Difference between revisions of "Team:CPU CHINA/Model"

 
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    <li style="margin-top:23px;list-style:none;">  </li>
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            <a href="#LGD"><li style="font-size:18px!important; z-index:10000000000;">Model of Liposome Gene Delivery</li></a>
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            <a href="#CEA" style="font-size:18px!important;"><li style="font-size:18px!important;z-index:10000000000;">Cost-effectiveness analysis model</a></li>   
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<center><h1 id="LGD">Model of Liposome Gene Delivery</center>
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<br>
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<br>
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<h3>Background
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<h4>Liposomes or plasmids may become lost and not able to reach the nucleus due to degradation in cells during transmission. This loss, among many, brings difficulties to the development and clinical application of gene drugs. Quantitative study of plasmid loss and transfection efficiency during lipofection is of great significance for the delivery of gene drugs. Therefore, we simulated the transfection and plasmid loss of a liposome gene delivery system in <i>silico</i>. In our model, we used queuing network and memoryless Markov process to describe the transmission of liposomes and plasmids.
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<br>
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<br>
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<h3>Model description
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<h4>There are ten states and nine transmission processes during the lipofection. The first step of liposome gene delivery is endocytosis, a process that liposomes in the surrounding are delivered to the cell in the form of endosomes (from ① to ②). The second step is endosomal escape. In this step, some of the liposomes in endosome could escape（from ② to ④） but some others are degraded by lysosome（from ② to ③）. What happens next is that the liposomes are tagged with a nuclear locus signal (NLS)（from ④ to ⑦） or ruptured to release the naked plasmid（from ④ to ⑤）. The naked plasmids in the cytoplasm then could also be added with a nuclear locus signal（from ⑤ to ⑧） or degraded（from ⑤ to ⑥）. Eventually, liposomes or naked plasmids with a nuclear locus signal are successfully delivered into the nucleus （from ⑦ to ⑨ and from ⑧ to ⑩）(Figure.1). These plasmids in the nucleus are then transcribed to do their job. Plasmids that degrade at any point during the whole process  are unavoidably lost.
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<center><image src=https://static.igem.org/mediawiki/2018/6/67/T--CPU_CHINA--hp-Figure.1_Primary_transmission_chain_between_cell_membrane_and_nucleus.png></center>
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<center><h5>Figure.1  Primary transmission chain between cell membrane and nucleus</h5></center>
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<br>
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<h4>In our model, we assumed that there were 90000 plasmids packed in 9000 liposomes and all the liposomes enter the cells in the form of endosome. Then we generate 9000 random numbers following exponential distribution to describe the internalization time.
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<h4>For those transmission step that have two probable routes(A and B), Figure.2 shows the algorithm of what happened in a millisecond. All of the steps that have two proper routes act like this, including endosome escape or degradation (from ② to ③ or ④), liposome adding NLS or degradation(from ④ to ⑤ or ⑦) and plasmid adding NLS or degradation (from ⑤ to ⑥ or ⑧).
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<center><image src=https://static.igem.org/mediawiki/2018/a/a8/T--CPU_CHINA--hp-Figure.2_Algorithm_of_transmission_that_have_two_probable_routes.png></center>
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<center><h5>Figure.2 Algorithm of transmission that have two probable routes</h5></center>
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<br>
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<h4>For those transmission step that only have one probable route, Figure.3 shows the algorithm of what happened in a millisecond. Liposomes or naked plasmids that successfully enter the nucleus （from ⑦ to ⑨ and from ⑧ to ⑩）act like this.
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<center><image src=https://static.igem.org/mediawiki/2018/4/40/T--CPU_CHINA--hp-Figure.3_Algorithm_of_transmission_that_have_one_probable_routes.png></center>
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<center><h5>Figure.3 Algorithm of transmission that have one probable routes</h5></center>
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<br>
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<h4>In summary, we generated 9000 exponentially distributed numbers to describe the moment of each liposome internalization and then took a millisecond as a time interval. During every millisecond, we checked the number of liposomes/plasmids in every queue and calculated the transfer probability according to our algorithm. We then generate random numbers subject to normal distribution and compared it with the transfer probability, then conclude where it should go. What happens in such a millisecond have been actually repeated for 64800000 times in 18 hours after liposomes are added to the cell.
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<br>
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<br>
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<h3>Significance
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<h4>It is reported that the saturation number of plasmids that can be delivered to one cancer cell is 90000. By conducting our Model of Liposome Gene Delivery, we find that an injection of 90000 plasmids can lead to 44270 of which (49.19%) been transported into the nucleus successfully, what’s more, this result is promising since it enables us to predict the minimum transfection amount to guarantee enough number of of plasmids in nucleus during our experiments. Furthermore, we are able to calculate the amount of the plasmids we need to administrate in order to obtain therapeutic efficiency which is very instructional for our further application in <i>vivo</i>.
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<br>
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<br>
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<h4>Click <a href="https://2018.igem.org/Team:CPU_CHINA/Model/LGD"><u>here</u></a> to get the parameter, formula, results and reference.
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<h4>Click <a href="https://static.igem.org/mediawiki/2018/6/65/T--CPU_CHINA--M2_code.txt"  download="Model2_Code.txt"><u>here</u></a> to get the code.
  
