Mathematical Modelling of Regeneration of a Tissue-Engineered Trachea - Computational Modeling in Tissue Engineering - page 408

þ d mac ð 1 1 þ C ilk
K mi

N mac Þ;

o N mac
ot

¼ 1
r

o
or

rvN mac þ rD mac o N mac
or

ð 30 Þ

dt ¼ v ð R l ; t Þ h I epi þ b epi N epi ð 1 C tgf ð R l ; t Þ

dN epi

N epi þ 2

N epi Þ; ð 31 Þ

R l K et

o N msc
ot

¼ 1
r

o
or

rvN msc þ rD msc o N msc
or

k cm f ð r Þ C tgf N msc ;

ð 32 Þ

C tgf
K mt

þ C tnf
K mn

þ b msc N msc N msc

þ 2

o N fib
ot

¼ 1
r

o
or

rvN fib þ rD fib o N fib
or

h I fib þ b fib N fib ð 1 N fib Þ;

ð 33 Þ

o N chn
ot

¼ 1
r

o
or

ð rvN chn Þ b chn N chn ð 1 N chn Þþ pk cm C tgf N msc d chn C tnf N chn ;

ð 34 Þ

þ d ilk ð N mac C ilk Þ;

o C ilk
ot

¼ 1
r

o
or

rvC ilk þ rD ilk o C ilk
or

ð 35 Þ

þ b tch N chn ð 1 N chn Þþ d tgf ð N mac C tgf Þ;

o C tgf
ot

¼ 1
r

o
or

rvC tgf þ rD tgf o C tgf
or

ð 36 Þ

þ d tnf ;

K ti
K ti 2 þ C ilk

o C tnf
ot

¼ 1
r

o
or

rvC tnf þ rD tnf o C tnf
or

N mac C tnf ð 37 Þ

o C col

ot ¼ 1

o
or

Þ d col ð 1 þ C tgf
K ct

ð C col Þ N fib ; ð 38 Þ

rvC col

r

þ d gch ð 1 C gag Þ N chn d gag C gag ;

o C gag
ot

¼ 1
r

o
or

rvC gag ð 39 Þ

r ðÞ¼ H A vc d col ð 1 þ C tgf
K ct

1
r

o
or

C col Þ N fib

ð 40 Þ

þ H A vg d gch ð 1 C gag Þ N chn d gag C gag ;

dR l
dt ¼ v ð R l ; t Þ;

dR c
dt ¼ v ð R c ; t Þ:

ð 41 Þ

The boundary conditions are