cellml-discussion - [cellml-discussion] Content MathML editing language: Feedback on initial MathML => editing language output sought

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[cellml-discussion] Content MathML editing language: Feedback on initial MathML => editing language output sought

From: ak.miller at auckland.ac.nz (Andrew Miller)
Subject: [cellml-discussion] Content MathML editing language: Feedback on initial MathML => editing language output sought
Date: Fri, 24 Nov 2006 15:34:43 +1300

Hi all,

At the last CellML meeting, some people were keen to see what the
editable math format looked like for some models. I have now got the
code to generate this working, so please let me know what you think. I
am particularly keen to hear opinions on the notation we should use for
power (we could use power(x,2.0) or something like x^2.0 (another option
would be to use ^ to mean exclusive-OR). Opinions on precedence, the
bracket minimisation algorithm used to generate the below, and the
notation for attaching things like units are also wanted.

Note that equations will be edited one at a time, not all together as
listed below...

Coupled pendulum model...
==== Component environment ====
==== Component PendulumUpperSegment ====
d(a)/d(time) = a_angular_velocity
==== Component PendulumLowerSegment ====
d(b)/d(time) = b_angular_velocity
==== Component Pendulum ====
d(a_angular_velocity)/d(time) = -2.0{units="dimensionless"} * a + b
d(b_angular_velocity)/d(time) = 2.0{units="dimensionless"} * a -
2{units="dimensionless"} * b
==== Component analytic_solution ====
a_ = 0.5{units="dimensionless"} *
cos(0.765366864730179{units="dimensionless"} * time) +
0.25{units="dimensionless"} * 1.41421356237310{units="dimensionless"} *
cos(0.765366864730179{units="dimensionless"} * time) +
0.5{units="dimensionless"} * cos(1.84775906502257{units="dimensionless"}
* time) + -0.25{units="dimensionless"} *
1.41421356237310{units="dimensionless"} *
cos(1.84775906502257{units="dimensionless"} * time)
b_ = 0.5{units="dimensionless"} *
1.41421356237310{units="dimensionless"} *
cos(0.765366864730179{units="dimensionless"} * time) +
0.5{units="dimensionless"} *
cos(0.765366864730179{units="dimensionless"} * time) +
-0.5{units="dimensionless"} * 1.41421356237310{units="dimensionless"} *
cos(1.84775906502257{units="dimensionless"} * time) +
0.5{units="dimensionless"} * cos(1.84775906502257{units="dimensionless"}
* time)
==== Component errors ====
error_A = power(a - a_, 2{units="dimensionless"})
error_B = power(b - b_, 2{units="dimensionless"})
RSS = error_A + error_B

Beeler-Reuter...
==== Component environment ====
==== Component membrane ====
d( V )/d( time ) ={id="membrane_voltage_diff_eq"} (Istim - i_Na + i_s
+ i_x1 + i_K1 ) / C
IStimC ={id="IStim_for_cmiss"} Istim
==== Component sodium_current ====
i_Na ={id="i_Na_calculation"} ( g_Na * power( m , 3.0
{units="dimensionless"}) * h * j + g_Nac ) * ( V - E_Na )
==== Component sodium_current_m_gate ====
alpha_m ={id="alpha_m_calculation"} ( -1 {units="per_mV_ms"} * ( V +
47.0 {units="mV"})) / (exp( -0.1 {units="per_mV"} * ( V + 47.0
{units="mV"})) - 1.0 {units="dimensionless"})
beta_m ={id="beta_m_calculation"} 40.0 {units="per_ms"} * exp( -0.056
{units="per_mV"} * ( V + 72.0 {units="mV"}))
d( m )/d( time ) ={id="dm_dt"} alpha_m * ( 1.0 {units="per_mV"} - m )
- beta_m * m
==== Component sodium_current_h_gate ====
alpha_h ={id="alpha_h_calculation"} 0.126 {units="per_ms"} * exp(
-0.25 {units="per_mV"} * ( V + 77.0 {units="mV"}))
beta_h ={id="beta_h_calculation"} 1.7 {units="per_ms"} / (exp( -0.082
{units="per_mV"} * ( V + 22.5 {units="mV"})) + 1.0
{units="dimensionless"})
d( h )/d( time ) ={id="dh_dt"} alpha_h * ( 1.0 {units="dimensionless"}
- h ) - beta_h * h
==== Component sodium_current_j_gate ====
alpha_j ={id="alpha_j_calculation"} ( 0.055 {units="per_ms"} * exp(
-0.25 {units="per_mV"} * ( V + 78.0 {units="mV"}))) / (exp( -0.2
{units="per_mV"} * ( V + 78.0 {units="mV"})) + 1.0
{units="dimensionless"})
beta_j ={id="beta_j_calculation"} 0.3 {units="per_ms"} / (exp( -0.1
{units="per_mV"} * ( V + 32.0 {units="mV"})) + 1.0
{units="dimensionless"})
d( j )/d( time ) ={id="dj_dt"} alpha_j * ( 1.0 {units="dimensionless"}
- j ) - beta_j * j
==== Component slow_inward_current ====
E_s ={id="E_s_calculation"} -82.3 {units="mV"} - 13.0287
{units="mV"} * ln( Cai * 0.001{units="per_concentration_units"})
i_s ={id="i_s_calculation"} g_s * d * f * ( V - E_s )
d( Cai )/d( time ) ={id="dCai_dt"} -0.01 {units="dimensionless"} *
i_s + 0.07 {units="dimensionless"} * ( 0.0001 {units="dimensionless"}
- Cai )
==== Component slow_inward_current_d_gate ====
alpha_d ={id="alpha_d_calculation"} ( 0.095 {units="per_ms"} * exp((
V - 5.0 {units="mV"}) / 100.0 {units="mV"})) / ( 1.0