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<h5 style="font-family:new times Roman">Cost-Effectiveness Analysis</h5>
 
  
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<h4>Model part</h4>
 
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<h4>Q: How to determine if a new therapy is interesting for practical application?</h4>
 
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<h4>Q: Also, how to balance the pay and gain of the patients? How to set up a reasonable price for the patients?</h4>
 
  
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<br>
 
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<h2>Background</h2>
 
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<h4>According to the World Health Organization, primary liver cancer is globally the sixth most frequent cancer (6%) and the second leading cause of death from cancer (9%) <sup>[1]</sup>.</h4>
 
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<h4>  China has a particularly high incidence of liver cancer in its population. The number of new cases of liver cancer every year accounts for about half the total number worldwide. This disease takes the lives of about 110,000 people each year, which is also nearly 45% of the number worldwide. Especially in recent years, liver cancer has risen from the third place to the second place in the cause of cancer-related death in China <sup>[2]</sup>. </h4>
 
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<h4>  Hepatocellular carcinoma (HCC) has a huge impact on human health and remains a huge burden to people all over the world. Intense research has been and will be made against this disease, so the number of available medical treatments should be expected to continue growing. For researchers and investors, the current market and competition tend to be obscured by ever-new attractions and tendencies. In such case, mathematical modeling would come in handy as it helps to explain and to study the effects of different factors, and to make predictions about new products. Therefore, efforts have been made by us to set up a model that estimates the efficiency and cost of these medical treatments.</h4>
 
