deletions | additions       diff --git a/textbf_C1_This_is_the__.tex b/textbf_C1_This_is_the__.tex  index 689d0e5..09fadba 100644  --- a/textbf_C1_This_is_the__.tex  +++ b/textbf_C1_This_is_the__.tex 
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\textbf{[C1].} This is the basic error about Pr pointed out above. Pr is not based on the assumption that there are no waves during diastole. In our first paper we suggested that the arterial pressure $P(x,t)$ could be separated into a Windkessel pressure $P_{Wk}(T)$ and an excess pressure   $P_exc(x,t)$, where $P = P_{Wk} + P_{exc}$. We did not use the term 'reservoir pressure' in that paper. After publishing that paper we realised that this definition was not viable, mainly because we observed in our experiments that what we had defined as the Windkessel pressure was propagating down the aorta which is incompatible with the Windkessel pressure as defined by Frank. In our subsequent papers we coined the term 'reservoir pressure' so that it would not be confused with the Windkessel pressure. Obviously our efforts to distinguish the two failed because WSW have confused reservoir pressure with Frank's Windkessel pressure.  \textbf{[C2].} The sequence of definitions is wrong. No \textit{a priori} assumptions are made about $P_{exc}$; it is simply defined as the difference between P and Pr. Pr is defined in the following way: During diastole we assume that Pr falls exponentially   $P_{res}(t - T_N) - P_{inf} = (P(T_N) - P_{inf}) e^{-(t - T_N)/\tau}$, where $T_N$ is the time of the start of diastole. $P_{inf}$ is, as WSW state, the asymptotic pressure that would be reached after long asystole and is included in the definition because we found that this 2-parameter model proveded a significantly better fit to measured diastolic pressures than the more common 1-parameter that fit the time constant $\tau$ to a curve that decays to zero pressure. The form of Pr during systole is then determined in one of two ways. If local flow measurements $Q(x,t)$ are available, as they are in our experiments on dogs, then Pr is obtained by solving the differential equation describing overall mass conservation (assuming that net arterial compliance $C$ is constant.   \[  P_{res}(x,t) - P_{inf} = \frac{e^{-t/\tau}}{C} \int\limits_{t'=0}^t Q(x,t') e^{t'/\tau} dt' + (P(x,0) - P_{inf}) e^{-t/\tau}  \]  where $t=0$ is taken at the diastolic time when $P(x,0)=P_D(x)$.