deletions | additions       diff --git a/textbf_C1_This_is_the__.tex b/textbf_C1_This_is_the__.tex  index fa7ab89..a530d1d 100644  --- a/textbf_C1_This_is_the__.tex  +++ b/textbf_C1_This_is_the__.tex 
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$P_{ex}(x,t)$, where $P = P_{Wk} + P_{ex}$. 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 $P_{res}$. $P_{res}$ is defined in the following way: During diastole we assume that $P_{res}$ 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 a long asystole. $P_{inf}$ is included in the definition because we found that this 2-parameter model achieved a significantly better fit to measured diastolic pressures than the more common 1-parameter equation that fits the time constant $\tau$ to a curve that decays to zero pressure. We note that the existence of $P_{inf}$ (i.e. a positive pressure at zero flow) is supported by considerable experimental evidence from several groups. [refs] The form of Pr $P_{res}$  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 $P_{res}$ is obtained by solving the differential equation describing overall mass conservation (assuming that net arterial compliance $C$ is 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 to be the time of end diastole, when $P(x,0)=P_D(x)$. Using this definition of $P_{res} $P_{res}$  we observed experimentally that for measurements in the ascending aorta the morphology of 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 $P_{res}$ 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 not yet 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 of the aorta, $Z_c$ , but we do not assume that it is equal to $Z_c$ as is stated here.  \textbf{[C3].} It is generally agreed by the originators of the reservoir-wve hypothesis that $P_{res}$ propagates down the aorta, as observed experimentally. By the very broad definition of 'wave' in the first sentence of WSW, this would mean that $P_{res}$ is a wave, but some disagree with WSW's definition of 'wave' and prefer not to think of $P_{res}$ as a wave. Others see $P_{res}$ as the summation of those waves that are responsible for the exponentially falling pressure during diastole. If one prefer to think of arterial waves as sinusoidal wavetrains, then these will be the long wavelength components that are affected by the whole of the arterial circulation. If one prefers to think of arterial waves as successive wavefronts, then these will be the wavefronts that have been in the arterial system long enough to have visited all of the arterial circulation, in a statistical sense. These long-wavelength/old waves that determine $P_{res}$ during diastole will also be present in systole and their summation determines $P_{res}$ 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 or reflections from local sites of impedance mismatching which have not had sufficient time to travel extensively throughout the arterial system. This is the sense in which we have asserted that $P_{res}$ is determined by the global compliance and resistance and $P_{exc}$ is determined primarily by local conditions. 
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