{units="dimensionless"} + exp(( V - 5.0 {units="mV"}) / 13.89
{units="mV"}))
beta_d ={id="beta_d_calculation"} ( 0.07 {units="per_ms"} * exp(( V
+ 44.0 {units="mV"}) / 59.0 {units="mV"})) / ( 1.0
{units="dimensionless"} + exp(( V + 44.0 {units="mV"}) / 20.0
{units="mV"}))
d( d )/d( time ) ={id="dd_dt"} alpha_d * ( 1.0 {units="dimensionless"}
- d ) - beta_d * d
==== Component slow_inward_current_f_gate ====
alpha_f ={id="alpha_f_calculation"} ( 0.012 {units="per_ms"} * exp((
V + 28.0 {units="mV"}) / 125.0 {units="mV"})) / ( 1.0
{units="dimensionless"} + exp(( V + 28.0 {units="mV"}) / 6.67
{units="mV"}))
beta_f ={id="beta_f_calculation"} ( 0.0065 {units="per_ms"} * exp(( V
+ 30.0 {units="mV"}) / 50.0 {units="mV"})) / ( 1.0
{units="dimensionless"} + exp(( V + 30.0 {units="mV"}) / 5.0
{units="mV"}))
d( f )/d( time ) ={id="df_dt"} alpha_f * ( 1.0 {units="dimensionless"}
- f ) - beta_f * f
==== Component time_dependent_outward_current ====
i_x1 ={id="i_x1_calculation"} x1 * 8.0e-3 {units="dimensionless"} *
(exp( 0.04 {units="per_mV"} * ( V + 77.0 {units="mV"})) - 1.0
{units="dimensionless"}) / exp( 0.04 {units="per_mV"} * ( V + 35.0
{units="mV"}))
==== Component time_dependent_outward_current_x1_gate ====
alpha_x1 ={id="alpha_x1_calculation"} 5e-4 {units="per_ms"} * exp((
V + 50.0 {units="mV"}) / 12.1 {units="mV"}) / ( 1.0
{units="dimensionless"} + exp(( V + 50.0 {units="mV"}) / 17.5
{units="mV"}))
beta_x1 ={id="beta_x1_calculation"} 0.0013 {units="per_ms"} * exp((
V + 20.0 {units="mV"}) / 16.67 {units="mV"}) / ( 1.0
{units="dimensionless"} + exp(( V + 20.0 {units="mV"}) / 25.0
{units="mV"}))
d( x1 )/d( time ) ={id="dx1_dt"} alpha_x1 * ( 1.0 {units="per_mV"} -
x1 ) - beta_x1 * x1
==== Component time_independent_outward_current ====
i_K1 ={id="i_K1_calculation"} 0.0035 {units="dimensionless"} * ( 4.0
{units="per_ms"} * (exp( 0.04 {units="per_mV"} * ( V + 85.0
{units="mV"})) - 1.0 {units="dimensionless"}) / (exp( 0.08
{units="per_mV"} * ( V + 53 {units="mV"})) + exp( 0.04
{units="per_mV"} * ( V + 53.0 {units="mV"}))) + 0.2 {units="per_ms"}
* ( V + 23.0 {units="mV"}) / ( 1.0 {units="dimensionless"} - exp(
-0.04 {units="per_mV"} * ( V + 23.0 {units="mV"}))))

Andre's version of the ten Tusscher model, in the increasing frequency
epicardial experiment...
=== Summary of Equations ===
==== Component time ====
==== Component stimulus_protocol_params ====
stimPeriod = piecewise(case time < 600e3{units="ms"} then
4e3{units="ms"} case time >= 600e3{units="ms"} & time <
1200e3{units="ms"} then 2e3{units="ms"} case time >= 1200e3{units="ms"}
& time < 1800e3{units="ms"} then 1e3{units="ms"} case time >=
1800e3{units="ms"} & time < 2400e3{units="ms"} then 666.66{units="ms"}
case time >= 2400e3{units="ms"} & time < 3000e3{units="ms"} then
500{units="ms"} case time >= 3000e3{units="ms"} & time <
3600e3{units="ms"} then 400{units="ms"} case time >= 3600e3{units="ms"}
& time < 4200e3{units="ms"} then 333.33{units="ms"} else 1e3{units="ms"})
==== Component parameters ====
==== Component initial_conditions ====
==== Component interface ====
==== Component membrane_potential ====
d(V)/d(time) ={id="membrane_voltage_diff_eq"} (Istim - INa + IK1 + Ito +
IKr + IKs + ICaL + INaCa + INaK + IbNa + IbCa + IpCa + IpK) / Cm
==== Component one_ion ====
reversal_potential = ((R * T) / z * F) * ln(extracellular_concentration
/ intracellular_concentration)
==== Component two_ions ====
reversal_potential = ((R * T) / z * F) * ln((multiplier_1 *
extracellular_concentration_1 + multiplier_2 *
extracellular_concentration_2) / (multiplier_1 *
intracellular_concentration_1 + multiplier_2 *
intracellular_concentration_2))
==== Component one_ion ====
reversal_potential = ((R * T) / z * F) * ln(extracellular_concentration
/ intracellular_concentration)
==== Component two_ions ====
reversal_potential = ((R * T) / z * F) * ln((multiplier_1 *
extracellular_concentration_1 + multiplier_2 *
extracellular_concentration_2) / (multiplier_1 *
intracellular_concentration_1 + multiplier_2 *
intracellular_concentration_2))
==== Component one_ion ====
reversal_potential = ((R * T) / z * F) * ln(extracellular_concentration
/ intracellular_concentration)
==== Component two_ions ====
reversal_potential = ((R * T) / z * F) * ln((multiplier_1 *
extracellular_concentration_1 + multiplier_2 *
extracellular_concentration_2) / (multiplier_1 *
intracellular_concentration_1 + multiplier_2 *
intracellular_concentration_2))
==== Component one_ion ====
reversal_potential = ((R * T) / z * F) * ln(extracellular_concentration
/ intracellular_concentration)
==== Component two_ions ====
reversal_potential = ((R * T) / z * F) * ln((multiplier_1 *
extracellular_concentration_1 + multiplier_2 *
extracellular_concentration_2) / (multiplier_1 *
intracellular_concentration_1 + multiplier_2 *
intracellular_concentration_2))
