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\frac{d Q^{\downarrow}_{AQ}}{dt_D} = \frac{ B \cdot (p_i - p(t_D)) - Q_{AQ} \cdot p'_D(t)}{p_D(t) - t \cdot p'_D(t)}

q^{\downarrow}_{AQ}(t)=\frac{d Q^{\downarrow}_{AQ}}{dt} 

p_D= \frac{370.529 \, \sqrt{t_D} +137.528 \, t_D + 5.69549 \, t_D^{1.5}}
{328.834 +265.488 \, \sqrt{t_D} + 45.2157 \, t_D +  t_D^{1.5} }

p'_D= \frac
{716.441 + 46.7984 \, \sqrt{t_D} + 270.038 \, t_D + 71.0098 \, t_D^{1.5} }
{ 1296.86 \, \sqrt{t_D} + 1204.73 \, t_D + 618.618 \, t_D^{1.5} + 538.072 \, t_D^2 + 142.41 \, t_D^{2.5} }

t_D= \frac{\pi \, \chi \, t}{A_e}