  
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<br>
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<br>
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<h4>Concepts:</h4>
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<br>
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<h4>1. Utility</h4>
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<center><h1 id="CEA">Cost-effectiveness analysis model</center>
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<h4>Within economics the concept of utility is used to model worth or value, but its usage has evolved significantly over time. In the field of health care, the utility value associates with a given state of health by the years lived in that state <sup>[3]</sup>. Preference-based utility can be influenced by a lot of factors such as the patient’s age, income, and education. Usually and as it is in our model, an assumption is made. The assumption is that the utility of death is 0 and the utility of total health is 1 so that utility is always between 0 and 1. However, it also occurs sometime that the value becomes below 0, which indicates something that’s even worse than death, such as lying in bed for a long time with unbearable pain.</h4>
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<h4>2. QALY</h4>
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<h3>Background
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<h4>When we consider both mortality and disability that some diseases can bring, there appears a new index called QALY (Quality Adjusted Life Years). QALY combines both the length and quality of life, which summaries the influences medical treatments have on patients. This index can be used to inform personal decisions, evaluate programs, and set priorities for future program.
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<h4>Hepatocellular carcinoma (HCC) has a huge impact on human health and remains a huge burden to people all over the world. Intense research has been and will be made against this disease, so the number of available medical treatments should be expected to continue growing. For researchers and investors, the current market and competition tend to be obscured by ever-new attractions and tendencies.
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To determine QALYs, one multiplies the utility that we mentioned above. For example, a year of life in perfect health is worth 1 QALY (1 year of life × 1 Utility value). A year of life in a state of less than perfect health is therefore worth less than 1 QALY. 1 year of life lived in a situation with utility 0.5 (e.g. bedridden, 1 year × 0.5 Utility) is assigned 0.5 QALYs. Similarly, half a year in perfect health is equivalent to 0.5 QALYs (0.5 years × 1 Utility). Death is assigned a value of 0, and in some circumstances, it is possible to accrue negative QALYs to reflect health states deemed "worse than dead."<sup>[3]</sup>
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<h4>In this cases, there are two main questions:
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</h4>
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<h4>1. How to determine if a new therapy is interesting for practical application?
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<h4>3. Cost-utility analysis (CUA) and incremental cost-effectiveness ratio (ICER)</h4>
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<h4>2. How to balance the pay and gain of the patients? How to set up a reasonable price for the patients?
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<h4>CUA (cost-utility analysis) is well-known in Pharmaco-Economics. It is a type of financial analysis used to guide procurement decisions. Cost is measured in monetary units while the benefits often are expressed in QALYs.</h4>
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<h4>To solve these problems, mathematical modeling would come in handy as it helps to explain and to study the effects of different factors, and to make predictions about new products. Therefore, efforts have been made by us to set up a model that estimates the efficiency and cost of these medical treatments.  
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<h4>The incremental cost-effectiveness ratio (ICER) is a statistic for summarizing the cost-effectiveness of a health care intervention. It is defined by the difference in cost between two possible interventions, divided by the difference in their effect [5]. It represents the average incremental cost associated with 1 additional unit of the measure of effect.</h4>
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<br>
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<br>
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<h3>Model description
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<h4>During the clinical trials, researchers can’t really follow and record the patients until they die. However, in this model, we can define several states of the patients in advance. After every month’s medical intervention and collection of the data, we can put patients into the corresponding states and calculate the transfer probabilities (Figure.1). By running the program that we have written based on this model, we can predict the survival curve of each medical treatment.  
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<div><h3><i>ICER =</i></h3></div>
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<center><image src=https://static.igem.org/mediawiki/2018/6/64/T--CPU_CHINA--hp-Figure.1_The_state_space_and_the_transfer_relationship_in_our_model.png></image></center>
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<div style="float:right;position:relative;left:-60%;top:-8em;">
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<h5><center>Figure.1 The state space and the transfer relationship in our model</center></h5>
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<div style="border-bottom:2px solid black;"><h3><i>C<sub>1</sub> and C<sub>0</sub></i></h3></div>
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<br>
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<div><h3><i>E<sub>1</sub> and E<sub>0</sub></i></h3></div>
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<h4>Then the utility can be estimated by doing some questionnaire survey and lab tests in specific disease contexts. As we mentioned before, with the life span and the utility, the quality-adjusted life years then can be calculated.  
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<h4>Since we can get the efficacy of different medical intervention in the model, the next step is to estimate a reasonable price (Figure.2). Companies can calculate the ICER of their products with their prospect price and compare it to other drugs of the same type contemporarily on the market.
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<center><image src=https://static.igem.org/mediawiki/2018/5/53/T--CPU_CHINA--hp-Figure2._Schematic_of_how_to_set_up_a_reasonable_price_for_the_patients_through_CUA.png></image></center>
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<h5><center>Figure2. Schematic of how to set up a reasonable price for the patients through CUA.</center></h5>
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<br>
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<br>
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<h3>Significance
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<h4><b>Based on clinical data, we can learn the efficacy of different drugs through our Cost-effectiveness analysis model, then further estimate a reasonable price (Figure.2). This model enables us to predict the price of our system when it comes to a drug in future which contributes to <a href="https://static.igem.org/mediawiki/2018/c/cb/T--CPU_CHINA--hp-shangyejihuashu.pdf">our business plan</a> and the realizable analyze of our project. Furthermore, we are proud to notice that not only our team but also the whole iGEM community and public can also benefit from this model. Since they can understand the efficacy as well as calculate the ICER of their products to know their prospect price, then compare it to other drugs of the same type contemporarily on the market to test products’ practicability. </b></h4>
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<br>
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<br>
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<h4>Click <a href="https://2018.igem.org/Team:CPU_CHINA/Model/CEA"><u>here</u></a> to get the parameter, formula result and reference.</h4>
