Limits...
Methodological framework for estimating the correlation dimension in HRV signals.

Bolea J, Laguna P, Remartínez JM, Rovira E, Navarro A, Bailón R - Comput Math Methods Med (2014)

Bottom Line: Each approach for slope estimation leads to a correlation dimension estimate, called D₂, D(2(⊥)), and D(2(max)).D₂ and D(2(max)) estimate the theoretical value of correlation dimension for the Lorenz attractor with relative error of 4%, and D(2(⊥)) with 1%.D₂ keeps the 81% of accuracy previously described in the literature while D(2(⊥)) and D(2(max)) approaches reach 91% of accuracy in the same database.

View Article: PubMed Central - PubMed

Affiliation: Communications Technology Group (GTC), Aragón Institute for Engineering Research (I3A), IIS Aragón, University of Zaragoza, 50018 Zaragoza, Spain ; CIBER de Bioingeniería, Biomateriales y Nanomedicina (CIBER-BBN), 50018 Zaragoza, Spain.

ABSTRACT
This paper presents a methodological framework for robust estimation of the correlation dimension in HRV signals. It includes (i) a fast algorithm for on-line computation of correlation sums; (ii) log-log curves fitting to a sigmoidal function for robust maximum slope estimation discarding the estimation according to fitting requirements; (iii) three different approaches for linear region slope estimation based on latter point; and (iv) exponential fitting for robust estimation of saturation level of slope series with increasing embedded dimension to finally obtain the correlation dimension estimate. Each approach for slope estimation leads to a correlation dimension estimate, called D₂, D(2(⊥)), and D(2(max)). D₂ and D(2(max)) estimate the theoretical value of correlation dimension for the Lorenz attractor with relative error of 4%, and D(2(⊥)) with 1%. The three approaches are applied to HRV signals of pregnant women before spinal anesthesia for cesarean delivery in order to identify patients at risk for hypotension. D₂ keeps the 81% of accuracy previously described in the literature while D(2(⊥)) and D(2(max)) approaches reach 91% of accuracy in the same database.

Show MeSH

Related in: MedlinePlus

Log-log curves for a dynamic system. Data correspond to an RR interval series extracted from 30 mins of ECG recording.
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC3926396&req=5

fig1: Log-log curves for a dynamic system. Data correspond to an RR interval series extracted from 30 mins of ECG recording.

Mentions: Since the size of the time series is finite, choosing small values of r to evaluate this limit is problematic. For values of r close to 0, very few distances contribute to the correlation sum, making the estimation unreliable. The evaluation of this expression is usually done in a linear region in the log⁡(Cm(r)) versus log⁡(r) representation, called the log-log curve. The slope of this linear region is considered an estimate of D2m. There are different approaches for estimating this slope. Maximum slope searching can be done by directly computing the increments in the log-log curve. Another approach is to estimate numerically the maximum of the first derivative of the log-log curve. Nevertheless these approaches encounter some limitations due to the usual nonequidistant sampling of r values in the logarithmic scale. Yet another limitation arises in the presence of dynamic systems whose log-log curves display several linear regions, as can be seen in Figure 1 where the data corresponds to an RR interval series extracted from a 30 minute ECG recording. In order to estimate the slope of the linear region of the log-log curve, an attempt to artificially extend the linear region is made by excluding the self-comparisons (di,i) from the correlation sums.


Methodological framework for estimating the correlation dimension in HRV signals.

Bolea J, Laguna P, Remartínez JM, Rovira E, Navarro A, Bailón R - Comput Math Methods Med (2014)

Log-log curves for a dynamic system. Data correspond to an RR interval series extracted from 30 mins of ECG recording.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3926396&req=5

fig1: Log-log curves for a dynamic system. Data correspond to an RR interval series extracted from 30 mins of ECG recording.
Mentions: Since the size of the time series is finite, choosing small values of r to evaluate this limit is problematic. For values of r close to 0, very few distances contribute to the correlation sum, making the estimation unreliable. The evaluation of this expression is usually done in a linear region in the log⁡(Cm(r)) versus log⁡(r) representation, called the log-log curve. The slope of this linear region is considered an estimate of D2m. There are different approaches for estimating this slope. Maximum slope searching can be done by directly computing the increments in the log-log curve. Another approach is to estimate numerically the maximum of the first derivative of the log-log curve. Nevertheless these approaches encounter some limitations due to the usual nonequidistant sampling of r values in the logarithmic scale. Yet another limitation arises in the presence of dynamic systems whose log-log curves display several linear regions, as can be seen in Figure 1 where the data corresponds to an RR interval series extracted from a 30 minute ECG recording. In order to estimate the slope of the linear region of the log-log curve, an attempt to artificially extend the linear region is made by excluding the self-comparisons (di,i) from the correlation sums.

Bottom Line: Each approach for slope estimation leads to a correlation dimension estimate, called D₂, D(2(⊥)), and D(2(max)).D₂ and D(2(max)) estimate the theoretical value of correlation dimension for the Lorenz attractor with relative error of 4%, and D(2(⊥)) with 1%.D₂ keeps the 81% of accuracy previously described in the literature while D(2(⊥)) and D(2(max)) approaches reach 91% of accuracy in the same database.

View Article: PubMed Central - PubMed

Affiliation: Communications Technology Group (GTC), Aragón Institute for Engineering Research (I3A), IIS Aragón, University of Zaragoza, 50018 Zaragoza, Spain ; CIBER de Bioingeniería, Biomateriales y Nanomedicina (CIBER-BBN), 50018 Zaragoza, Spain.

ABSTRACT
This paper presents a methodological framework for robust estimation of the correlation dimension in HRV signals. It includes (i) a fast algorithm for on-line computation of correlation sums; (ii) log-log curves fitting to a sigmoidal function for robust maximum slope estimation discarding the estimation according to fitting requirements; (iii) three different approaches for linear region slope estimation based on latter point; and (iv) exponential fitting for robust estimation of saturation level of slope series with increasing embedded dimension to finally obtain the correlation dimension estimate. Each approach for slope estimation leads to a correlation dimension estimate, called D₂, D(2(⊥)), and D(2(max)). D₂ and D(2(max)) estimate the theoretical value of correlation dimension for the Lorenz attractor with relative error of 4%, and D(2(⊥)) with 1%. The three approaches are applied to HRV signals of pregnant women before spinal anesthesia for cesarean delivery in order to identify patients at risk for hypotension. D₂ keeps the 81% of accuracy previously described in the literature while D(2(⊥)) and D(2(max)) approaches reach 91% of accuracy in the same database.

Show MeSH
Related in: MedlinePlus