deletions | additions       diff --git a/textbf_C1_This_is_the__.tex b/textbf_C1_This_is_the__.tex  index 224e2b7..3d892e2 100644  --- a/textbf_C1_This_is_the__.tex  +++ b/textbf_C1_This_is_the__.tex 
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\]  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 Pr 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 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 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, $Z$ , 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 of small intensity  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 components  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.      
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