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<h4>Click <a href="https://static.igem.org/mediawiki/2018/3/30/T--CPU_CHINA--Model1_Code.txt" download="Model1_Code1.txt"><u>here</u></a> to get the code.</h4>
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<h4><i>C<sub>1</sub> and E<sub>1</sub></i> are the cost and effect in the intervention group while <i>C<sub>0</sub> and E<sub>0</sub></i> are the cost and effect in the control group. Costs are usually described in monetary units, while effects can be measured in terms of health status or another outcome of interest. A common application of the ICER is in CUA, where the ICER gets synonymous with the cost per quality-adjusted life year (QALY) gained.</h4>
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<img src="https://static.igem.org/mediawiki/2018/b/b0/T--CPU_CHINA--M1_figure1.png">
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$(this).scroll(function(){
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<h6>Figure1. Clinical stages and treatment pipeline of liver cancer<sup>[6]</sup></h6>
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</center>
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<h4><b><i>PS (performance status): It is an attempt to quantify cancer patients' general well-being and activities of daily life. This measure is used to determine whether they can receive chemotherapy, whether dose adjustment is necessary, and as a measure for the required intensity of palliative care. It is also used in oncological randomized controlled trials as a measure of quality of life.</i></b></h4>
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<h4><b><i>TACE (Transarterial chemoembolization): It is a minimally invasive procedure performed in interventional radiology to restrict a tumor's blood supply. Small embolic particles coated with chemotherapeutic drugs are injected selectively through a catheter into an artery directly supplying the tumor. These particles both block the blood supply and induce cytotoxicity, attacking the tumor in several ways.</i></b></h4>
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<h4>Great efforts have been taken to cure liver cancer and different therapies in different stage are shown in Figure.1. We performed CUA of some of the therapies and set up a mathematical model to figure out which one costs less and benefits the patients more. This model is expected to be capable of stimulating a situation that helps us to determine if a new therapy is interesting enough to be introduced into the market, on both the medical level and the financial level.</h4>
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<h2>Assumption</h2>
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<h4>1. All patients can be divided into three stages: if the patient is dead, we call it the Death stage; if the tumor does not grow or the health state of the patients doesn’t deteriorate, we call it a Progression-Free Survival (PFS) stage; else it’s a Progression Disease (PD) stage.</h4>
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<h4>2. Patients cannot switch from Death stage to any other stage.</h4>
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<h2>Our Model</h2>
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<h4><b>Introduction</b></h4>
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<h4>A Markov chain is a stochastic process with the Markov property. The term "Markov chain" refers to the sequence of random variables such a process moves through, with the Markov property defining serial dependence only between adjacent periods (as in a "chain"). It can thus be used for describing systems that follow a chain of linked events, where what happens next depends only on the current state of the system <sup>[7,8]</sup>.</h4>
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<h4><b>The construction of the model</b></h4>
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<h4>Here we discuss a discrete-time Markov chain. When an actual problem is being described by a Markov chain, the first thing to determine is its state space and parameter set, and then its one-step transition probability. Since we assume that the patients have only three statuses, the state space would be <i>E</i>={0,1,2} (0 is PFS, 1 is PD, 2 is death) and patients are distributed into the three states. Every month the state of the patients (&epsilon;<sub>n</sub>) changes and we can record these information in the form of a month sequence {&epsilon;<sub>n</sub>,n=1,2,...} <i>&epsilon;<sub>n</sub>=j,j&isin;E</i></h4>
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<center>
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<img src="https://static.igem.org/mediawiki/2018/e/ee/T--CPU_CHINA--M1_figure2.png">
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<h6>Figure.2 The state space and the transfer relationship in our model</h6>
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</center>
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<br>
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<h4>Transfer probabilities (P) can be obtained from the inherent laws of the problem, experience, or estimation from observational data. In our model, we use the monthly transition probabilities derived from the survival data and a formula described by previous studies. The transfer matrix is shown below:</h4>
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<center>
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<h6>Table.1 The transition probability of the Sorafenib and combination therapy <sup>[9]</sup></h6>
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<h4>
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<table border="2">
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<tr>
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<td></td>
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<td>Sorafenib</td>
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<td>Combination therapy</td>
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</tr>
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<tr>
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<td>P<sub>PFS-PFS</sub></td>
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<td>0.6639</td>
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<td>0.7826</td>
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</tr>
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<tr>
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<td>P<sub>FS-PD</sub></td>
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<td>0.2264</td>
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<td>0.1399</td>
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</tr>
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<tr>
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<td>P<sub>PFS-death</sub></td>
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<td>0.1097</td>
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<td>0.0739</td>
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</tr>
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<tr>
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<td>P<sub>PD-PD</sub></td>
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<td>0.8088</td>
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<td>0.8553</td>
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</tr>
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<tr>
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<td>P<sub>PD-death</sub></td>
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<td>0.1912</td>
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<td>0.1447</td>
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</tr>
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</table>
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</h4>
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<h6>Table.2 The transition probability of the Sorafenib and SBRT<sup>[10]</sup></h6>
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<h4>
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<table border="2">
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<tr>
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<td></td>
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<td>Sorafenib</td>
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<td>SBRT</td>
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</tr>
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<tr>
