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 discarding and accepting self-comparisons. Arrows show the slope of the scaling range. Data correspond to an RR interval series of 300 beats.
© Copyright Policy
Related In: Results  -  Collection

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

fig2: Log-log curves discarding and accepting self-comparisons. Arrows show the slope of the scaling range. Data correspond to an RR interval series of 300 beats.

Mentions: However, the basis of the approach proposed in this work to improve D2 estimation lies in considering self-comparisons. Figure 2 illustrates how log-log curves behave in both situations, considering or not considering self-comparisons. As it is shown, both share part of the linear region. Our proposal is to use sigmoidal curve fitting (SCF) over the log-log curves to obtain an analytic function whose maximum slope in the linear region is well defined. These log-log curves are reminiscent of the biasymptotic fractals studied by Rigaut [20] and Dollinger et al. in [21] in which exponential fittings were proposed. The sigmoidal fitting is applied to the interpolated log-log curves computed with evenlyspaced r values.


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 discarding and accepting self-comparisons. Arrows show the slope of the scaling range. Data correspond to an RR interval series of 300 beats.
© Copyright Policy
Related In: Results  -  Collection

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

fig2: Log-log curves discarding and accepting self-comparisons. Arrows show the slope of the scaling range. Data correspond to an RR interval series of 300 beats.
Mentions: However, the basis of the approach proposed in this work to improve D2 estimation lies in considering self-comparisons. Figure 2 illustrates how log-log curves behave in both situations, considering or not considering self-comparisons. As it is shown, both share part of the linear region. Our proposal is to use sigmoidal curve fitting (SCF) over the log-log curves to obtain an analytic function whose maximum slope in the linear region is well defined. These log-log curves are reminiscent of the biasymptotic fractals studied by Rigaut [20] and Dollinger et al. in [21] in which exponential fittings were proposed. The sigmoidal fitting is applied to the interpolated log-log curves computed with evenlyspaced r values.

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