My Girlfriend is going to prison…Save her with Math

Similar to previous answers, only I don't make the instantaneous absorption assumption since it isn't really necessary. The equation can be found here on page three, where ka and ke are the rates of absorption and elimination, respectively, D is the initial dose (in ng), V/F is the Volume of Distribution. The range of apparent volumes of distribution I've seen for Adderall are from 271 (F = 0.92, V = 250 mL) to 485 mL. The previous references give estimates for the absorption rate constant of ~ 1/h and since the elimination rate must be much less than ka in order to get the observed concentration profile, we have parameter estimates of (d = 30000, v = 250, f = 0.92, ka = 1, ke = 0.1). I combine fd/v = const = 110 since the model cannot discriminate these values. I'm assuming that the y axis in the original data is in ng/mL.

f1[t_, ka_, ke_, const_: 0.92*30000/250] := 
 const ka/(ka - ke) (Exp[-ke t] - Exp[-ka t])
nlm = NonlinearModelFit[dmethyl1, 
  f1[t, ka, ke, const], {{ka, 1}, {ke, 0.1}, {const, 110}}, t]

Nonlinear model fitting with reasonable parameter estimates yields a reasonable fit, with ka = 0.72 h^-1, ke = 0.072 h^-1 and fd/v = 56. ke and fd/v appear to be highly correlated; however fixing fd/v to the range of literature values does not appear to change the best-fit parameter values beyond the range of the standard errors.

The bottom of page 3 here provides the multi-dose first-order adsorption/elmination equation, which can be written as

f3[t_, ka_, ke_, const_, dt_, n_] :=
 Sum[const ka/(ka - ke) (Exp[-ke (t - dt i)] - 
     Exp[-ka (t - dt i)]) UnitStep[t - dt i], {i, 0, n}]

where dt is the dosing interval and n is the number of doses. In my simplified case, the dosing interval must be constant and must be the same amount as the original dose. An example with 6 doses spaced 12 hours apart:

Plot[f3[t, ka, ke, const, 12, 6] /. nlm["BestFitParameters"], {t, 0, 
  96}, Frame -> {True, True, False, False}, 
 FrameLabel -> {"Time (h)", "Amount (ng/mL)"}, 
 PlotLabel -> "Multi-dose absorption/elimination curve"]

Assuming the simplest kinetic model for elimination (and making the simplifying assumption of "instant absorption" to peak concentration):

conc = {{0, 0}, {.25, 1}, {.5, 7}, {1, 26}, {1.5, 40}, {2, 45}, {2.5, 
    45}, {3, 44}, {3.5, 44}, {4, 43}, {4.5, 41}, {5, 39}, {6, 38}, {7,
     37}, {8, 35}, {9, 33}, {10, 32}, {11, 29}, {12, 24}, {24, 
    13}, {48, 4}, {60, 2}, {72, 0}};
lp = ListPlot[conc];
em = conc[[6 ;;]];
nlm = NonlinearModelFit[em, { a Exp[- k t]}, {a, k}, t]
Show[lp, Plot[Evaluate@nlm[t], {t, 2, 72}]]
tc = k /. nlm["BestFitParameters"];
halflife = t /. Quiet[Solve[f[45, t] == 22.5, t][[1]]]
f[a_, t_] := a Exp[- tc t]
p[i_, n_] := Nest[f[#, i] + 45 &, 45, n]
pf[i_, n_] := 
  Total@Table[
    f[p[i, j], t - j i] UnitBox[(t - j i )/i - 1/2], {j, 0, n}];
Manipulate[
 Plot[pf[interval, 10], {t, 0, 10 interval}, Exclusions -> None, 
  PlotRange -> {0, 200}, Frame -> True, 
  GridLines -> {{4 halflife}, None}], {interval, {5, 8, 10, 12, 24}}]

From the single dose the half-life is approximately 12 hours. Therefore, approximately 48 hours to steady state. The Manipulate shows effect of different dosing intervals (10 intervals shown):

I have no experience with what you are trying to do so this is entirely guesswork but maybe you want something like this?

cmaxd = Interpolation[dmethyl1, InterpolationOrder -> 1];

f1[t_?NumericQ] := If[0 <= t <= 72, cmaxd[t], 0]

f2[t_] := Sum[f1[t - i], {i, 0, t, 12}]

Plot[f2[i], {i, 0, 120}, AxesLabel -> {"hour", "concentration"}]

You can also do it with some timeseries arithmetic.

Construct $n$ shifted by 12 hours series:

n = 10

doses = Table[TimeSeriesShift[dmethyl1, {k, 12}], {k, 0, n-1}];

Combine them with interpolation order of 0 (extrapolation would be zero outside the domain intervals this way):

Off[InterpolatingFunction::dmval] (* Disable extrapolation warnings *)

ListLinePlot@TimeSeriesThread[Total, doses , 
   ResamplingMethod -> {"Interpolation", InterpolationOrder -> 0}]