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<td>P<sub>PFS-PFS</sub></td>
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<td>0.784</td>
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<td>0.805</td>
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</tr>
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<tr>
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<td>P<sub>FS-PD</sub></td>
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<td>0.063</td>
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<td>0.109</td>
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</tr>
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<tr>
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<td>P<sub>PFS-death</sub></td>
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<td>0.153</td>
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<td>0.086</td>
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</tr>
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<tr>
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<td>P<sub>PD-PD</sub></td>
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<td>0.882</td>
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<td>0.960</td>
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</tr>
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<tr>
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<td>P<sub>PD-death</sub></td>
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<td>0.118</td>
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<td>0.040</td>
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</tr>
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</table>
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</h4>
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<h6>Table.3 The transition probability of the FOLFOX4 and Sorafenib<sup>[11]</sup></h6>
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<table border="2">
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<td></td>
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<td>FOLFOX4</td>
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<td>Sorafenib</td>
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<tr>
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<td>P<sub>PFS-PFS</sub></td>
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<td>0.686</td>
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<td>0.680</td>
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</tr>
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<td>P<sub>FS-PD</sub></td>
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<td>0.211</td>
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<td>0.219</td>
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<td>P<sub>PFS-death</sub></td>
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<td>0.103</td>
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<td>0.101</td>
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<td>0.819</td>
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<td>0.829</td>
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<td>P<sub>PD-death</sub></td>
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<td>0.181</td>
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<td>0.171</td>
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<img src="https://static.igem.org/mediawiki/2018/c/cc/T--CPU_CHINA--M1_juzhen.png">
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<h4>Transfer matrix example of FOLFOX verses Sorafenib</h4>
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<h4>We simulated the life course of 1,000 patients treated with the above drugs in silico. At the beginning, each patient's state is determined by a random function to make our simulation close to the practical situation. Also, the switch between states of every patient in every month is random but the probability complies with transfer probabilities. The simulation ended when all the patients die and the output is the number of death in every month.</h4>
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<h4>a. FOLFOX4 versus Sorafenib</h4>
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<img src="https://static.igem.org/mediawiki/2018/5/53/T--CPU_CHINA--M1_figure3b.png">
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<h4>b. SBRE versus Sorafenib</h4>
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<img src="https://static.igem.org/mediawiki/2018/7/75/T--CPU_CHINA--M1_figure3c.png">
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<h4>c.Sorafenib combination versus monotherapy</h4>
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<h4><b>Figure3. The comparison of the survival curves in different cases.</b> We have found that Sorafenib monotherapy is not better than the SBRT therapy or the Sorafenib combination therapy, while it shows little advantage over FOLFOX4.
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<h4>During the clinical trials, researchers can’t really follow and record the patients until they die. However, in this model, we can define several states of the patients in advance. After every month’s medical intervention and collection of the data, we can put patients into the corresponding states and calculate the transfer probabilities. By running the program that we have written based on this model, we can predict the survival curve of each medical treatment.</h4>
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<h4>Then the utility can be estimated by doing some questionnaire survey and lab tests in specific disease contexts. As we mentioned before, with the life span and the utility, the quality-adjusted life years then can be calculated.</h4>
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<h4>Since we can get the efficacy of different medical intervention in the model, the next step is to estimate a reasonable price (Figure 4). Companies can calculate the ICER of their products with their prospect price and compare it to other drugs of the same type contemporarily on the market. </h4>
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<center><img src="https://static.igem.org/mediawiki/2018/1/1c/T--CPU_CHINA--M1_figure4.png">
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<h6>Figure4. Schematic of how to set up a reasonable price for the patients through CUA.</h6></center>
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<h4>Reference</h4>
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<h4>[1].World Cancer Report 2014. World Health Organization. 2014. pp. Chapter 5.6. ISBN 9283204298.</h4>
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<h4>[2]. http://www.a-hospital.com/w/%E8%82%9D%E7%99%8C</h4>
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<h4>[3]. Weinstein, M. C., Torrance, G., & McGuire, A. (2009). QALYs: the basics. Value in health, 12, S5-S9.</h4>
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<h4>[4]. National Institute for Health and Care Excellence. Retrieved 2017-05-30.</h4>
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<h4>[5]. What is the incremental cost-effectiveness ratio (ICER)? GaBI Online.</h4>
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<h4>[6]. 中华人民共和国卫生和计划生育委员会医政医管局. (2017). 原发性肝癌诊疗规范(2017年版). 中华消化外科杂志, 16(7), 705-720.</h4>
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<h4>[7]. "Markov chain | Definition of Markov chain in US English by Oxford Dictionaries". Oxford Dictionaries | English. Retrieved 2017-12-14</h4>
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<h4>[8]. Gagniuc, Paul A. (2017). Markov Chains: From Theory to Implementation and Experimentation. USA, NJ: John Wiley & Sons. pp. 1–235. ISBN 978-1-119-38755-8.</h4>
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<h4>[9]. Ho, J.-C., Hsieh, M.-L., Chuang, P.-H., & Hsieh, V. C.-R. (2018). Cost-Effectiveness of Sorafenib Monotherapy and Selected Combination Therapy with Sorafenib in Patients with Advanced Hepatocellular Carcinoma. Value in Health Regional Issues, 15, 120-126.</h4>
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<h4>[10]. Leung, H. W., Liu, C. F., & Chan, A. L. (2016). Cost-effectiveness of sorafenib versus SBRT for unresectable advanced hepatocellular carcinoma. Radiat Oncol, 11, 69.</h4>
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<h4>[11]. Zhang, P., Wen, F., & Li, Q. (2016). FOLFOX4 or sorafenib as the first-line treatments for advanced hepatocellular carcinoma: A cost-effectiveness analysis. Dig Liver Dis, 48(12), 1492-1497.</h4>
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Latest revision as of 03:58, 8 December 2018

