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AD_QSP_model.py
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AD_QSP_model.py
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# -*- coding: utf-8 -*-
"""
This software is released under the MIT License, see LICENSE.txt.
Copyright (c) 2021 Takuya Miyano
QSP model simulates %improved EASI and EASI-75
"""
import numpy as np
from scipy.integrate import odeint
from numba import jit
def simulate(mu, sigma, n_patients):
"""
Parameters
----------
mu : ndarray of shape (51, 1)
51 distribution parameters that represent mean of ln(k_n)
sigma : ndarray of shape (51, 1)
51 distribution parameters that represent standard deviation of ln(k_n)
n_patients : int
number of virtual patients
Returns
----------
mean_ss : ndarray of shape (15)
mean of baseline levels of 15 biological factors
EASI score, skin barrier integrity, infiltrated pathogens, Th1, Th2, Th17, Th22, IL4, IL13, IL17, IL22, IL31, IFNg, TSLP, OX40L
cv_ss : ndarray of shape (15)
%CV of baseline levels of 15 biological factors
EASI score, skin barrier integrity, infiltrated pathogens, Th1, Th2, Th17, Th22, IL4, IL13, IL17, IL22, IL31, IFNg, TSLP, OX40L
impEASI : ndarray of shape (241, 10)
%improved EASI
241 time points from week 0 to 24
10 invterventions of placebo, dupilumab, nemolizumab, tezepelumab, GBR 830, fezakinumab, secukinumab, rIFNg, tralokinumab, lebrikizumab
e75 : ndarray of shape (241, 10)
EASI-75
241 time points from week 0 to 24
10 invterventions of placebo, dupilumab, nemolizumab, tezepelumab, GBR 830, fezakinumab, secukinumab, rIFNg, tralokinumab, lebrikizumab
"""
class ODE(object):
def __init__(self, diff_eq, init_con):
self.diff_eq = diff_eq
self.init_con = init_con
def cal_equation(self, t_end, drug_effect, x):
dt = 0.1 # delta time (week)
N = round(t_end/dt) + 1 #Time steps
t = np.linspace(0, t_end, N) # prepare time
v = odeint(self.diff_eq, self.init_con, t, rtol=1e-8, atol=1e-6, args=(drug_effect, x))
return v
@jit('f8[:](f8[:,:])', nopython=True)
def EASI(sim):
s = sim[:,0]
p = sim[:,1]
e = 72 * (2*p + 2*(1-s)) /4
return e
@jit('f8[:](f8[:],f8,f8[:],f8[:])', nopython=True, debug=True)
def diff_eq(c, t, de, x):
# c : levels of 14 biological factors at t. ndarray of shape (14)
# c[0] : skin barrier integrity
# c[1] : infiltrated pathogens
# c[2] : Th1
# c[3] : Th2
# c[4] : Th17
# c[5] : Th22
# c[6] : IL4
# c[7] : IL13
# c[8] : IL17
# c[9] : IL22
# c[10]: IL31
# c[11]: IFNg
# c[12]: TSLP
# c[13]: OX40L
# t : time (int)
# de: effects of [placebo, IL4, IL13, IL17A, IL22, IL31, TSLP, OX40, rIFNg]
# x : 51 parameter values
# prepare parameter values
k1 = x[0]
k2 = x[1]
k3 = min([x[2],de[0]])
b1 = x[3]
b2 = x[4]
b3 = x[5]
b4 = x[6]
b5 = x[7]
d1 = x[8]
d2 = x[9]
d3 = x[10]
b6 = x[11]
d4 = x[12]
