Problem with manipulate solution NDSolve and initial condition

I'm getting crazy with this Manipulate :

Clear[l, L, nc, phic, tauC, tauG, tauS, phi0, Vinitphi, Vphi0, nL0, \
V, Vphi, VinitR, VinitR0, dV, V0, Vphi0]

VinitR0 = 0
L = 6000
nL0 = 1
phi0 = 0.4

model[Vinitphi_?NumberQ, l_?NumberQ, nc_?NumberQ, phic_?NumberQ,
tauC_?NumberQ, tauG_?NumberQ, tauS_?NumberQ] =
Module[{V, t, Vphi, VinitR},
First[V[t] /.
NDSolve[{V'[
t] == (-((
4 l L nL0 \[Pi] Csch[((3/\[Pi])^(1/3) V[t]^(1/3))/(
2^(2/3) l)] (-l^2 Sinh[((3/\[Pi])^(1/3) V[t]^(1/3))/(
2^(2/3) l)] + (
l (3/\[Pi])^(1/3)
Cosh[((3/\[Pi])^(1/3) V[t]^(1/3))/(2^(2/3) l)] V[t]^(
1/3))/2^(2/3)))/(-l -
L Coth[((3/\[Pi])^(1/3) V[t]^(1/3))/(
2^(2/3) l)] + ((3/\[Pi])^(1/3)
Coth[((3/\[Pi])^(1/3) V[t]^(1/3))/(2^(2/3) l)] V[t]^(
1/3))/2^(2/3))) - nc V[t]) /tauG  +
1/tauS*(1 - VinitR[t]/Vinitphi)/phi0 -
1/tauC*(1 - (1 - (Vphi[t]/V[t]))^2)*
V[t]^(2/3)*(-((
2 (Vphi[t]/V[t]) (-2 + 2 (1 - (Vphi[t]/V[t])) +
phic) (-(Vphi[t]/V[t]) + phic))/(1 - phic)^2)),
V == 1,
Vphi'[
t] == ((-((
4 l L nL0 \[Pi] Csch[((3/\[Pi])^(1/3) V[t]^(1/3))/(
2^(2/3) l)] (-l^2 Sinh[((3/\[Pi])^(1/3) V[t]^(1/3))/(
2^(2/3) l)] + (
l (3/\[Pi])^(1/3)
Cosh[((3/\[Pi])^(1/3) V[t]^(1/3))/(2^(2/3) l)] V[t]^(
1/3))/2^(2/3)))/(-l -
L Coth[((3/\[Pi])^(1/3) V[t]^(1/3))/(
2^(2/3) l)] + ((3/\[Pi])^(1/3)
Coth[((3/\[Pi])^(1/3) V[t]^(1/3))/(2^(2/3) l)] V[t]^(
1/3))/2^(2/3))) - nc V[t]) (Vphi[t]/V[t]))/tauG  +
1/tauS*(1 - VinitR[t]/Vinitphi), Vphi == phi0,
VinitR'[t] == 1/tauS*(1 - VinitR[t]/Vinitphi),
VinitR == VinitR0}, {V}, {t, 0, 170}]]]

Manipulate[
Plot[Evaluate@({model[Vinitphi, l, nc, phic, tauC, tauG, tauS][t]}), {t, 0,
170}], {{Vinitphi, 10^5}, 10^5, 2*10^6,
Appearance -> "Labeled"}, {{l, 5}, 5, 40,
Appearance -> "Labeled"}, {{nc, 0.3}, 0.3, 0.6,
Appearance -> "Labeled"}, {{phic, 0.6}, 0.6, 75,
Appearance -> "Labeled"}, {{tauC, 0.1}, 0.1, 1.5,
Appearance -> "Labeled"}, {{tauG, 1}, 1, 20,
Appearance -> "Labeled"}, {{tauS, 10^(-5)}, 10^(-5), 10^(-4),
Appearance -> "Labeled"}]

I'm getting the error :

NDSolve::ndnum: Encountered non-numerical value for a derivative at t\$174887 == 0.`.

