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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.

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SampEni=j(m, r) surface for a 300-beat RR interval series. For each embedded dimension maximum point is marked with solid triangle. Circles correspond to the r values which define .
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fig4: SampEni=j(m, r) surface for a 300-beat RR interval series. For each embedded dimension maximum point is marked with solid triangle. Circles correspond to the r values which define .

Mentions: Another new approach for D2 estimation based on sample entropy (SampEn) is now presented. SampEn was defined by Zurek et al. [17] as(16)SampEn(m,r,N)=log⁡(Cm(r))−log⁡(Cm+1(r)),where, in this case, Cm(r) is computed as in (3), but without considering self-comparisons. Let us define SampEni=j(m, r) as the sample entropy considering self-pairs, which is easily computed for all embedded dimensions m and a huge set of thresholds r using the fast algorithm described in Section 2.2. We can generate a SampEni=j(m, r) surface from the fitted sigmoid curves, as can be seen in Figure 4, an example of a 300-beat RR interval series extracted from one recording of the database used in [10]. For each embedded dimension, the value of r which maximizes SampEni=j(m, r) is used to evaluate the slope of the linear region of the SCF log-log curves, , yielding another D2 estimate, called in this paper .


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)

SampEni=j(m, r) surface for a 300-beat RR interval series. For each embedded dimension maximum point is marked with solid triangle. Circles correspond to the r values which define .
© Copyright Policy
Related In: Results  -  Collection

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

fig4: SampEni=j(m, r) surface for a 300-beat RR interval series. For each embedded dimension maximum point is marked with solid triangle. Circles correspond to the r values which define .
Mentions: Another new approach for D2 estimation based on sample entropy (SampEn) is now presented. SampEn was defined by Zurek et al. [17] as(16)SampEn(m,r,N)=log⁡(Cm(r))−log⁡(Cm+1(r)),where, in this case, Cm(r) is computed as in (3), but without considering self-comparisons. Let us define SampEni=j(m, r) as the sample entropy considering self-pairs, which is easily computed for all embedded dimensions m and a huge set of thresholds r using the fast algorithm described in Section 2.2. We can generate a SampEni=j(m, r) surface from the fitted sigmoid curves, as can be seen in Figure 4, an example of a 300-beat RR interval series extracted from one recording of the database used in [10]. For each embedded dimension, the value of r which maximizes SampEni=j(m, r) is used to evaluate the slope of the linear region of the SCF log-log curves, , yielding another D2 estimate, called in this paper .

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