The role of oxygen intake and liver enzyme on the dynamics of damaged hepatocytes: Implications to ischaemic liver injury via a mathematical model

Ischaemic Hepatitis (IH) or Hypoxic Hepatitis (HH) also known as centrilobular liver cell necrosis is an acute liver injury characterized by a rapid increase in serum aminotransferase. The liver injury typically results from different underlying medical conditions such as cardiac failure, respiratory failure and septic shock in which the liver becomes damaged due to deprivation of either blood or oxygen. IH is a potentially lethal condition that is often preventable if diagnosed timely. The role of mechanisms that cause IH is often not well understood, making it difficult to diagnose or accurately quantify the patterns of related biomarkers. In most patients, currently, the only way to determine a case of IH is to rule out all other possible conditions for liver injuries. A better understanding of the liver’s response to IH is necessary to aid in its diagnosis, measurement, and improve outcomes. The goal of this study is to identify mechanisms that can alter associated biomarkers for reducing the density of damaged hepatocytes, and thus reduce the chances of IH. We develop a mathematical model capturing dynamics of hepatocytes in the liver through the rise and fall of associated liver enzymes aspartate transaminase (AST), alanine transaminase (ALT) and lactate dehydrogenase (LDH) related to the condition of IH. The model analysis provides a novel approach to predict the level of biomarkers given variations in the systemic oxygen in the body. Using IH patient data in the US, novel model parameters are described and then estimated for the first time to capture real-time dynamics of hepatocytes in the presence and absence of IH condition. The results may allow physicians to estimate the extent of liver damage in an IH patient based on their enzyme levels and receive faster treatment on a real-time basis.

The other paper used for parameter estimation is that by Henrion [20]. From [20], rows from two columns of Table 2 are extracted. These columns present peak AST, ALT, and LDH data for Ischaemic Hepatitis resulting from the conditions acute cardiac failure (ACF) and congestive heart failure (CHF), both of which fall under our scope of interest. Sheet 3 of the excel document presents the tables [20]. The second and third columns of the tables discuss these cases. Table 1 discusses clinical findings of the groups. Table 2 and Table 3 present laboratory and hemodynamic  data. Tables 4 and 5 show results of a hemodynamic assessment and measurements of hepatic blood flow for these groups. Tables 6 and 7 describe the clinical and laboratory data sets from which their analysis was made. This includes the numbers of cases, gender, age, causes of hypoxia, and their associated serum values. The Raurich [34] paper and the two sections from the Henrion[20] paper provide three values for each serum (AST, ALT, and LDH). These three values are averaged to estimate the aforementioned parameters.
To validate the model, the numbers are extracted from the four other articles. Three numbers for each serum (AST, ALT, and LDH) came from Birrer [4]. These nine numbers came from the paper's third table for cases of decreased oxygen (Group 1), decreased oxygen delivery (Group 2), and decreased oxygen availability (Group 3). In the second sheet of the excel document, this table, as well as the other [4] are attached. The first table provides data readings such as cardiac index, central venous pressure, and hepatic blood flow. The second table provides statistics on the conditions that caused the diagnosis of hypoxia. The third table, from which our information was acquired, provides the ages, serum levels, and laboratory data for the three groups used.
From the Drolz [10], four values are extracted from the text, two for AST and two for ALT. These values represent average peak serum values for patients with and without statin therapy treatment. The values themselves are found written in the manuscript's outcomes section which is in the fourth sheet of the excel document. Details such as mortality, complications, and creatinine concentrations were also found in the text. Tables 1 and 2 provide the associated information regarding the number of patients, ages, causes, outcomes, and treatment administered.
The Tapper [40] provide a table (Table 2) that include AST and ALT peak values. In order to extract a single AST and a single ALT value, the columns of the table are averaged. In the Tapper section of the excel spreadsheet, details about the sources of their data can be found. In Table 1, this information includes the years and authors of the data. It also includes the sample size and number of ischaemia cases. In Table 2, the serum values can be found, as well as the percentage of hypotensive events, cardiac events, sepsis, and survival rates. Table 7. Once again, the peak values are averaged such that only one value for each serum is taken from this paper. In the last sheet of the excel document, the tables from [18] can be found. The first two tables provide data on patient hospital and intensive care unit admittance. Table 3 details the underlying conditions that contributed to the hypoxic hepatitis cases. Tables 4-6 detail hemodynamic data associated with each underlying condition such as oxygen delivery and cardiac index. Table 7, from which the values were extracted, contains data about the number of cases, age, sex, survival, and serum levels.

Henrion's[18], presents AST, ALT, and LDH values in
The resulting values were compiled in a table which can be found at the bottom of the first sheet in the excel document. These nine AST, nine ALT, and five LDH values not used in parameter estimation are averaged. The resulting average values are compared with the peak values from our mathematical model for validation. This analysis weighed data from individual papers or sections of papers equally and only constrained the data in cases where decreased oxygen or heart conditions are explicitly differentiated in the sources. The data analysis did not consider patient numbers, demographic information, or the severity of a patient's condition.