d5 = x[13]
d6 = x[14]
d7 = x[15]
b7 = x[16]
b8 = x[17]
d8 = x[18]
k5 = x[19]
k9 = x[20]
d9 = x[21]
b9 = x[22]
k6 = x[23]
k10 = x[24]
k7 = x[25]
k8 = x[26]
k11 = x[27]
k12 = x[28]
d10 = x[29]
k13 = x[30]
k14 = x[31]
d11 = x[32]
k15 = x[33]
k16 = x[34]
d12 = x[35]
k17 = x[36]
k18 = x[37]
d13 = x[38]
k19 = x[39]
k20 = x[40]
d14 = x[41]
k21 = x[42]
k22 = x[43]
d15 = x[44]
k23 = x[45]
k24 = x[46]
d16 = x[47]
k25 = x[48]
k26 = x[49]
d17 = x[50]
ea2 = max([0.4396, de[9]])
k4 = d8
# effective concentration of cytokines (drug effects on cytokines)
IL4 = (1 - de[1])*c[6]
IL13 = (1 - de[2]*ea2)*c[7]
IL17 = (1 - de[3])*c[8]
IL22 = (1 - de[4])*c[9]
IL31 = (1 - de[5])*c[10]
TSLP = (1 - de[6])*c[12]
OX40 = (1 - de[7])*c[13]
IFNg = c[11] + de[8]
# ODEs
# skin barrier integrity
dc0dt = (1 - c[0])*(k1 + k2*IL22 +k3)/((1 + b1*IL4)*(1 + b2*IL13)*(1 + b3*IL17)*(1 + b4*IL22)*(1 + b5*IL31)) - c[0]*(d1*(1 + d3*c[1]) + d2*IL31)
# infiltrated pathogens
dc1dt = k4/(1 + b6*c[0]) - c[1]*(((1 + d4*c[1])*(1 + d5*IL17)*(1 + d6*IL22)*(1 + d7*IFNg))/((1 + b7*IL4)*(1 + b8*IL13)) + d8)
# Th cells
dc2dt = k5*c[1]*(1 + k9*IFNg) /(4 + k9*IFNg + k10*IL4) - d9*c[2]/(1 + b9*OX40) # Th1
dc3dt = k6*c[1]*(1 + k10*IL4) /(4 + k9*IFNg + k10*IL4) - d9*c[3]/(1 + b9*OX40) # Th2
dc4dt = k7*c[1] /(4 + k9*IFNg + k10*IL4) - d9*c[4]/(1 + b9*OX40) # Th17
dc5dt = k8*c[1] /(4 + k9*IFNg + k10*IL4) - d9*c[5]/(1 + b9*OX40) # Th22
# cytokines
dc6dt = k11*c[3] + k12 - d10*c[6] # IL4
dc7dt = k13*c[3] + k14 - d11*c[7] # IL13
dc8dt = k15*c[4] + k16 - d12*c[8] # IL17
dc9dt = k17*c[5] + k18 - d13*c[9] # IL22
dc10dt = k19*c[3] + k20 - d14*c[10] # IL31
dc11dt = k21*c[2] + k22 - d15*c[11] # IFNg
dc12dt = k23*c[1] + k24 - d16*c[12] # TSLP
dc13dt = k25*TSLP + k26 - d17*c[13] # OX40L
dcdt = np.array([dc0dt, dc1dt, dc2dt, dc3dt, dc4dt, dc5dt,
dc6dt, dc7dt, dc8dt, dc9dt, dc10dt, dc11dt, dc12dt, dc13dt])
return dcdt
def simulate_one(x):
# simulate steady state (1000 weeks) /baseline levels
# initial conditions for simulating steady-state levels of biological factors
s_0 = np.float64(0.5931)
p_0 = np.float64(0.4069)
Th1_0 = np.float64(3.1)
Th2_0 = np.float64(8.7)
Th17_0 = np.float64(2.0)
Th22_0 = np.float64(21.0)
IL4_0 = np.float64(38.0)
IL13_0 = np.float64(40.5)
IL17_0 = np.float64(5.4)
IL22_0 = np.float64(3.0)
IL31_0 = np.float64(2.0)
IFNg_0 = np.float64(1.5)
TSLP_0 = np.float64(4.4)
OX40_0 = np.float64(9.7)
init_cond = np.array([s_0, p_0, Th1_0, Th2_0, Th17_0, Th22_0, IL4_0,
IL13_0, IL17_0, IL22_0, IL31_0, IFNg_0, TSLP_0, OX40_0], dtype='float64')
ode = ODE(diff_eq, init_cond)
drug_effect = np.array([0, 0, 0, 0, 0, 0, 0, 0, 0, 1], dtype='float64')
sim_0 = ode.cal_equation(1000, drug_effect, x) # 1000 days for steady state
init_cond2 = sim_0[10000,:]
