distribution of Benzene in a 4-compartment PBK model after an exposure of 6h. Convert Berkeley Madonna code to Matlab.
distribution of Benzene in a 4-compartment PBK model after an exposure of 6h.
Convert Berkeley Madonna code to Matlab.
Note: The parameters in the table below are for a mouse model.
1a) What are the two type of products containing Benzene consumers were recently concerned about. Which of these two different type of products is likely more harmful? (hint: check news/reports and social media channels)
1b) Plot Jresp along with the concentrations of Benzene in blood, fat, non-fat and liver in a 24h window (pdf). Why is Jresp slightly decreasing within 6h of exposure?
Here is the Berkeley Madonna code:
{Top model}
METHOD RK4
STARTTIME = 0
STOPTIME = 24
DT = 0.02
{Reservoirs Blood, Fat, NonFat and Liver}
d/dt (NF) = + Jnf
INIT NF = 0
d/dt (F) = + Jf
INIT F = 0
d/dt (B) = - Jnf - Jf - Jl + Jresp
INIT B = 0
d/dt (L) = + Jl - Jmetab
INIT L = 0
{Flows}
Jnf = Qnf*(Cb-Cnf)
Jf = Qf*(Cb-Cfv)
Jl = Ql*(Cb - Clv)
Jmetab = vmax*Cl/(Km + Cl)
{Replace squarepulse with " IF t>6h Jresp=0 "}
Jresp = Qp*(Ci - (Cb/Pb))*squarepulse(0,6)
{Functions}
Vnf = 1
Cnf = NF/Vnf
Qnf = 1
Vf = 1
Cf = F/Vf
Qf = 1
Cb = B/Vb
Vb = 1
Cfv = Cf/Pf
Pf = 20
Vl = 1
Cl = L/Vl
Ql = 1
vmax = 1
Km = 1
Pl = 2
Clv = Cl/Pl
Pb = 18
{Benzene conc in inhaled air}
Ci = 0.32
{alveolar ventilation rate}
Qp = 5.74
Summary of variables and constants
![Summary of variables and constants
C₁
Init B
Init F
Init L
Init Nf
Km
Pb
Pf
P₁
Qf
Q₁
Qnf
V₂
Vf
V₁
Vmax
Vnf
Alveolar ventilation rate [L hr¯¹]
Benzene concentration in inspired air [mg L²¹]
Initial condition blood
Initial condition fat
Initial condition liver
Initial condition non-fat
5.74
0.32
0
0
0
0
0.4
Michaelis-Menten constant [mg L²¹]
18
Blood/air partition coefficient
28 Fat/blood partition coefficient
2
Liver/blood partition coefficient
Blood flow to fat [L hr¯
0.517
1.44
Blood flow to liver [L hrˇ¹]
Blood flow to non-fat [L hr²¹]
3.79
0.024
Volume blood [L]
0.027
Volume fat tissue [L]
0.012
Volume liver tissue [L]
Maximum velocity of metabolism [mg hr`¹]
Volume non-fat tissue [L]
1.42
0.234](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb4ce4869-8ffb-4d6f-acad-72e7a2106c79%2Fcea29c13-7171-4285-94d8-9350db5bb5bd%2F7yr7hbd_processed.png&w=3840&q=75)
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1b) Plot Jresp along with the concentrations of Benzene in blood, fat, non-fat and liver in a 24h window (
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