**5. Modified DFA and DFA**

**Figure 6.** HPLC chart indicating the detection of adrenaline (A) in a Japanese lobster (*Panulirus japonicus*) specimen*.* Adrenaline release was induced by stress from human handling. Very little adrenaline was detected 20 min and 1.5 hour after the stress stimulus. Therefore, the adrenaline content measured at these times indicates the basal adrenaline

**Figure 7.** EKG recording and MD experiment in a Japanese spiny lobster (*Panulirus japonicus*). A, a human approached the lobster tank and conducted an MD experiment. B, continuous recording from A (note: the time scale is different).

Micro-dialysis HPLC (MD-HPLC) analysis detected a few substances in the blood samples before, during, and after stress stimulation. EKGs were continuously recorded to check stress responses. Figure 7 shows a lobster's response to a human, observed through EKG recordings. Significant features are evident in Figure 7. First, approach by a human interrupted the slow, repetitive heartbeat pattern (Figure 7A). Second, the micro-dialysis experiment resulted in continuous stress to the animal (MD period in Figure 7A). Third, the stressful reaction lasted

for approximately one day, the period shown by a white arrow (Figure 7B).

content in the blood. Note: noradrenaline (NA) was not detected.

364 Advances in Bioengineering

In this article, I compare the methodologies of original and modified DFA. While most of the computation sequences in DFA and mDFA are similar, there is one difference in the compu‐ tation process.

In DFA and mDFA, the scaling exponent (Peng used the Greek letter alpha) or scaling index (SI) is calculated from time series data that obey the scaling law. Here, I use SI to refer to both.

In the mid-1980s, Goldberger pioneered the application of nonlinear dynamics to clinical cardiology [9]. Thereafter, a voluminous literature appeared on chaos and nonlinear analysis 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 under my supervision using C++programming language).

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

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 of the section.

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