Model of Liposome Gene Delivery



Background

Liposomes or plasmids may become lost and not able to reach the nucleus due to degradation in cells during transmission. This loss, among many, brings difficulties to the development and clinical application of gene drugs. Quantitative study of plasmid loss and transfection efficiency during lipofection is of great significance for the delivery of gene drugs. Therefore, we simulated the transfection and plasmid loss of a liposome gene delivery system in silico. In our model, we used queuing network and memoryless Markov process to describe the transmission of liposomes and plasmids.

Model description

There are ten states and nine transmission processes during the lipofection. The first step of liposome gene delivery is endocytosis, a process that liposomes in the surrounding are delivered to the cell in the form of endosomes (from ① to ②). The second step is endosomal escape. In this step, some of the liposomes in endosome could escape（from ② to ④） but some others are degraded by lysosome（from ② to ③）. What happens next is that the liposomes are tagged with a nuclear locus signal (NLS)（from ④ to ⑦） or ruptured to release the naked plasmid（from ④ to ⑤）. The naked plasmids in the cytoplasm then could also be added with a nuclear locus signal（from ⑤ to ⑧） or degraded（from ⑤ to ⑥）. Eventually, liposomes or naked plasmids with a nuclear locus signal are successfully delivered into the nucleus （from ⑦ to ⑨ and from ⑧ to ⑩）(Figure.1). These plasmids in the nucleus are then transcribed to do their job. Plasmids that degrade at any point during the whole process are unavoidably lost.
Figure.1 Primary transmission chain between cell membrane and nucleus

In our model, we assumed that there were 90000 plasmids packed in 9000 liposomes and all the liposomes enter the cells in the form of endosome. Then we generate 9000 random numbers following exponential distribution to describe the internalization time.

