**5. Biophysics**

*Noise and Vibration Control - From Theory to Practice*

**36**

**Figure 3.**

**Figure 2.**

*[10], Chapter 2.*

heart stopped its beating 11 h after TY left (**Figure 3**). We define this "unpredictable death." Unpredictable death is a rare event among ~1000 specimens. We always check and dissect all specimens' body after the death. In case of **Figure 3** animal, dissection revealed that the myocardium of relevant crab partially got slightly injured by an EKG electrode (see the electrode in **Figure 1B**). It is the fault of researchers. We are very sorry that the innocent specimen suffered from the human-caused heart injury for 2

*A long-term EKG from "Mokuzu" crab (Eriocheir japonica). Recording for 11 h. Inset: SI values for the corresponding period from (A) to (D). Note: No fibrillation remained after beating stops: cf.* **Figure 2***.* 

*Inset: spike configuration not distorted. Modified from Yazawa [10], Chapter 2.*

*A long-term EKG from coconut crab (Birgus latro) with state space representation. Recording for 18 h. Inset: SI values for the corresponding period from (A) to (F). Note: fibrillation after beating stops. State space representation of cardiac action potentials shows a normal action potential shape in (A), gradually changing to distorted pattern (B, E, F), and finally becomes erratic and unstable at the end (Fz). Modified from Yazawa* 

#### **5.1 Quantitative analysis**

In 1982, Kobayashi and Musha reported that healthy hearts exhibit 1/f spectrum [8]. Mathematically, 1/f slope is almost equal to SI = 1.0, while not 100% equivalent. This metric analysis based on SI is not fully proven as far as we know. The criterion-based strategy is better than qualitative research for diagnosing the CS.

For the quantitative expression for the CS state, we need computation. However, in the 1980s, we did not have a PC to calculate SI. Poor biologists found difficulty to use a computer that was installed in a building of a top university. It took until 2001 to prove the idea of mDFA by ourselves. The Windows XP machine was introduced in the year 2001. XP-PC helped us calculate mDFA on the second time scale.

What we liked was Kobayashi-Musha's concept that one (SI = 1.0) is "healthy" [8]. There is a fixed baseline for diagnosing the heart system, that is, healthy or not.

In the 1990s, Peng and Goldberger and others demonstrated that healthy hearts exhibit the scaling exponent ONE (1.0) by detrended fluctuation analysis (DFA) [9] [DFA is not mDFA (see below)]. These results add critical evidence to the issue of Kobayashi-Musha's concept.

Moreover, Peng and Goldberger's group reported that sick hearts exhibit a higher SI, which is SI = ~1.2. It sounds like providing evidence that a sick heart was consistently higher in the scaling exponent. But they only suggested. The truth was unclear. At least we were excited about our crab's high-SI discovery (**Figure 3**) because it coincides with it.

Most of the data in [8] and [9] were obtained from in-hospital patients. Peng and Goldberger's group did not extend their detailed experiments to general population as far as we know.

One is a baseline number for the health. This is testable hypothesis. We began to examine EKGs on general population and model animals. Currently we have ~500 individuals' EKG and ~1000 animal data. Some EKGs are collected from long-term follow up. Some subjects have passed away. We take medical record with all data including animal data. We never use website data. Physiological interpretation of data is impossible without medical record based on our own physiological observation.

#### **5.2 Accurate data sampling**

EKG signal was captured by two commercially available Ag/AgCl electrodes and a lab-made amplifier that can damp undulatory noise. The amplifier has a short input-time-constant (*tau* = 0.1 or 0.22 s, depending on capacitor used, 0.01 or 0.022 μF). The *tau* value for EKG-machine in hospital-use is set at about 10 s under the international regulation. A large *tau* amplifier makes signal-baseline drift when subjects move. We thus needed to make a small-*tau* amplifier in order to reduce "movement-induced noise and drift" (see **Figure 4**).

Peaks are captured automatically by a lab-made program. R-peaks are the time point at which Vmax is attained over threshold voltage. Once R-peaks were captured, all peaks were 100% affirmed by eye observation on PC screen after the end of recording. If incorrect peaks are captured, or correct peaks are NOT captured, we

#### **Figure 4.**

*Accurate peak detection. Human EKG recorded with a lab-made amplifier. A physician diagnosed this heart as a sinus arrhythmia, but not life-threatening; male age: 60s.*

#### **Figure 5.**

*Accurate data collection. Peak identification from EKG (A) and construction of time series (B). P, Q, R, S, and T peaks are indicated (see A). Small arrows in A point all the P-peaks. Double arrowhead indicates that there is no P-peak within one heartbeat period. Therefore, this is premature ventricular contraction (PCV). Within 474 beat time period, 10 PVCs are visible.* **Figure 5** *was recorded 5 years before* **Figure 4** *from the same subject.*

**39**

**Figure 6.**

*making additions of each values one by one (C).*

*mDFA Detects Abnormality: From Heartbeat to Material Vibration*

manually made a correction on PC screen. As a result, all peak interval time series become accurate. It is time consuming work but inevitable for accurate interpretation of data. The sampling rate is 1 kHz for the heartbeat (20–40 kHz for material-