==== Component INa ====
INa ={id="INa_calculation"} g_Na * power(m, 3.0{units="dimensionless"})
* h * j * (V - E_Na)
==== Component m_gate ====
m_infinity ={id="m_infinity_calculation"} 1.0{units="dimensionless"} /
power(1.0{units="dimensionless"} + exp((-56.86{units="mV"} - V) /
9.03{units="mV"}), 2.0{units="dimensionless"})
alpha_m ={id="alpha_m_calculation"} 1.0{units="per_ms"} /
(1.0{units="dimensionless"} + exp((-60.0{units="mV"} - V) /
5.0{units="mV"}))
beta_m ={id="beta_m_calculation"} 0.1{units="per_ms"} /
(1.0{units="dimensionless"} + exp((35.0{units="mV"} + V) /
5.0{units="mV"})) + 0.1{units="per_ms"} / (1.0{units="dimensionless"} +
exp((V - 50.0{units="mV"}) / 200.0{units="mV"}))
tau_m ={id="tau_m_calculation"} 1.0{units="mscu"} * alpha_m * beta_m
d(m)/d(time) ={id="dm_dt"} (m_infinity - m) / tau_m
==== Component h_gate ====
h_infinity ={id="h_infinity_calculation"} 1.0{units="dimensionless"} /
power(1.0{units="dimensionless"} + exp((71.55{units="mV"} + V) /
7.43{units="mV"}), 2.0{units="dimensionless"})
alpha_h ={id="alpha_h_calculation"} piecewise(case V < -40.0{units="mV"}
then 0.057{units="per_ms"} * exp(((80.0{units="mV"} + V)) /
6.8{units="mV"}) else 0.0{units="per_ms"})
beta_h ={id="beta_h_calculation"} piecewise(case V < -40.0{units="mV"}
then 2.7{units="per_ms"} * exp(0.079{units="per_mV"} * V) +
3.1E5{units="per_ms"} * exp(0.3485{units="per_mV"} * V) else
0.77{units="dimensionless"} / 0.13{units="ms"} *
(1.0{units="dimensionless"} + exp(((V + 10.66{units="mV"})) /
11.1{units="mV"})))
tau_h ={id="tau_h_calculation"} 1.0{units="dimensionless"} / (alpha_h +
beta_h)
d(h)/d(time) ={id="dh_dt"} (h_infinity - h) / tau_h
==== Component j_gate ====
j_infinity ={id="j_infinity_calculation"} 1.0{units="dimensionless"} /
power(1.0{units="dimensionless"} + exp((71.55{units="mV"} + V) /
7.43{units="mV"}), 2.0{units="dimensionless"})
alpha_j ={id="alpha_j_calculation"} piecewise(case V < -40.0{units="mV"}
then ((-2.5428E4{units="per_mV_per_ms"} * exp(0.2444{units="per_mV"} *
V) - 6.948E-6{units="per_mV_per_ms"} * exp(-0.04391{units="per_mV"} *
V)) * (V + 37.78{units="mV"})) / (1.0{units="dimensionless"} +
exp(0.311{units="per_mV"} * (V + 79.23{units="mV"}))) else
0.0{units="per_ms"})
beta_j ={id="beta_j_calculation"} piecewise(case V < -40.0{units="mV"}
then (0.02424{units="per_ms"} * exp(-0.01052{units="per_mV"} * V)) /
(1.0{units="dimensionless"} + exp(-0.1378{units="per_mV"} * (V +
40.14{units="mV"}))) else (0.6{units="per_ms"} *
exp(0.057{units="per_mV"} * V)) / (1.0{units="dimensionless"} +
exp(-0.1{units="per_mV"} * (V + 32.0{units="mV"}))))
tau_j ={id="tau_j_calculation"} 1.0{units="dimensionless"} / (alpha_j +
beta_j)
d(j)/d(time) ={id="dj_dt"} (j_infinity - j) / tau_j
==== Component IK1 ====
IK1 ={id="i_K1_calculation"} g_K1 * root(Ko / 5.4{units="mM"}) *
K1_infinity * (V - E_K)
==== Component K1_gate ====
K1_infinity ={id="K1_infinity_calculation"} alpha_K1 / (alpha_K1 + beta_K1)
alpha_K1 ={id="alpha_K1_calculation"} 0.1{units="dimensionless"} /
(1.0{units="dimensionless"} + exp(0.06{units="per_mV"} * (V - E_K +
200.0{units="mV"})))
beta_K1 ={id="beta_K1_calculation"} (3.0{units="dimensionless"} *
exp(0.0002{units="per_mV"} * ((V - E_K) + 100.0{units="mV"})) +
exp(0.1{units="per_mV"} * (V - E_K + 10.0{units="mV"}))) /
(1.0{units="dimensionless"} + exp(-0.5{units="per_mV"} * (V - E_K)))
==== Component current ====
Ito ={id="i_to_calculation"} g_to * r * s * (V - E_K)
==== Component r_gate ====
d(r)/d(time) ={id="r_diff_eq"} (r_infinity - r) / tau_r
r_infinity ={id="r_infinity_calculation"} 1.0{units="dimensionless"} /
(1.0{units="dimensionless"} + exp((20.0{units="mV"} - V) / 6.0{units="mV"}))
tau_r ={id="tau_r_calculation"} 9.5{units="ms"} * exp((power(V +
40.0{units="mV"}, 2.0{units="dimensionless"})) / 1800.0{units="mVsq"}) +
0.8{units="ms"}
==== Component epi_M_s_gate ====
d(s)/d(time) ={id="s_diff_eq"} (s_infinity - s) / tau_s
s_infinity ={id="s_infinity_calculation"} 1.0{units="dimensionless"} /
(1.0{units="dimensionless"} + exp((20.0{units="mV"} + V) / 5.0{units="mV"}))
tau_s ={id="tau_s_calculation"} 85.0{units="ms"} * exp((power(V +
45.0{units="mV"}, 2.0{units="dimensionless"})) / 320.0{units="mVsq"}) +
5.0{units="ms"} / (1.0{units="dimensionless"} + exp((V -
20.0{units="mV"}) / 5.0{units="mV"})) + 3.0{units="ms"}
==== Component endo_s_gate ====
d(s)/d(time) ={id="s_diff_eq"} (s_infinity - s) / tau_s
s_infinity ={id="s_infinity_calculation"} 1.0{units="dimensionless"} /
(1.0{units="dimensionless"} + exp((28.0{units="mV"} + V) / 5.0{units="mV"}))
tau_s ={id="tau_s_calculation"} 1000.0{units="ms"} * exp((power(V +
67.0{units="mV"}, 2.0{units="dimensionless"})) / 1000.0{units="mVsq"}) +
8.0{units="ms"}
==== Component IKr ====
IKr ={id="i_Kr_calculation"} g_Kr * root(Ko / 5.4{units="mM"}) * Xr1 *
