Date of Award

Summer 2005

Document Type


Degree Name

Master of Science in Biomedical Engineering - (M.S.)


Biomedical Engineering

First Advisor

Stanley S. Reisman

Second Advisor

Ronald H. Rockland

Third Advisor

Tara L. Alvarez


Physiological signals are complex and carry information of human health. Recent studies reveal that under normal conditions, the heart rate time series shows multifractal behavior. In contrast, HRV in the pathological state such as congestive heart failure exhibits more monofractal-like structure. Recent advances in the assessment of heart rate variability (HRV) uses a nonlinear dynamics approach. In this study, the main objective is to use the wavelet-transform modulus-maxima method for the multifractal analysis of the heart rate time senes.

The degree of the multifractality is defined by the singularities (a point in time series where a mathematical function is not differentiable). For monofractal signals, the output of a system contains the same type of singularities regardless of the initial condition, while multifractal signals generate outputs with different fractal properties that depend on the input conditions. That is, the output of the system over extended periods of time will display different types of singularities [7]. Multifractality in the heart rate signal is evaluated by the singularity spectrum, which can be found by the local maxima in WTMM method (a method of multifractal analysis that calculates the singularity spectrum to differentiate between normal subjects and congestive heart failure subjects). The multifractal analysis by the WTMM method calculates the spectrum of singularities. For healthy subjects, the singularity spectrum is wide with non-zero singularities. On the other hand, for congestive heart failure subjects the singularity spectrum is a very narrow range. Moreover, multifractal analysis method provides the calculation of the scaling exponent (τ(q)). For healthy subjects, the τ(q) spectrum displays nonlinear behavior, while the τ(q) spectrum is linear for congestive heart failure subjects.

To validate the theory, analysis was performed on 50 subjects and we are clearly able to identify normal and congestive heart failure subjects using the WTMM method of multifractal analysis.