Modeling of hemoglobin response to Erythropoietin therapy through constrained optimization

Haemoglobin response modelling under erythropoietin treatment: Physiological model‐informed machine learning method

“…In the PK model equations, E t ð Þ denotes the amount of exogenous recombinant human EPO, E en denotes the endogenous EPO, E p t ð Þ is the total EPO of the dynamic pool in plasma, k in t ð Þ is the RBC production rate, and dose t ð Þ is the EPO dosing in international units (IU) which is modelled as a train of impulses. [18] Additionally, the model contains some parameters: H en is the Hgb level due to endogenous EPO, μ represents the mean RBC life span, V is the maximum exogenous EPO clearance rate, K m stands for the exogenous EPO level that produces half-maximum clearance rate, α is the linear clearance constant, S represents the maximal RBC production rate stimulated by EPO, and C is the amount of EPO that produces half-maximum RBC production rate. [15] In the PD model, state R t ð Þ represents the population of RBC, states x 1 t ð Þ and x 2 t ð Þ are internal states that aid in calculating R t ð Þ, Hgb t ð Þ is the Hgb level which can be detected clinically, parameter D is the time required for EPO-stimulated RBCs to start forming, and K H is the average amount of Hgb per RBC (mean corpuscular Hgb, or MCH, in a complete blood count) which takes the value of K H ¼ 29:5 pg=cell.…”

“…A related paper has proposed an ARX model for this erythropoiesis modelling. [18] The applied classical ARX model uses Equation 27:…”

“…For the physiological modelling with the least squares method, the delay differential equations in the physiological model are solved by the dde23 function in Matlab and parameters are optimized using the lsqnonlin function in Matlab. [18] The first half part of the data is used to train parameters, and the second half of the data is tested for model error. This parameter estimation based on the least squares is time-consuming because it involves the solution of the delay differential equations many times.…”

EPO Dosage Optimization for Anemia Management: Stochastic Control under Uncertainty Using Conditional Value at Risk

“…In this work, the patient's model parameters are relearnt after each measurement, based on a moving window of estimation data. In the absence of validation data, constraints are used in the modeling formulation to ensure model stability, as well as to enforce that the model parameters follow patterns that are well described by many patients [26]. The complete constrained ARX (C-ARX) model parameter estimation problem can be represented by Equation (5).…”

“…Equation (5e) enforces that the model parameters are always positive, because the response of the system to the inputs is always positive. Equations (5f)-(5i) are defined through experience, and are used to enforce a particular parameter shape learned in [26]. Finally, Equation (5i) is used to ensure the model relies somewhat on the inputs to the system, and was determined through trial and error.…”