Xr2 * (V - E_K)
==== Component Xr1_gate ====
d(Xr1)/d(time) ={id="Xr1_diff_eq"} (Xr1_infinity - Xr1) / tau_Xr1
Xr1_infinity ={id="Xr1_infinity_calculation"} 1.0{units="dimensionless"}
/ (1.0{units="dimensionless"} + exp((-26.0{units="mV"} - V) /
7.0{units="mV"}))
alpha_Xr1 ={id="alpha_Xr1_calculation"} 450{units="per_ms"} /
(1.0{units="dimensionless"} + exp((-45.0{units="mV"} - V) /
10.0{units="mV"}))
beta_Xr1 ={id="beta_Xr1_calculation"} 6.0{units="per_ms"} /
(1.0{units="dimensionless"} + exp((V + 30.0{units="mV"}) /
11.5{units="mV"}))
tau_Xr1 ={id="tau_Xr1_calculation"} 1.0{units="mscu"} * alpha_Xr1 * beta_Xr1
==== Component Xr2_gate ====
d(Xr2)/d(time) ={id="Xr2_diff_eq"} (Xr2_infinity - Xr2) / tau_Xr2
Xr2_infinity ={id="Xr2_infinity_calculation"} 1.0{units="dimensionless"}
/ (1.0{units="dimensionless"} + exp((88.0{units="mV"} + V) /
24.0{units="mV"}))
alpha_Xr2 ={id="alpha_Xr2_calculation"} 3.0{units="per_ms"} /
(1.0{units="dimensionless"} + exp((-60.0{units="mV"} - V) /
20.0{units="mV"}))
beta_Xr2 ={id="beta_Xr2_calculation"} 1.12{units="per_ms"} /
(1.0{units="dimensionless"} + exp((V - 60.0{units="mV"}) /
20.0{units="mV"}))
tau_Xr2 ={id="tau_Xr2_calculation"} 1.0{units="mscu"} * alpha_Xr2 * beta_Xr2
==== Component IKs ====
IKs ={id="i_Ks_calculation"} g_Ks * power(Xs,
2.0{units="dimensionless"}) * (V - E_Ks)
==== Component Xs_gate ====
d(Xs)/d(time) ={id="Xs_diff_eq"} (Xs_infinity - Xs) / tau_Xs
Xs_infinity ={id="Xs_infinity_calculation"} 1.0{units="dimensionless"} /
(1.0{units="dimensionless"} + exp((-5.0{units="mV"} - V) /
14.0{units="mV"}))
alpha_Xs ={id="alpha_Xs_calculation"} 1100{units="per_ms"} /
root(1.0{units="dimensionless"} + exp((-10.0{units="mV"} - V) /
6.0{units="mV"}))
beta_Xs ={id="beta_Xs_calculation"} 1.0{units="per_ms"} /
(1.0{units="dimensionless"} + exp((V - 60.0{units="mV"}) /
20.0{units="mV"}))
tau_Xs ={id="tau_Xs_calculation"} 1.0{units="mscu"} * alpha_Xs * beta_Xs
==== Component INaK ====
INaK ={id="i_NaK_calculation"} P_NaK * (Ko * Nai) / (Ko + K_mK) * (Nai +
K_mNa) * (1.0{units="dimensionless"} + 0.1245{units="dimensionless"} *
exp((-0.1{units="dimensionless"} * V * F) / R * T) +
0.0353{units="dimensionless"} * exp(((V) * F) / R * T))
==== Component IpK ====
IpK ={id="i_pK_calculation"} g_pK * (V - E_K) /
(1.0{units="dimensionless"} + exp((25.0{units="mV"} - V) /
5.98{units="mV"}))
==== Component IbNa ====
IbNa ={id="i_bNa_calculation"} g_bNa * (V - E_Na)
==== Component ICaL ====
ICaL ={id="i_CaL_calculation"} g_CaL * d * f * fCa *
4.0{units="dimensionless"} * (V * power(F, 2.0{units="dimensionless"}))
/ R * T * (Cai * exp((2.0{units="dimensionless"} * V * F) / R * T) -
0.341{units="dimensionless"} * Cao) / (exp((2.0{units="dimensionless"} *
V * F) / R * T) - 1.0{units="dimensionless"})
==== Component d_gate ====
d_infinity ={id="d_infinity_calculation"} 1.0{units="dimensionless"} /
(1.0{units="dimensionless"} + exp((-5.0{units="mV"} - V) / 7.5{units="mV"}))
alpha_d ={id="alpha_d_calculation"} 1.4{units="per_ms"} /
(1.0{units="dimensionless"} + exp((-35.0{units="mV"} - V) /
13.0{units="mV"})) + 0.25{units="per_ms"}
beta_d ={id="beta_d_calculation"} 1.4{units="per_ms"} /
(1.0{units="dimensionless"} + exp((5.0{units="mV"} + V) / 5.0{units="mV"}))
gamma_d ={id="gamma_d_calculation"} 1.0{units="ms"} /
(1.0{units="dimensionless"} + exp((50.0{units="mV"} - V) /
20.0{units="mV"}))
tau_d ={id="tau_d_calculation"} 1.0{units="mscu"} * alpha_d * beta_d +
gamma_d
d(d)/d(time) ={id="dd_dt"} (d_infinity - d) / tau_d
==== Component f_gate ====
f_infinity ={id="f_infinity_calculation"} 1.0{units="dimensionless"} /
(1.0{units="dimensionless"} + exp((20.0{units="mV"} + V) / 7.0{units="mV"}))
tau_f ={id="tau_f_calculation"} 1125.0{units="ms"} * exp((power(V +
27.0{units="mV"}, 2.0{units="dimensionless"})) / 240.0{units="mVsq"}) +
165.0{units="ms"} / (1.0{units="dimensionless"} + exp((25.0{units="mV"}
- V) / 10.0{units="mV"})) + 80.0{units="ms"}
d(f)/d(time) ={id="df_dt"} (f_infinity - f) / tau_f
==== Component fCa_gate ====
fCa_infinity ={id="fCa_infinity_calculation"} (alpha_fCa + beta_fCa +
gamma_fCa + 0.23{units="dimensionless"}) / 1.46{units="dimensionless"}
alpha_fCa ={id="alpha_fCa_calculation"} 1.0{units="dimensionless"} /
(1.0{units="dimensionless"} + power(Cai / 0.000325{units="mM"},
8.0{units="dimensionless"}))
beta_fCa ={id="beta_fCa_calculation"} 0.1{units="dimensionless"} /
(1.0{units="dimensionless"} + exp((Cai - 0.0005{units="mM"}) /
0.0001{units="mM"}))
gamma_fCa ={id="gamma_fCa_calculation"} 0.2{units="dimensionless"} /
(1.0{units="dimensionless"} + exp((Cai - 0.00075{units="mM"}) /
0.0008{units="mM"}))
d(fCa)/d(time) ={id="dfCa_dt"} piecewise(case fCa_infinity > fCa & V >
-60.0{units="mV"} then 0.0{units="per_ms"} else (fCa_infinity - fCa) /
tau_fCa)
==== Component IpCa ====
