<p>有几个问题:</p>
<ul>
<li>最后两个方程是代数方程,不是微分方程。它应该是<code>mu==...</code>而不是<code>mu.dt()==...</code></li>
<li>一些方程式有被零除的可能性。像<code>x.dt() = z/y</code>这样的方程可以用<code>y * x.dt()==z</code>代替,这样当<code>y</code>接近零时,方程就变成<code>0 * x.dt() == z</code>。你知道吗</li>
<li>一些初始条件没有设置,因此它们使用默认值0。这可能会产生一个零的解决方案。你知道吗</li>
</ul>
<p>我输入了一些不同的值,并使用<code>m.options.COLDSTART=2</code>帮助它找到一个初始解决方案。我还使用中间词来帮助可视化任何正在变大的术语。我把细胞浓度以每公升数百万个细胞为单位,以帮助进行缩放。你知道吗</p>
<p><a href="https://i.stack.imgur.com/972aL.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/972aL.png" alt="results"/></a></p>
<pre class="lang-py prettyprint-override"><code>import numpy as np
from gekko import GEKKO
import matplotlib.pyplot as plt
m = GEKKO(remote=False) # create GEKKO model
#constants 3L continuous fed-batch
KdQ = 0.001 #degree of degradation of glutamine (1/h)
mG = 1.1e-10 #glucose maintenance coefficient (mmol/cell/hour)
YAQ = 0.90 #yield of ammonia from glutamine
YLG = 2 #yield of lactate from glucose
YXG = 2.2e8 #yield of cells from glucose (cells/mmol)
YXQ = 1.5e9 #yield of cells from glutamine (cells/mmol)
KL = 150 #lactate saturation constant (mM)
KA = 40 #ammonia saturation constant (mM)
Kdmax = 0.01 #maximum death rate (1/h)
mumax = 0.044 #maximum growth rate (1/h)
KG = 1 #glucose saturation constant (mM)
KQ = 0.22 #glutamine saturation constant (mM)
mQ = 0 #glutamine maintenance coefficient (mmol/cell/hour)
kmu = 0.01 #intrinsic death rate (1/h)
Klysis = 2e-2 #rate of cell lysis (1/h)
Ci_star = 100 #inhibitor saturation concentration (mM)
qi = 2.5e-10 #specific inhibitor production rate (1/h)
#Flow, volume and concentration
Fo = 0.001 #feed-rate (L/h)
Fi = 0.001 #feed-rate (L/h)
V = 3 #volume (L)
SG = 653 #glucose concentration in the feed (mM)
SQ = 58.8 #glutamine concentration in the feed (mM)
# create GEKKO parameter
t = np.linspace(0,50,121)
m.time = t
XTMM = m.Var(value=1,name='XT') #total cell density (MMcells/L)
XVMM = m.Var(value=1,lb=0, name='XV') #viable cell density (MMcells/L)
XDMM = m.Var(value=1.0,name='XD') #dead cell density (MMcells/L)
G = m.Var(value = 20, name='G') #glucose concentration (mM)
Q = m.Var(value = 4.5, name='Q') #glutamine concentration (mM)
L = m.Var(value=1,name='L') #lactate concentration (mM)
A = m.Var(value=1.6,name='A') #ammonia concentration (mM)
Ci = m.Var(value=0.1,name='Ci') #inhibitor concentration (mM)
mu = m.Var(value=0.1,name='mu') #growth rate (1/h)
Kd = m.Var(value=0.5,name='Kd') #death rate(1/h)
# scale back to cells/L from million cells/L
XT = m.Intermediate(XTMM*1e7)
XV = m.Intermediate(XVMM*1e7)
XD = m.Intermediate(XDMM*1e7)
e1 = m.Intermediate((mu*XV - Klysis*XD - XT*Fo/V)/1e7)
e2 = m.Intermediate(((mu - Kd)*XV - XV*Fo/V)/1e7)
e3 = m.Intermediate((Kd*XV - Klysis*XD - XV*Fo/V)/1e7)
e4 = m.Intermediate((Fi/V)*SG - (Fo/V)*G + (-mu/YXG - mG)*XV)
e5 = m.Intermediate((Fi/V)*SQ - (Fo/V)*Q + (-mu/YXQ - mQ)*XV - KdQ*Q)
e6 = m.Intermediate(-YLG*(-mu/YXG -mG)*XV-(Fo/V)*L)
e7 = m.Intermediate(-YAQ*(-mu/YXQ - mQ)*XV +KdQ*Q-(Fo/V)*A)
e8 = m.Intermediate(qi*XV - (Fo/V)*Ci)
e9a = m.Intermediate((Ci_star*(KG+G)*(KQ+Q)*(L/KL + 1)*(A/KA + 1)))
e9b = m.Intermediate((mumax*G*Q*(Ci_star-Ci)))
e10a = m.Intermediate((mu+kmu))
e10b = m.Intermediate(Kdmax*kmu)
# create GEEKO equations
m.Equation(XTMM.dt() == e1)
m.Equation(XVMM.dt() == e2)
m.Equation(XDMM.dt() == e3)
m.Equation(G.dt() == e4)
m.Equation(Q.dt() == e5)
m.Equation(L.dt() == e6)
m.Equation(A.dt() == e7)
m.Equation(Ci.dt() == e8)
m.Equation(e9a * mu == e9b)
m.Equation(e10a*Kd == e10b)
# solve ODE
m.options.IMODE = 4
m.options.SOLVER = 1
m.options.NODES = 3
m.options.COLDSTART = 2
#m.open_folder()
m.solve(display=False)
plt.figure()
plt.subplot(3,1,1)
plt.plot(m.time, XV.value,label='XV')
plt.plot(m.time, XT.value,label='XT')
plt.plot(m.time, XD.value,label='XD')
plt.legend()
plt.subplot(3,1,2)
plt.plot(m.time, G.value,label='G')
plt.plot(m.time, Q.value,label='Q')
plt.plot(m.time, L.value,label='L')
plt.plot(m.time, A.value,label='A')
plt.legend()
plt.subplot(3,1,3)
plt.plot(m.time, mu.value,label='mu')
plt.plot(m.time, Kd.value,label='Kd')
plt.legend()
plt.xlabel('Time (hr)')
plt.figure()
plt.plot(m.time, e1.value,'r-.',label='eqn1')
plt.plot(m.time, e2.value,'g:',label='eqn2')
plt.plot(m.time, e3.value,'b:',label='eqn3')
plt.plot(m.time, e4.value,'b ',label='eqn4')
plt.plot(m.time, e5.value,'y:',label='eqn5')
plt.plot(m.time, e6.value,'m ',label='eqn6')
plt.plot(m.time, e7.value,'b-.',label='eqn7')
plt.plot(m.time, e8.value,'g ',label='eqn8')
plt.plot(m.time, e9a.value,'r:',label='eqn9a')
plt.plot(m.time, e9b.value,'r ',label='eqn9b')
plt.plot(m.time, e10a.value,'k:',label='eqn10a')
plt.plot(m.time, e10b.value,'k ',label='eqn10b')
plt.legend()
plt.show()
</code></pre>