import matplotlib.pyplot as plt import math # drug_dosage_start.py # # VARIABLE DICTIONARY DRUG DOSAGE MODEL: # -------------------------------------------------------------------- # Drug levels in the blood, for certain drugs, can be modeled by a pair of # coupled first-order linear differential equations. For compactness, let # A= medicine_in_intestines and B = plasma_level. Variable names are defined # below. # dA/dt = -absorption_rate*A + intake # dB/dt = -excretion_rate*B + absorption_rate*A def drug_dosage_sensitivity(e_rate): # Model parameters time_step = 0.25 # simulation time step in hours start_time = 0 # in hours end_time = 48 # in hours doses_per_day = 4 dosage_per_day = 11800 #mg of the drug absorption_rate = 0.25 # absorption rate constant half_life = 6 # in hours blood_volume = 4.6 # in liters medicinal_level = 800 # level at which drug becomes effective mg/l toxic_level = 1000 # level at which drug becomes toxic mg/l # Derived constants N = int((end_time - start_time) / time_step) # number of simulation steps dosage = dosage_per_day / doses_per_day # amount of each dose dosage_interval = 24 / doses_per_day # in hours excretion_rate = math.log(float(e_rate)) / half_life steps_between_doses = dosage_interval / time_step # Time-varying quantities, arrays with one value per time step # The syntax, "[0]*(N+1)," creates a one-dimensional array of length N+1 whose values are all zero. t = [0]*(N+1) # time in hours intake = [0]*(N+1) # dose at this time step medicine_in_intestines = [0]*(N+1) # level of drug in intestines plasma_level = [0]*(N+1) # level of drug in the blood plasma_concentration = [0]*(N+1) # concentration of drug in blood absorption = [0]*(N+1) # amount absorbed at this time step excretion = [0]*(N+1) # amount excreted at this time step # Initialize variables - assume all others start at 0 t[0] = start_time step_next_dose = 1 # give first dose at start time # Loop to calculate intake of drug over time # Euler's method # this part calculates when each dose of the drug is added based on # the number of doses over a 24 hour period. Number of doses must be an # integer divisor of 24 for this to work. Otherwise change the time step for i in range(N): t[i+1] = t[i] + time_step # Is it time for a dose? if i == step_next_dose: intake[i] = dosage step_next_dose = i + steps_between_doses else: intake[i] = 0 for i in range(N): # Otherwise, run the model absorption[i] = time_step*absorption_rate*medicine_in_intestines[i] excretion[i] = time_step * excretion_rate * plasma_level[i] medicine_in_intestines[i+1] = medicine_in_intestines[i] - absorption[i] + intake[i] plasma_level[i+1] = plasma_level[i] - excretion[i] + absorption[i] plasma_concentration[i+1] = plasma_level[i+1]/blood_volume #TODO: Create another loop that calculates the absorption, excretion, #plasma level, and plasma concentration over time return plasma_concentration