# use steady-state level as baseline levels (initial condition)
ode = ODE(diff_eq, init_cond2)
T_end = 24 # weeks
# Placebo (other)
drug_effect = np.array([1E20, 0, 0, 0, 0, 0, 0, 0, 0, 1], dtype='float64')
sim_1 = ode.cal_equation(T_end, drug_effect, x)
# Dupilumab (IL4/13)
drug_effect = np.array([1E20, 0.99, 0.99, 0, 0, 0, 0, 0, 0, 1], dtype='float64')
sim_2 = ode.cal_equation(T_end, drug_effect, x)
# Nemolizumab (IL31)
drug_effect = np.array([1E20, 0, 0, 0, 0, 0.99, 0, 0, 0, 1], dtype='float64')
sim_3 = ode.cal_equation(T_end, drug_effect, x)
# Tezepelumab (TSLP)
drug_effect = np.array([1E20, 0, 0, 0, 0, 0, 0.99, 0, 0, 1], dtype='float64')
sim_4 = ode.cal_equation(T_end, drug_effect, x)
# GBR830 (OX40)
drug_effect = np.array([1E20, 0, 0, 0, 0, 0, 0, 0.99, 0, 1], dtype='float64')
sim_5 = ode.cal_equation(T_end, drug_effect, x)
# Fezakinumab (IL22)
drug_effect = np.array([1E20, 0, 0, 0, 0.99, 0, 0, 0, 0, 1], dtype='float64')
sim_6 = ode.cal_equation(T_end, drug_effect, x)
# Secukinumab
drug_effect = np.array([1E20, 0, 0, 0.99, 0, 0, 0, 0, 0, 1], dtype='float64')
sim_7 = ode.cal_equation(T_end, drug_effect, x)
# rIFNg (IFNg)
drug_effect = np.array([1E20, 0, 0, 0, 0, 0, 0, 0, 210, 1], dtype='float64')
sim_8 = ode.cal_equation(T_end, drug_effect, x)
# Tralokinumab (IL13 * e_a2)
drug_effect = np.array([1E20, 0, 0.99, 0, 0, 0, 0, 0, 0, 0], dtype='float64')
sim_9 = ode.cal_equation(T_end, drug_effect, x)
# Lebrikizumab (IL13)
drug_effect = np.array([1E20, 0, 0.99, 0, 0, 0, 0, 0, 0, 1], dtype='float64')
sim_10 = ode.cal_equation(T_end, drug_effect, x)
b = np.concatenate([np.array([EASI(sim_0)[10000]]), sim_0[10000,:]])
Res_series = np.concatenate([b, \
EASI(sim_1), EASI(sim_2), EASI(sim_3), EASI(sim_4),\
EASI(sim_5), EASI(sim_6), EASI(sim_7), EASI(sim_8),\
EASI(sim_9), EASI(sim_10)])
return Res_series
# prepare virtual patients
random_list = np.random.randn(51, n_patients)
virtual_subjects = random_list*np.abs(sigma) + mu
virtual_subjects = np.exp(virtual_subjects)
sampleList = [(i, virtual_subjects) for i in range(n_patients)]
# simulation using the virtual patients
res_i = np.zeros([n_patients, 2425])
for i in range(n_patients):
res_i[i] = simulate_one(sampleList[i][1][:,i])
a = res_i.T
a = a[:, np.all(a[15:,:] < 72, axis=0)]
mean_ss = np.mean(a[:15,:], axis = 1)
cv_ss = 100*np.std(a[:15,:], axis = 1)/np.mean(a[:15,:], axis = 1)
impEASI = 100*(a[0,:].reshape(1,-1) - a[15:,:])/a[0,:].reshape(1,-1)
e75 = (np.count_nonzero(impEASI > 75, axis=1)/n_patients*100).T.reshape(-1,241).T
return mean_ss, cv_ss, impEASI, e75
if __name__ == "__main__":
mu = np.loadtxt("mu.csv", delimiter = ",", dtype = float).reshape(-1,1)
sigma = np.loadtxt("sigma.csv", delimiter = ",", dtype = float).reshape(-1,1)
n_patients = 1000
mean_ss, cv_ss, impEASI, e75 = simulate(mu, sigma, n_patients)