For those transmission step that have two probable routes(A and B), Figure.2 shows the algorithm of what happened in a millisecond. All of the steps that have two proper routes act like this, including endosome escape or degradation (from ② to ③ or ④), liposome adding NLS or degradation(from ④ to ⑤ or ⑦) and plasmid adding NLS or degradation (from ⑤ to ⑥ or ⑧).
Figure.2 Algorithm of transmission that have two probable routes

For those transmission step that only have one probable route, Figure.3 shows the algorithm of what happened in a millisecond. Liposomes or naked plasmids that successfully enter the nucleus （from ⑦ to ⑨ and from ⑧ to ⑩）act like this.
Figure.3 Algorithm of transmission that have one probable routes

In summary, we generated 9000 exponentially distributed numbers to describe the moment of each liposome internalization and then took a millisecond as a time interval. During every millisecond, we checked the number of liposomes/plasmids in every queue and calculated the transfer probability according to our algorithm. We then generate random numbers subject to normal distribution and compared it with the transfer probability, then conclude where it should go. What happens in such a millisecond have been actually repeated for 64800000 times in 18 hours after liposomes are added to the cell.

Significance

It is reported that the saturation number of plasmids that can be delivered to one cancer cell is 90000. By conducting our Model of Liposome Gene Delivery, we find that an injection of 90000 plasmids can lead to 44270 of which (49.19%) been transported into the nucleus successfully, what’s more, this result is promising since it enables us to predict the minimum transfection amount to guarantee enough number of of plasmids in nucleus during our experiments. Furthermore, we are able to calculate the amount of the plasmids we need to administrate in order to obtain therapeutic efficiency which is very instructional for our further application in vivo.

Click here to get the parameter, formula, results and reference.

Click here to get the code.

Cost-effectiveness analysis model

Background

Hepatocellular carcinoma (HCC) has a huge impact on human health and remains a huge burden to people all over the world. Intense research has been and will be made against this disease, so the number of available medical treatments should be expected to continue growing. For researchers and investors, the current market and competition tend to be obscured by ever-new attractions and tendencies.

In this cases, there are two main questions:

1. How to determine if a new therapy is interesting for practical application?

2. How to balance the pay and gain of the patients? How to set up a reasonable price for the patients?

To solve these problems, mathematical modeling would come in handy as it helps to explain and to study the effects of different factors, and to make predictions about new products. Therefore, efforts have been made by us to set up a model that estimates the efficiency and cost of these medical treatments.

Model description

During the clinical trials, researchers can’t really follow and record the patients until they die. However, in this model, we can define several states of the patients in advance. After every month’s medical intervention and collection of the data, we can put patients into the corresponding states and calculate the transfer probabilities (Figure.1). By running the program that we have written based on this model, we can predict the survival curve of each medical treatment.

Figure.1 The state space and the transfer relationship in our model

Then the utility can be estimated by doing some questionnaire survey and lab tests in specific disease contexts. As we mentioned before, with the life span and the utility, the quality-adjusted life years then can be calculated.

Since we can get the efficacy of different medical intervention in the model, the next step is to estimate a reasonable price (Figure.2). Companies can calculate the ICER of their products with their prospect price and compare it to other drugs of the same type contemporarily on the market.

Figure2. Schematic of how to set up a reasonable price for the patients through CUA.


Significance

Based on clinical data, we can learn the efficacy of different drugs through our Cost-effectiveness analysis model, then further estimate a reasonable price (Figure.2). This model enables us to predict the price of our system when it comes to a drug in future which contributes to our business plan and the realizable analyze of our project. Furthermore, we are proud to notice that not only our team but also the whole iGEM community and public can also benefit from this model. Since they can understand the efficacy as well as calculate the ICER of their products to know their prospect price, then compare it to other drugs of the same type contemporarily on the market to test products’ practicability.



Click here to get the parameter, formula result and reference.

Click here to get the code.