or zoom in 1/10 to show all the outcomes of HBV infection, and to analyze the influence of parameters on outcomes. The parameters favoring the immune system ate doubled and those favoring HBV are reduced to 1/2, so as it find out the most effective measures. The simulation results show that the most efficient measures change with different goals under different states. Treatment by blocking the denovo rate of infection or by reducing the production of visions is always the most efficient measure.
引文
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