IpCa ={id="i_pCa_calculation"} g_pCa * Cai / (K_pCa + Cai)
==== Component INaCa ====
INaCa ={id="Na_Ca_exchanger"} k_NaCa * (exp((gamma * V * F) / R * T) *
power(Nai, 3.0{units="dimensionless"}) * Cao - exp(((gamma -
1.0{units="dimensionless"}) * V * F) / R * T) * power(Nao,
3.0{units="dimensionless"}) * Cai * alpha) / (power(K_mNai,
3.0{units="dimensionless"}) + power(Nao, 3.0{units="dimensionless"})) *
(K_mCa + Cao) * (1.0{units="dimensionless"} + k_sat * exp(((gamma -
1.0{units="dimensionless"}) * V * F) / R * T))
==== Component IbCa ====
IbCa ={id="i_bCa_calculation"} g_bCa * (V - E_Ca)
==== Component sodium_dynamics ====
d( Nai )/d(time) ={id="Nai_total_diff"} (Am / vC * F ) * ( INa +
IbNa + INaK * 3.0 {units="dimensionless"} + INaCa * 3.0
{units="dimensionless"})
==== Component potassium_dynamics ====
d( Ki )/d(time) ={id="Ki_total_diff"} (Am / vC * F ) * (( IK1 +
Ito + IKr + IKs + IpK ) - INaK * 2.0 {units="dimensionless"} +
Istim)
==== Component calcium_dynamics ====
aCai = -1.0{units="dimensionless"}
bCai = Cai_total + Kbufc + Bufc
cCai = Bufc * Cai_total
Cai_buf = (root(power(bCai, 2.0{units="dimensionless"}) -
4.0{units="dimensionless"} * aCai * cCai) - bCai) /
2.0{units="dimensionless"} * aCai
Cai = Cai_total - Cai_buf
d( Cai_total )/d(time) ={id="Cai_total_diff"} (Jleak + Jrel) - Jup + (Am
/ vC * 2.0{units="dimensionless"} * F ) * ((ICaL + IbCa + IpCa) -
2.0{units="dimensionless"} * INaCa)
aCaSR = -1.0{units="dimensionless"}
bCaSR = CaSR_total + Kbufsr + Bufsr
cCaSR = Bufsr * CaSR_total
CaSR_buf = (root(power(bCaSR, 2.0{units="dimensionless"}) -
4.0{units="dimensionless"} * aCaSR * cCaSR) - bCaSR) /
2.0{units="dimensionless"} * aCaSR
CaSR = CaSR_total - CaSR_buf
d( CaSR_total )/d(time) ={id="CaSR_total_diff"} (vC / vSR) * (Jup -
Jleak + Jrel)
==== Component Jleak ====
Jleak ={id="Jleak_calculation"} V_leak * (CaSR - Cai)
==== Component Jup ====
Jup ={id="Jup_calculation"} Vmax_up / (1.0{units="dimensionless"} +
power(K_up, 2.0{units="dimensionless"}) / power(Cai,
2.0{units="dimensionless"}))
==== Component Jrel ====
Jrel ={id="j_rel_calculation"} (a_rel * power(CaSR,
2.0{units="dimensionless"}) / (power(b_rel, 2.0{units="dimensionless"})
+ power(CaSR, 2.0{units="dimensionless"})) + c_rel) * d * g
==== Component g_gate ====
g_infinity ={id="g_infinity_calculation"} piecewise(case Cai <=
0.00035{units="mM"} then 1.0{units="dimensionless"} /
(1.0{units="dimensionless"} + power(Cai, 6.0{units="dimensionless"}) /
power(0.00035{units="mM"}, 6.0{units="dimensionless"})) else
1.0{units="dimensionless"} / (1.0{units="dimensionless"} + power(Cai,
16.0{units="dimensionless"}) / power(0.00035{units="mM"},
16.0{units="dimensionless"})))
d(g)/d(time) ={id="dg_dt"} piecewise(case g_infinity > g & V >
-60.0{units="mV"} then 0.0{units="per_ms"} else (g_infinity - g) / tau_g)
==== Component stimulus_protocol ====
IStim ={id="stimulus_calculation"} piecewise(case rem(time, stimPeriod)
< stimDuration then stimCurrent / Am else 0.0{units="uA_per_mmsq"})

Winslow et. al., 1999:
=== Summary of Equations ===
==== Component environment ====
==== Component membrane ====
d( V )/d( time ) ={id="membrane_voltage_diff_eq"} ( i_Na + i_Ca +
i_Ca_K + i_Kr + i_Ks + i_to1 + i_K1 + i_Kp + i_NaCa +
i_NaK + i_p_Ca + i_Na_b + i_Ca_b )
==== Component fast_sodium_current ====
i_Na ={id="i_Na_calculation"} g_Na * power( m , 3.0
{units="dimensionless"}) * h * j * ( V - E_Na )
E_Na ={id="E_Na_calculation"} (( R * T ) / F ) * ln( Nao / Nai )
==== Component fast_sodium_current_m_gate ====
alpha_m ={id="alpha_m_calculation"} ( 0.32
{units="per_millivolt_millisecond"} * ( V + 47.13
{units="millivolt"})) / ( 1.0 {units="dimensionless"} - exp( -0.1
{units="per_millivolt"} * ( V + 47.13 {units="millivolt"})))
beta_m ={id="beta_m_calculation"} 0.08 {units="per_millisecond"} *
exp(( V ) / 11.0 {units="millivolt"})
d( m )/d( time ) ={id="dm_dt"} alpha_m * ( 1.0 {units="dimensionless"}
- m ) - beta_m * m
==== Component fast_sodium_current_h_gate ====
alpha_h ={id="alpha_h_calculation"} piecewise(case V < -40.0
{units="millivolt"} then 0.135 {units="per_millisecond"} * exp(( 80.0
{units="millivolt"} + V ) / -6.8 {units="millivolt"}) else 0.0
{units="per_millisecond"})
beta_h ={id="beta_h_calculation"} piecewise(case V < -40.0
{units="millivolt"} then 3.56 {units="per_millisecond"} * exp( 0.079
{units="millivolt"} * V ) + 310000.0 {units="per_millisecond"} * exp(
0.35 {units="per_millivolt"} * V ) else 1.0 {units="dimensionless"} /
0.13 {units="millisecond"} * ( 1.0 {units="dimensionless"} + exp(( V +
10.66 {units="millivolt"}) / -11.1 {units="millivolt"})))
d( h )/d( time ) ={id="dh_dt"} alpha_h * ( 1.0 {units="dimensionless"}
- h ) - beta_h * h
==== Component fast_sodium_current_j_gate ====
alpha_j ={id="alpha_j_calculation"} piecewise(case V < -40.0
