deletions | additions       diff --git a/Figures_2_and_3_shows__.tex b/Figures_2_and_3_shows__.tex  index ce2416e..c09c3a4 100644  --- a/Figures_2_and_3_shows__.tex  +++ b/Figures_2_and_3_shows__.tex 
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Figures 2 and 3 shows the mutual information for the separated forward and backward changes in pressure for two cases: in Figure 2 we have used all of the measured pressure and velocity $P$ and $U$, in Figure 3 we have used only the ensemble average data $pe$ and $ue$. We see that the wave speeds calculated using the sum-of-squares method and with $\rho = 1040 \; kg/m^3$ are very different for the two cases: $c_{ss} = 16.3 \; m/s$ when calculated from the measured data and $c_{ss} = 43.9 \; m/s$ when calculated from the ensemble averaged data. The minimum of the mutual information occurs at a wave speed that is fairly similar for both cases: $c_{MI} = 64.1 \; m/s$ for the measured data and $c_{MI} = 70.6 \; m/s$ for the ensemble averaged data.  These calculations are sensitive to the way that the probabilities $p(dp_+)$, $p(dp_-)$ and $p(dp_+,dp_-)$ are calculated. In particular, the results are sensitive to the choice of the number of bins used to calculate the histograms. Further work is required to find an algorithm for selecting the number of bins, and hence the bin sizes, that minimises the sensitivity of the method.   A fundamental problem in exploring this method is the absence of any direct measurements of the wave speed in coronary arteries. Until a method for direct measurement is discovered, the validity of any estimation of coronary artery wave speed can only be inferred, not demonstrated. The values given above are somewhat higher than most estimates of coronary wave speeds, but not outside of the realms of possibility. The large coronary arteries run in grooves in the surface of the myocardium and are covered by the pericardial membrane. It is therefore unlikely that their distensibility is only a function of the distensibility of their walls. Values of the wave speed in other muscular systemic arteries of similar diameter to the coronary arteries frequently are generally well in excess of 10 m/s. and the value increases as the distensibility of the artery decreases. The preliminary results given above seem promising and warrant further investigation.