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Landesberg, Sideman, 1994
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Mechanical regulation of cardiac muscle by coupling calcium kinetics with cross-bridge cycling: a dynamic model
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Model Mathematics
Component based math viewer is available
Component: environment
Component: parameters
L_m
=
L_prime_m
-
L_b
K_1
=
k_1
Ca
K_m
=
k_m
Ca
k_m
=
k_1
k_minus_1
=
k_1
K_max
k_minus_m
=
k_minus_1
g_prime_0
=
g_0
g_prime_1
=
g_1
Component: non_overlap
Rbar_n
=
A_n
k_minus_1
1
+
K_1
R_n
=
Rbar_n
alpha
L_m
Abar_n
=
R_n
K_1
1
+
k_minus_1
A_n
=
Abar_n
alpha
L_m
Component: single_overlap
dRbar_s_dt
=
-
K_1
R_s
+
k_minus_1
A_s
+
g_prime_0
+
g_prime_1
V
U_s
d
d
time
Rbar_s
=
dRbar_s_dt
d
d
time
R_s
=
dRbar_s_dt
alpha
L_m
-
Rbar_s
L_m
V
if
V
>
0
dRbar_s_dt
alpha
L_m
+
2
Rbar_d
-
Rbar_s
L_m
|
V
|
if
V
<
0
dRbar_s_dt
alpha
L_m
otherwise
dAbar_s_dt
=
K_1
R_s
+
-
f
-
k_minus_1
A_s
+
g_0
+
g_1
V
T_s
d
d
time
Abar_s
=
dAbar_s_dt
d
d
time
A_s
=
dAbar_s_dt
alpha
L_m
-
Abar_s
L_m
V
if
V
>
0
dAbar_s_dt
alpha
L_m
+
2
Abar_d
-
Abar_s
L_m
|
V
|
if
V
<
0
dAbar_s_dt
alpha
L_m
otherwise
dTbar_s_dt
=
f
A_s
+
-
g_0
-
g_1
V
-
k_minus_m
T_s
+
K_m
U_s
d
d
time
Tbar_s
=
dTbar_s_dt
d
d
time
T_s
=
dTbar_s_dt
alpha
L_m
-
Tbar_s
L_m
V
if
V
>
0
dTbar_s_dt
alpha
L_m
+
2
Tbar_d
-
Tbar_s
L_m
|
V
|
if
V
<
0
dTbar_s_dt
alpha
L_m
otherwise
dUbar_s_dt
=
k_minus_m
T_s
+
-
K_m
-
g_prime_0
-
g_prime_1
V
U_s
d
d
time
Ubar_s
=
dUbar_s_dt
d
d
time
U_s
=
dUbar_s_dt
alpha
L_m
-
Ubar_s
L_m
V
if
V
>
0
dUbar_s_dt
alpha
L_m
+
2
Ubar_d
-
Ubar_s
L_m
|
V
|
if
V
<
0
dUbar_s_dt
alpha
L_m
otherwise
Component: double_overlap
d
d
time
Rbar_d
=
-
K_1
R_d
+
k_minus_1
A_d
+
g_prime_0
+
g_prime_1
V
U_d
R_d
=
Rbar_d
alpha
L_m
d
d
time
Abar_d
=
K_1
R_d
+
-
f
-
k_minus_1
A_d
+
g_0
+
g_1
V
T_d
A_d
=
Abar_d
alpha
L_m
d
d
time
Tbar_d
=
f
A_d
+
-
g_0
-
g_1
V
-
k_minus_m
T_d
+
K_m
U_d
T_d
=
Tbar_d
alpha
L_m
d
d
time
Ubar_d
=
k_minus_m
T_d
+
-
K_m
-
g_prime_0
-
g_prime_1
V
U_d
U_d
=
Ubar_d
alpha
L_m
Component: calcium_flux
I_o
=
Q_o
Ca
I_s
=
Q_s
1
-
ⅇ
-
time
tau_SR
ⅇ
-
time
tau_SF
+
I_l
Ca_0
I_i
=
Q_i
1
-
ⅇ
-
time
tau_iR
ⅇ
-
time
tau_iF
+
I_l
Ca_r
I_u
=
Q_u
Ca
K_mu
+
Ca
d
d
time
Ca
=
I_s
+
I_i
-
I_o
+
I_u
Component: bound_calcium
BCa_L
=
A_s
+
T_s
+
A_d
+
T_d
+
A_n
d
d
time
BCa_h
=
2
TRo
-
BCa_h
Ca
k_h
-
BCa_h
k_minus_h
Component: force_equations
F_CB
=
F_bar
-
eta
V
F_CE
=
T_s
+
U_s
F_CB
F_PE
=
E
ⅇ
D
SL
Sp_0
-
1
-
1
+
eta_PE
V_SL
if
SL
≥
Sp_0
-
B
1
-
SL
Sp_0
+
eta_PE
V_SL
otherwise
F
=
F_CE
+
F_PE
Component: input
V
=
d_alpha_dt
Source
Derived from workspace
Landesberg, Sideman, 1994
at changeset
614313fee8ac
.
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Creative Commons Attribution 3.0 Unported License
.
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Mechanical regulation of cardiac muscle by coupling calcium kinetics with cross-bridge cycling: a dynamic model