{units="millivolt"} then ( -127140.0
{units="per_millivolt_millisecond"} * exp( 0.2444
{units="per_millivolt"} * V ) - 0.00003474
{units="per_millivolt_millisecond"} * exp( -0.04391
{units="per_millivolt"} * V )) * ( V + 37.78 {units="millivolt"}) / (
1.0 {units="dimensionless"} + exp( 0.311 {units="per_millivolt"} * ( V
+ 79.23 {units="millivolt"}))) else 0.0 {units="per_millisecond"})
beta_j ={id="beta_j_calculation"} piecewise(case V < -40.0
{units="millivolt"} then ( 0.1212 {units="per_millisecond"} * exp(
-0.01052 {units="per_millivolt"} * V )) / ( 1.0 {units="dimensionless"}
+ exp( -0.1378 {units="per_millivolt"} * ( V + 40.14
{units="millivolt"}))) else ( 0.3 {units="per_millisecond"} * exp(
-0.0000002535 {units="per_millivolt"} * V )) / ( 1.0
{units="dimensionless"} + exp( -0.1 {units="per_millivolt"} * ( V +
32.0 {units="millivolt"}))))
d( j )/d( time ) ={id="dj_dt"} alpha_j * ( 1.0 {units="dimensionless"}
- j ) - beta_j * j
==== Component rapid_activating_delayed_rectifiyer_K_current ====
E_K ={id="E_K_calculation"} (( R * T ) / F ) * ln( Ko / Ki )
i_Kr ={id="i_Kr_calculation"} g_Kr * f_Ko * R_V * X_kr * ( V
- E_K )
f_Ko ={id="f_Ko_calculation"} root( Ko / 4.0 {units="millimolar"})
R_V ={id="R_V_calculation"} 1.0 {units="dimensionless"} / ( 1.0
{units="dimensionless"} + 1.4945 {units="dimensionless"} * exp( 0.0446
{units="dimensionless"} * V ))
==== Component rapid_activating_delayed_rectifiyer_K_current_X_kr_gate ====
d( X_kr )/d( time ) ={id="X_kr_diff_eq"} K12 * ( 1.0
{units="dimensionless"} - X_kr ) - K12 * X_kr
K12 ={id="K12_calculation"} exp( -5.495 {units="dimensionless"} +
0.169 {units="dimensionless"} * V )
K21 ={id="K21_calculation"} exp( -7.677 {units="dimensionless"} -
0.0128 {units="dimensionless"} * V )
==== Component slow_activating_delayed_rectifiyer_K_current ====
i_Ks ={id="i_Ks_calculation"} g_Ks * power( X_ks , 2.0
{units="dimensionless"}) * ( V - E_Ks )
E_Ks ={id="E_Ks_calculation"} (( R * T ) / F ) * ln(( Ko +
0.01833 {units="dimensionless"} * Nao ) / ( Ki + 0.01833
{units="dimensionless"} * Nai ))
==== Component slow_activating_delayed_rectifiyer_K_current_X_ks_gate ====
d( X_ks )/d( time ) ={id="X_ks_diff_eq"} ( X_ks_infinity - X_ks ) /
tau_X_ks
X_ks_infinity ={id="X_ks_infinity_calculation"} 1.0
{units="dimensionless"} / ( 1.0 {units="dimensionless"} + exp((( V -
24.7 {units="millivolt"})) / 13.6 {units="millivolt"}))
tau_X_ks ={id="tau_X_ks_calculation"} 1.0 {units="dimensionless"} /
(( 0.0000719 {units="dimensionless"} * ( V - 10.0
{units="millivolt"})) / ( 1.0 {units="dimensionless"} - exp( -0.148
{units="dimensionless"} * ( V - 10.0 {units="millivolt"}))) + (
0.000131 {units="dimensionless"} * ( V - 10.0 {units="millivolt"})) /
(exp( 0.0687 {units="dimensionless"} * ( V - 10.0
{units="millivolt"})) - 1.0 {units="dimensionless"}))
==== Component transient_outward_potassium_current ====
i_to1 ={id="i_to1_calculation"} g_to1 * X_to1 * Y_to1 * ( V -
E_K )
==== Component transient_outward_potassium_current_X_to1_gate ====
d( X_to1 )/d( time ) ={id="dX_to1_dt"} alpha_X_to1 * ( 1.0
{units="dimensionless"} - X_to1 ) - beta_X_to1 * X_to1
alpha_X_to1 ={id="alpha_X_to1_calculation"} 0.04561
{units="per_millisecond"} * exp( 0.03577 {units="dimensionless"} * V )
beta_X_to1 ={id="beta_X_to1_calculation"} 0.0989
{units="per_millisecond"} * exp( -0.06237 {units="dimensionless"} * V )
==== Component transient_outward_potassium_current_Y_to1_gate ====
d( Y_to1 )/d( time ) ={id="dY_to1_dt"} alpha_Y_to1 * ( 1.0
{units="dimensionless"} - Y_to1 ) - beta_Y_to1 * Y_to1
alpha_Y_to1 ={id="alpha_Y_to1_calculation"} ( 0.005415
{units="per_millisecond"} * exp(( V + 33.5 {units="millivolt"}) / 5.0
{units="millivolt"})) / ( 1.0 {units="dimensionless"} + 0.051335
{units="dimensionless"} * exp(( V + 33.5 {units="millivolt"}) / 5.0
{units="millivolt"}))
beta_Y_to1 ={id="beta_Y_to1_calculation"} ( 0.005415
{units="per_millisecond"} * exp(( V + 33.5 {units="millivolt"}) / 5.0
{units="millivolt"})) / ( 1.0 {units="dimensionless"} + 0.051335
{units="dimensionless"} * exp(( V + 33.5 {units="millivolt"}) / 5.0
{units="millivolt"}))
==== Component time_independent_potassium_current ====
i_K1 ={id="i_K1_calculation"} g_K1 * K1_infinity_V * Ko / ( Ko
+ K_mK1 ) * ( V - E_K )
==== Component time_independent_potassium_current_K1_gate ====
K1_infinity_V ={id="alpha_K1_calculation"} 1.0
{units="dimensionless"} / ( 2.0 {units="dimensionless"} + exp( 1.5
{units="dimensionless"} * F / R * T * ( V - E_K )))
==== Component plateau_potassium_current ====
i_Kp ={id="i_Kp_calculation"} g_Kp * Kp_V * ( V - E_K )
==== Component plateau_potassium_current_Kp_gate ====
Kp_V ={id="Kp_V_calculation"} 1.0 {units="dimensionless"} / ( 1.0
{units="dimensionless"} + exp(( 7.488 {units="millivolt"} - V ) / 5.98
{units="millivolt"}))
