Session P82.1

On Exact Number of Baroreflex Sequences in Surrogate Data Sets

T Loncar Turukalo, N Japundzic Zigon, O Sarenac, D Bajic*

University of Novi Sad
Novi Sad, Serbia

Surrogate data mimic statistical properties of the data under study, but not the property that is tested. Spontaneous baroreflex (sBR) sequences exhibit strong temporal dependence, so scrambled (isodistributional) surrogates are used to test the hypothesis that interactions of systolic blood pressure (SBP) and pulse interval (PI) are real sBR events and not the accidental occurrences. However, if the time series are short, the amount of the sBR sequence realizations in scrambled sets is limited and it is often difficult to estimate the reliability of the test results. This paper evaluates an exact formula for the number of SBP/PI ramps and sBR sequences within the surrogate sets. An alternative method for sBR sensitivity (sBRS) is proposed as well, based upon the sorting and random sampling the original time series. Number of sequences is an inverse function of a sBR cycle length, when a sBR cycle (and, similarly, ramp cycle) comprises a sequence (ramp) followed by inter-sequence (inter-ramp) interval. A cycle can be observed as a renewal process and it can be modeled with a finite ergodic Markov state-diagram. The model order depends upon the minimal sequence/ramp length N, and upon the decision whether to use threshold to mark a change. State transition probabilities are reliably estimated from the original SBP and PI time series. Inter-ramp (inter-sequence) duration is evaluated as the first passage time. The method is tested using 30 minutes records of 13 Wistar rats at baseline conditions. For each one a set of 15 surrogates is generated and sBRS, effectiveness index (BEI) and number of ramps/sequences are estimated for N = 2, 3, and 4. Than the transition probabilities are estimated from the original time series and the same parameters are evaluated analytically. The calculated parameters are in excellent accordance with the surrogate data estimates. This method presents a powerful tool for analytical evaluation of sBR parameters, replacing isodistributional surrogate data method, both for short records with too few sBR sequences for reliable estimates and for long records that consume considerable amount of CPU time for repeated surrogate tests.

(Abstract Control Number: 158)