Could you help me please ?

ParametricNDSolve is designed for your purpose.

Clear[l, L, nc, phic, tauC, tauG, tauS, phi0, Vinitphi, Vphi0, nL0, \
V, Vphi, VinitR, VinitR0, dV, V0, Vphi0, pfun]
VinitR0 = 0;
L = 6000;
nL0 = 1;
phi0 = 0.4;
pfun = ParametricNDSolve[{V'[
t] == (-((4 l L nL0 \[Pi] Csch[((3/\[Pi])^(1/3) V[
t]^(1/3))/(2^(2/
3) l)] (-l^2 Sinh[((3/\[Pi])^(1/3) V[
t]^(1/3))/(2^(2/3) l)] + (l (3/\[Pi])^(1/
3) Cosh[((3/\[Pi])^(1/3) V[
t]^(1/3))/(2^(2/3) l)] V[t]^(1/3))/2^(2/3)))/(-l -
L Coth[((3/\[Pi])^(1/3) V[
t]^(1/3))/(2^(2/3) l)] + ((3/\[Pi])^(1/
3) Coth[((3/\[Pi])^(1/3) V[
t]^(1/3))/(2^(2/3) l)] V[t]^(1/3))/2^(2/3))) -
nc V[t])/tauG + 1/tauS*(1 - VinitR[t]/Vinitphi)/phi0 -
1/tauC*(1 - (1 - (Vphi[t]/V[t]))^2)*
V[t]^(2/3)*(-((2 (Vphi[t]/V[t]) (-2 + 2 (1 - (Vphi[t]/V[t])) +
phic) (-(Vphi[t]/V[t]) + phic))/(1 - phic)^2)),
V == 1,
Vphi'[t] == ((-((4 l L nL0 \[Pi] Csch[((3/\[Pi])^(1/3) V[
t]^(1/3))/(2^(2/
3) l)] (-l^2 Sinh[((3/\[Pi])^(1/3) V[
t]^(1/3))/(2^(2/3) l)] + (l (3/\[Pi])^(1/

3) Cosh[((3/\[Pi])^(1/3) V[
t]^(1/3))/(2^(2/3) l)] V[t]^(1/3))/2^(2/3)))/(-l -
L Coth[((3/\[Pi])^(1/3) V[
t]^(1/3))/(2^(2/3) l)] + ((3/\[Pi])^(1/
3) Coth[((3/\[Pi])^(1/3) V[
t]^(1/3))/(2^(2/3) l)] V[t]^(1/3))/2^(2/3))) -
nc V[t]) (Vphi[t]/V[t]))/tauG +
1/tauS*(1 - VinitR[t]/Vinitphi), Vphi == phi0,
VinitR'[t] == 1/tauS*(1 - VinitR[t]/Vinitphi),
VinitR == VinitR0}, {V}, {t, 0, 170}, {Vinitphi, l, nc, phic,
tauC, tauG, tauS}];
Manipulate[
Plot[Evaluate@({(V[Vinitphi, l, nc, phic, tauC, tauG, tauS] /. pfun)[
t]}), {t, 0, 170}, PlotRange -> All], {{Vinitphi, 10^5}, 10^5,
2*10^6, Appearance -> "Labeled"}, {{l, 5}, 5, 40,
Appearance -> "Labeled"}, {{nc, 0.3}, 0.3, 0.6,
Appearance -> "Labeled"}, {{phic, 0.6}, 0.6, 75,
Appearance -> "Labeled"}, {{tauC, 0.1}, 0.1, 1.5,
Appearance -> "Labeled"}, {{tauG, 1}, 1, 20,
Appearance -> "Labeled"}, {{tauS, 10^(-5)}, 10^(-5), 10^(-4),
Appearance -> "Labeled"}] 