==== Component Na_Ca_exchanger ====
i_NaCa ={id="Na_Ca_exchanger"} K_NaCa * 5000.0
{units="dimensionless"} / (power( K_mNa , 3.0 {units="dimensionless"})
+ power( Nao , 3.0 {units="dimensionless"})) * 1.0
{units="dimensionless"} / ( K_mCa + Cao ) * 1.0
{units="dimensionless"} / ( 1.0 {units="dimensionless"} + K_sat *
exp(( eta - 1.0 {units="dimensionless"}) * V * F / R * T )) *
(exp( eta * V * F / R * T ) * power( Nai , 3.0
{units="dimensionless"}) * Cao - exp(( eta - 1.0
{units="dimensionless"}) * V * F / R * T ) * power( Nao , 3.0
{units="dimensionless"}) * Cai )
==== Component sodium_potassium_pump ====
f_NaK ={id="f_NaK_calculation"} 1.0 {units="dimensionless"} / (( 1.0
{units="dimensionless"} + 0.1245 {units="dimensionless"} * exp( -0.1
{units="dimensionless"} * ( V * F ) / R * T )) + 0.0365
{units="dimensionless"} * sigma * exp(( V * F ) / R * T ))
sigma ={id="sigma_calculation"} ( 1.0 {units="dimensionless"} / 7.0
{units="dimensionless"}) * (exp( Nao / 67.3 {units="dimensionless"})
- 1.0 {units="dimensionless"})
i_NaK ={id="i_NaK_calculation"} I_NaK * f_NaK * 1.0
{units="dimensionless"} / ( 1.0 {units="dimensionless"} + power( K_mNai
/ Nai , 1.5 {units="dimensionless"})) * Ko / ( Ko + K_mKo )
==== Component sarcolemmal_calcium_pump ====
i_p_Ca ={id="i_p_Ca_calculation"} I_pCa * Cai / ( K_mpCa + Cai )
==== Component calcium_background_current ====
E_Ca ={id="E_Ca_calculation"} (( R * T ) / 2.0
{units="dimensionless"} * F ) * ln( Cao / Cai )
i_Ca_b ={id="i_Ca_b_calculation"} g_Cab * ( V - E_Ca )
==== Component sodium_background_current ====
i_Na_b ={id="i_Na_b_calculation"} g_Nab * ( V - E_Na )
==== Component L_type_Ca_current ====
i_Ca ={id="i_Ca_calculation"} i_Ca_max * y * ( O + O_Ca )
i_Ca_K ={id="i_Ca_K_calculation"} ( p_k / C_sc ) * y * ( O +
O_Ca ) * ( V * power( F , 2.0 {units="dimensionless"})) / R * T *
( Ki * exp(( V * F ) / R * T ) - Ko ) / (exp(( V * F ) / R *
T ) - 1.0 {units="dimensionless"})
p_k ={id="p_k_calculation"} P_K / ( 1.0 {units="dimensionless"} +
i_Ca_max / i_Ca_half )
i_Ca_max ={id="i_Ca_max_calculation"} ( P_Ca / C_sc ) * ( 4.0
{units="dimensionless"} * V * power( F , 2.0
{units="dimensionless"})) / R * T * ( 0.001 {units="dimensionless"}
* exp(( 2.0 {units="dimensionless"} * V * F ) / R * T ) - 0.341
{units="dimensionless"} * Cao ) / (exp(( 2.0 {units="dimensionless"} *
V * F ) / R * T ) - 1.0 {units="dimensionless"})
alpha ={id="alpha_calculation"} 0.4 {units="per_millisecond"} * exp((
V + 2.0 {units="millivolt"}) / 10.0 {units="millivolt"})
beta ={id="beta_calculation"} 0.05 {units="per_millisecond"} * exp(((
V + 2.0 {units="millivolt"})) / 13.0 {units="millivolt"})
alpha_a ={id="alpha_a_calculation"} alpha * a
beta_b ={id="beta_b_calculation"} beta / b
gamma ={id="gamma_calculation"} 0.10375 {units="dimensionless"} * Ca_ss
d( C0 )/d( time ) ={id="C0_diff_eq"} ( beta * C1 + omega * C_Ca0 )
- ( 4.0 {units="dimensionless"} * alpha + gamma ) * C0
d( C1 )/d( time ) ={id="C1_diff_eq"} ( 4.0 {units="dimensionless"} *
alpha * C0 + 2.0 {units="dimensionless"} * beta * C2 + ( omega
/ b ) * C_Ca1 ) - ( beta + 3.0 {units="dimensionless"} * alpha +
gamma * a ) * C1
d( C2 )/d( time ) ={id="C2_diff_eq"} ( 3.0 {units="dimensionless"} *
alpha * C1 + 3.0 {units="dimensionless"} * beta * C3 + ( omega
/ power( b , 2.0 {units="dimensionless"})) * C_Ca2 ) - ( beta * 2.0
{units="dimensionless"} + 2.0 {units="dimensionless"} * alpha +
gamma * power( a , 2.0 {units="dimensionless"})) * C2
d( C3 )/d( time ) ={id="C3_diff_eq"} ( 2.0 {units="dimensionless"} *
alpha * C2 + 4.0 {units="dimensionless"} * beta * C4 + ( omega
/ power( b , 3.0 {units="dimensionless"})) * C_Ca3 ) - ( beta * 3.0
{units="dimensionless"} + alpha + gamma * power( a , 3.0
{units="dimensionless"})) * C3
d( C4 )/d( time ) ={id="C4_diff_eq"} ( alpha * C3 + g * O + (
omega / power( b , 4.0 {units="dimensionless"})) * C_Ca4 ) - ( beta
* 4.0 {units="dimensionless"} + f + gamma * power( a , 4.0
{units="dimensionless"})) * C4
d( O )/d( time ) ={id="O_diff_eq"} f * C4 - g * O
d( C_Ca0 )/d( time ) ={id="C_Ca0_diff_eq"} ( beta_b * C_Ca1 + gamma
* C_Ca0 ) - ( 4.0 {units="dimensionless"} * alpha_a + omega ) * C_Ca0
d( C_Ca1 )/d( time ) ={id="C_Ca1_diff_eq"} ( 4.0 {units="dimensionless"}
* alpha_a * C_Ca0 + 2.0 {units="dimensionless"} * beta_b *
C_Ca2 + gamma * a * C1 ) - ( beta_b + 3.0
{units="dimensionless"} * alpha_a + omega / b ) * C_Ca1
d( C_Ca2 )/d( time ) ={id="C_Ca2_diff_eq"} ( 3.0 {units="dimensionless"}
* alpha_a * C_Ca1 + 3.0 {units="dimensionless"} * beta_b *
C_Ca3 + gamma * power( a , 2.0 {units="dimensionless"}) * C2 ) - (
beta_b * 2.0 {units="dimensionless"} + 2.0 {units="dimensionless"} *
alpha_a + omega / power( b , 2.0 {units="dimensionless"})) * C_Ca2
d( C_Ca3 )/d( time ) ={id="C_Ca3_diff_eq"} ( 2.0 {units="dimensionless"}
