deletions | additions       diff --git a/textbf_C1_This_is_the__.tex b/textbf_C1_This_is_the__.tex  index e1779fd..fd26e23 100644  --- a/textbf_C1_This_is_the__.tex  +++ b/textbf_C1_This_is_the__.tex 
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$P_exc(x,t)$, 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. constant so that $dV/dt = C dP/dt$)  \[  P_{res}(x,t) - P_{inf} = \frac{e^{-k_d t}}{C} \int\limits_{t'=0}^t Q(x,t') e^{k_dt'} dt' + (P(x,0) - P_{inf}) e^{-k_d t}  \]  where $k_d$ is the diastolic rate constant (the inverse of the more usual diastolic time constant $\tau = 1/(RC)$, where $R$ is the net resistance of the microcirculation) and $t=0$ is taken at the diastolic time when $P(x,0)=P_D(x)$. Using this definition of Pr we observed experimentally that for measurements in the ascendng aorta the excess pressure waveform was remarkably similar to the flow waveform. Since local measurements of flow are not usually available we developed an algorithm for determining Pr during systole from P(t) alone. The critical assumption in this method is the assumption that $Q(0,t)$ is proportional to $P_{exc}(x,t)$ which is purely an assumption which has never been tested experimentally. We recognised that the constant of   proportionality, which is a fitting parameter in our algorithm, bears some relationship to the characteristic impedance $Z$, but we do not assume that it is equal to $Z$ as is stated here.  \textbf{[C3].} The statement that Pr is related to volume and excess pressure accounts for waves and reflections is wrong if 'waves' is assumed to be all of the waves. We view Pr as the summation of the waves that are responsible for the exponentially falling diastolic pressure. If you prefer to think of arterial waves as sinusoidal wavetrains, then these will be the long wavelength waves that are affected by the whole of the arterial circulation. If you prefer to thing of arterial waves as successive wavefronts, then these will be the wavefronts that have been in the arterial system long enough to have visited the whole of the arterial circulation. These long-wavelength/old waves that determine Pr during diastole will also be present in systole and their summation determines Pr during systole. The rest of the waves determine, by definition, the excess pressure. In terms of sinusoidal wavetrains, these will be the small-wavelength, higher-frequency waves. In terms of wavefronts, these will be the newer waves generated by the most recent ventricular contraction which have not had sufficient time to travel throughout the arterial system.