USER'S GUIDE - Biosignal Analysis and Medical Imaging Group
USER'S GUIDE - Biosignal Analysis and Medical Imaging Group
USER'S GUIDE - Biosignal Analysis and Medical Imaging Group
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3.3. Nonlinear methods 29987Time (min)6543211 2 3 4 5 6 7 8 9Time (min)Figure 3.4: Recurrence plot matrix for HRV time series (black = 1 <strong>and</strong> white = 0).Methods for quantifying recurrence plots were proposed in [47]. The methods included inthis software are introduced below.In the software the following selections were made. The embedding dimension <strong>and</strong> lagwere selected to be m =10<strong>and</strong>τ = 1, respectively. The threshold distance r was selectedto be √ m SD, where SD is the st<strong>and</strong>ard deviation of the RR time series. The selection aresimilar to those made in [7].The first quantitative measure of RP is the recurrence rate (REC) which is simply theratio of ones <strong>and</strong> zeros in the RP matrix. The number of elements in the RP matrix forτ =1isequaltoN − m + 1 <strong>and</strong> the recurrence rate is simply given asN−m+11 ∑REC =(N − m +1) 2 RP(j, k). (3.24)The recurrence rate can also be calculated separately for each diagonal parallel to the lineof-identity(main diagonal). The trend of REC as a function of the time distance betweenthese diagonals <strong>and</strong> the line-of-identity describes the fading of the recurrences for pointsfurther away.The rest of the RP measures consider the lengths of the diagonal lines. A thresholdl min = 2 is used for excluding the diagonal lines formed by tangential motion of the trajectory.The maximum line length is denoted l max <strong>and</strong> its inverse, the divergence,DIV = 1(3.25)l maxhas been shown to correlate with the largest positive Lyapunov exponent [46]. The averagej,k=1diagonal line length, on the other h<strong>and</strong>, is obtained asl mean =∑ lmaxl=l minlN l∑ lmaxl=l minN l(3.26)Kubios HRV <strong>Analysis</strong>version 2.0 beta<strong>Biosignal</strong> <strong>Analysis</strong> <strong>and</strong> <strong>Medical</strong> <strong>Imaging</strong> <strong>Group</strong>Department of PhysicsUniversity of Kuopio, FINLAND