* alpha_a * C_Ca2 + 4.0 {units="dimensionless"} * beta_b *
C_Ca4 + gamma * power( a , 3.0 {units="dimensionless"}) * C3 ) - (
beta_b * 3.0 {units="dimensionless"} + alpha_a + omega / power( b
, 3.0 {units="dimensionless"})) * C_Ca3
d( C_Ca4 )/d( time ) ={id="C_Ca4_diff_eq"} ( alpha_a * C_Ca3 + g_
* O_Ca + gamma * power( a , 4.0 {units="dimensionless"}) * C4 ) -
( beta_b * 4.0 {units="dimensionless"} + f_ + omega / power( b ,
4.0 {units="dimensionless"})) * C_Ca4
d( O_Ca )/d( time ) ={id="O_Ca_diff_eq"} f_ * C_Ca4 - g_ * O_Ca
==== Component L_type_Ca_current_y_gate ====
d( y )/d( time ) ={id="y_diff_eq"} ( y_infinity - y ) / tau_y
y_infinity ={id="y_infinity_calculation"} 0.8 {units="dimensionless"}
/ ( 1.0 {units="dimensionless"} + exp(( V + 12.5 {units="millivolt"})
/ 5.0 {units="millivolt"})) + 0.2 {units="dimensionless"}
tau_y ={id="tau_y_calculation"} 20.0 {units="dimensionless"} + 600.0
{units="dimensionless"} / ( 1.0 {units="dimensionless"} + exp(( V +
20.0 {units="millivolt"}) / 9.5 {units="millivolt"}))
==== Component RyR_channel ====
d( P_C1 )/d( time ) ={id="P_C1_diff_eq"} ( k_a_plus ) * power( Ca_ss ,
n ) * P_C1 + k_a_minus * P_O1
d( P_O1 )/d( time ) ={id="P_O1_diff_eq"} ( k_a_plus * power( Ca_ss , n
) * P_C1 - k_a_minus * P_O1 + k_b_plus * power( Ca_ss , m ) *
P_O1 + k_c_plus * P_O1 ) + k_b_minus * P_O2 + k_c_minus * P_C2
d( P_O2 )/d( time ) ={id="P_O2_diff_eq"} k_b_plus * power( Ca_ss , m
) * P_O1 - k_b_minus * P_O2
d( P_C2 )/d( time ) ={id="P_C2_diff_eq"} k_c_plus * P_O1 -
k_c_minus * P_C2
J_rel ={id="J_rel_calculation"} v1 * ( P_O1 + P_O2 ) * ( Ca_JSR
- Ca_ss )
==== Component SERCA2a_pump ====
J_up ={id="J_up_calculation"} K_SR * ( Vmaxf * fb - Vmaxr * rb
) / ( 1.0 {units="dimensionless"} + fb + rb )
fb ={id="fb_calculation"} power( Cai / K_fb , N_fb )
rb ={id="rb_calculation"} power( Ca_NSR / K_rb , N_rb )
==== Component intracellular_Ca_fluxes ====
J_tr ={id="J_tr_calculation"} ( Ca_NSR - Ca_JSR ) / tau_tr
J_xfer ={id="J_xfer_calculation"} ( Ca_ss - Cai ) / tau_xfer
J_trpn ={id="J_trpn_calculation"} J_HTRPNCa + J_LTRPNCa
J_HTRPNCa ={id="J_HTRPNCa_calculation"} d( HTRPNCa )/d( time )
d( HTRPNCa )/d( time ) ={id="HTRPNCa_diff_eq"} k_htrpn_plus * Cai *
( HTRPN_tot - HTRPNCa ) - k_htrpn_minus * HTRPNCa
J_LTRPNCa ={id="J_LTRPNCa_calculation"} d( LTRPNCa )/d( time )
d( LTRPNCa )/d( time ) ={id="LTRPNCa_diff_eq"} k_ltrpn_plus * Cai *
( LTRPN_tot - LTRPNCa ) - k_ltrpn_minus * LTRPNCa
==== Component intracellular_ion_concentrations ====
d( Cai )/d( time ) ={id="Cai_diff_eq"} beta_i * ( J_xfer - J_up +
J_trpn + (( i_Ca_b - 2.0 {units="dimensionless"} * i_NaCa ) +
i_p_Ca ) * ( A_cap * C_sc ) / 2.0 {units="dimensionless"} * V_myo
* F )
d( Nai )/d( time ) ={id="Nai_diff_eq"} (( i_Na + i_Na_b + i_NaCa *
3.0 {units="dimensionless"} + i_NaK * 3.0 {units="dimensionless"})) *
( A_cap * C_sc ) / V_myo * F
d( Ki )/d( time ) ={id="Ki_internal_diff_eq"} (( i_Ca_K + i_Kr +
i_Ks + i_K1 + i_Kp + i_to1 + i_NaK * -2.0
{units="dimensionless"})) * ( A_cap * C_sc ) / V_myo * F
beta_i ={id="beta_i_calculation"} 1.0 {units="dimensionless"} / ( 1.0
{units="dimensionless"} + ( CMDN_tot * K_mCMDN ) / ( K_mCMDN + power(
Cai , 2.0 {units="dimensionless"})))
beta_SS ={id="beta_SS_calculation"} 1.0 {units="dimensionless"} / (
1.0 {units="dimensionless"} + ( CMDN_tot * K_mCMDN ) / ( K_mCMDN +
power( Ca_ss , 2.0 {units="dimensionless"})))
beta_JSR ={id="beta_JSR_calculation"} 1.0 {units="dimensionless"} / (
1.0 {units="dimensionless"} + ( CSQN_tot * K_mCSQN ) / ( K_mCSQN +
power( Ca_JSR , 2.0 {units="dimensionless"})))
d( Ca_ss )/d( time ) ={id="Ca_ss_diff_eq"} beta_SS * (( J_rel *
V_JSR / V_SS - J_xfer * V_myo / V_SS ) - i_Ca * ( A_cap *
C_sc ) / 2.0 {units="dimensionless"} * V_SS * F )
d( Ca_JSR )/d( time ) ={id="Ca_JSR_diff_eq"} beta_JSR * ( J_tr - J_rel )
d( Ca_NSR )/d( time ) ={id="Ca_NSR_diff_eq"} J_up * V_myo / V_NSR
- J_tr * V_JSR / V_NSR
==== Component standard_ionic_concentrations ====

If you would like to see the results for another CellML model, please
ask me (I will be putting out a PCEnv snapshot with the Summarise
Equations mode soon too, so you could also use this yourself).

Best regards,
Andrew

[cellml-discussion] Content MathML editing language: Feedback on initial MathML => editing language output sought, Andrew Miller, 11/24/2006
- [cellml-discussion] Content MathML editing language: Feedback oninitial MathML => editing language output sought, David Nickerson, 11/24/2006
  - [cellml-discussion] CellML 1.1 editing workflows was Re: Content MathML editing language: Feedback oninitial MathML => editing language output sought, Andrew Miller, 11/24/2006

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[cellml-discussion] Content MathML editing language: Feedback on initial MathML => editing language output sought