**6. EKG recording before mDFA**

mDFA requires accurate heartbeat interval measurements without missing a single heartbeat. Stable EKG recordings are needed for accurate detection of peaks in the data. If subjects move (e.g., talk, touch, walk, squat, exercise, etc.) commercially available medical-EKG machines are

**Figure 9.** Range in box sizes used for mDFA (i.e., the slope from one particular box size to another).

in the life sciences [10]. The following literature provides information on nonlinear physics with respect to heart physiology and DFA: Peng [11], Glass [12], Stadnistski [13], Stanley [14], Goldberger [9], Katsuyama [15], Pérez [16], Liebovitch [17], Huikuri [18], Bigger [19], Scafetta [20], and other work cited in these references. In addition, the scaling exponent, DFA, and topics related to fractality research, for example, fractal, scaling, the Hurst exponent, and power spectral density, are well explained by T. Stadnistski [13]. DFA is based on the concepts of scaling and self-similarity [13]. Peng's DFA [7] deals with critical phenomena. (Details of the mathematics of DFA can be referenced elsewhere [9-19]). One DFA program, PhisoNet, provided by Goldberger, Peng and others is available on the internet. However, there is no web-based mDFA program available. Regardless, an mDFA program can be written with an understanding of DFA and programming skills (I am a biologist and received programming support from a graduate student, Katsunori Tanaka, who constructed an mDFA program

While the genesis of DFA was long ago, no one has since constructed a useful device/instru‐ ment to quantify stress using it. In this article, I argue that implementing power law concepts in DFA is a superior method for its practical use in biomedicine. In addition, I present the results of our mDFA applied to real-world data. I anticipate that this literature will initiate a public debate on whether to construct such a device/instrument, and hope that a functional DFA device will be constructed as a result. This work is being performed in collaboration with Symphodia Phil Confidential, Japan (President O. Takiguchi). Empirical data and the device concept were previously presented at a conference of the Society for Chaos Theory in Psy‐

Although DFA is not a recent development, the technique is somewhat difficult to understand. An important concept of DFA is that if data exhibit scaling characteristics and self-similar fluctuations [11, 14], recorded signals and their magnified/contracted copies are statistically similar. In general, statistical parameters such as the average and variance of fluctuating signals can be calculated by taking the average and corresponding variance of the signals across a certain section. In DFA and mDFA, however, the average is the squared average of the data. The calculation of the statistical parameter thus depends on the size

To use DFA as a practical tool for instantaneous determination of heart condition, the appro‐ priate section size, i.e. box size or number of heartbeats, needs to be determined. A practical DFA tool should NOT be subject-specific. Rather, it should be constructed for general use across the population. The section size, which is a restricted period of time, was determined

mDFA requires accurate heartbeat interval measurements without missing a single heartbeat. Stable EKG recordings are needed for accurate detection of peaks in the data. If subjects move (e.g., talk, touch, walk, squat, exercise, etc.) commercially available medical-EKG machines are

chology and Life Sciences in Milwaukee, Wisconsin, USA (August 2, 2014).

to range from 30 to 270 beats after conducting hundreds of tests.

**6. EKG recording before mDFA**

under my supervision using C++programming language).

of the section.

366 Advances in Bioengineering

not reliable because the EKG trace is frequently lost from the recorder chart or screen under these conditions. Accurate identification of peak heartbeat times were a necessary condition in this study. Therefore, I constructed a baseline-stable EKG recording amplifier with an input time constant of 0.1 or 0.22 s (C=0.1 μF, R=1 MΩ, or C=0.22 μF, R=1 MΩ, respectively) and amplification-gain of 2000 times. This made it possible to record baseline-stable EKGs. I used a 1-kHz sampling rate. Based on my own electro-physiological observations, I knew that the peak time of an action-potential always fluctuates in the order of milliseconds in response to a stimulus. Therefore, I used a 1-kHz sampling rate (1000 dots per 1000 milliseconds). After detecting peak heartbeat intervals, I constructed an inter-heartbeat interval time series (such as the R-R peak interval of conventional medical EKGs). This time series was analyzed using the mDFA program.

To conduct mDFA and obtain reliable scaling exponent (SI) values, a recording of ~2000 consecutive heartbeats was required; this number was used throughout my research. If a dataset contained 4000 or 5000 heartbeats, these were divided into two data sets. The ideal (minimum essential) number of heartbeats for use in an mDFA instrument would be ~2000. In fact, various data lengths of EKGs, ranging from 700 to 5000 heartbeats are used. In this article, analysis based on 2000 beats as well as shorter and/or longer data lengths are presented in some figures. To obtain stable results in a practical health-determining device, a 30-min EKG recording is ideal (here, 1900–2100 beats were used).

There are several ways to detect heartbeat timing; however, I prefer stable baseline EKGs. In terms of a stable baseline, short and constant EKG recordings are superior to finger pulse and light-sensor (infrared) blood flow recordings. However, consecutive R-R intervals of ~2000 beats are required irrespective of the type of recording used.

Several mDFA computations were performed simultaneously: scaling exponents in various box sizes were computed (Figure 9). Initially (from 2004 to 2006), program A was used, which


**Figure 10.** Box size (number of heartbeats) for the mDFA programs. Program A and Program B contained 53 and 136 boxes, respectively. Programming language C++.

included box-ranges [30: 60], [70: 140], [130: 270], and [30: 270]. These four ranges were automatically and simultaneously computed. However, any box size range could be manually computed if necessary. Then, program B was added in 2006, which included box-ranges [30: 70], [70; 140], [130: 270], [51; 100], [30; 140], [30; 270] (Figure 9). These automatic ranges were arbitrarily determined. Until now, programs A and B have been used simultaneously. All existing EKG-mDFA results were computed using both programs.

Program A computed 53 box points and program B computed 136 box points (Figure 10). This increase in box number occurred because of an increase in the PC calculation speed due to a Windows software improvement. A device requires relatively rapid computation of the scaling exponent. An average scaling exponent was computed in each computation, calculated as the average of the scaling exponents across the range of box sizes (see Figure 22 and 23).

mDFA calculations use recordings of approximately 2000 beats, digital recordings at a 1-KHz sampling ratio, and a box size range of [30: 270] in the following sections of this article, unless otherwise mentioned.