Since we consider that accurate data sampling before analysis is paramount for later interpretation of results, skipping heartbeats and irregular heartbeats should not be deleted before analyzing, like someone does. However, any artificial spiky

In summary, accurately recorded EKG without large noise, accurately captured R-peaks (stars in **Figures 4** and dots in **Figure 5A**), and accurate peakto-peak time interval time series is important for performing accurate mDFA

We first construct an accurate R-R interval time series from EKG recordings, which is [*Xi*] (**Figure 6A**, abscissa axis, the number of heart beat *i*, and vertical axis, rate of beating in beat per min). **Figure 6** shows only 1 - 30 beats among 2000 beats. We use "heart rate" instead of "interval time." If we use R-R-interval time, which is an inverse of "rate," mDFA results are the same. To biologists, using "rate" is intuitively more understandable about physiology of the heart than using "inter-

*A diagrammatic explanation of pretreatment of R-R peak data. Measuring a R-R peak interval time Xi, where i = 1, 2, 3, --- 2000 (A), obtaining an average of them, Xave, and thereafter subtracting it from Xi (B), and* 

*DOI: http://dx.doi.org/10.5772/intechopen.85798*

vibration as shown in below sections).

noise should not be counted as a pulse.

**Figure 6** shows the procedure of mDFA.

val." The seventh beat in **Figure 6A** shows an irregular beat.

(**Figure 5B**).

**5.3 Time series**

*5.3.1 First procedure*

*mDFA Detects Abnormality: From Heartbeat to Material Vibration DOI: http://dx.doi.org/10.5772/intechopen.85798*

manually made a correction on PC screen. As a result, all peak interval time series become accurate. It is time consuming work but inevitable for accurate interpretation of data. The sampling rate is 1 kHz for the heartbeat (20–40 kHz for materialvibration as shown in below sections).

Since we consider that accurate data sampling before analysis is paramount for later interpretation of results, skipping heartbeats and irregular heartbeats should not be deleted before analyzing, like someone does. However, any artificial spiky noise should not be counted as a pulse.

In summary, accurately recorded EKG without large noise, accurately captured R-peaks (stars in **Figures 4** and dots in **Figure 5A**), and accurate peakto-peak time interval time series is important for performing accurate mDFA (**Figure 5B**).

#### **5.3 Time series**

*Noise and Vibration Control - From Theory to Practice*

"movement-induced noise and drift" (see **Figure 4**).

*a sinus arrhythmia, but not life-threatening; male age: 60s.*

EKG signal was captured by two commercially available Ag/AgCl electrodes and

Peaks are captured automatically by a lab-made program. R-peaks are the time point at which Vmax is attained over threshold voltage. Once R-peaks were captured, all peaks were 100% affirmed by eye observation on PC screen after the end of recording. If incorrect peaks are captured, or correct peaks are NOT captured, we

*Accurate peak detection. Human EKG recorded with a lab-made amplifier. A physician diagnosed this heart as* 

a lab-made amplifier that can damp undulatory noise. The amplifier has a short input-time-constant (*tau* = 0.1 or 0.22 s, depending on capacitor used, 0.01 or 0.022 μF). The *tau* value for EKG-machine in hospital-use is set at about 10 s under the international regulation. A large *tau* amplifier makes signal-baseline drift when subjects move. We thus needed to make a small-*tau* amplifier in order to reduce

**5.2 Accurate data sampling**

**38**

**Figure 5.**

**Figure 4.**

*subject.*

*Accurate data collection. Peak identification from EKG (A) and construction of time series (B). P, Q, R, S, and T peaks are indicated (see A). Small arrows in A point all the P-peaks. Double arrowhead indicates that there is no P-peak within one heartbeat period. Therefore, this is premature ventricular contraction (PCV). Within 474 beat time period, 10 PVCs are visible.* **Figure 5** *was recorded 5 years before* **Figure 4** *from the same*  **Figure 6** shows the procedure of mDFA.

#### *5.3.1 First procedure*

We first construct an accurate R-R interval time series from EKG recordings, which is [*Xi*] (**Figure 6A**, abscissa axis, the number of heart beat *i*, and vertical axis, rate of beating in beat per min). **Figure 6** shows only 1 - 30 beats among 2000 beats. We use "heart rate" instead of "interval time." If we use R-R-interval time, which is an inverse of "rate," mDFA results are the same. To biologists, using "rate" is intuitively more understandable about physiology of the heart than using "interval." The seventh beat in **Figure 6A** shows an irregular beat.

#### **Figure 6.**

*A diagrammatic explanation of pretreatment of R-R peak data. Measuring a R-R peak interval time Xi, where i = 1, 2, 3, --- 2000 (A), obtaining an average of them, Xave, and thereafter subtracting it from Xi (B), and making additions of each values one by one (C).*

For mDFA computation, we use 2000 heartbeat data. Both data shorter or longer than 2000 can be usable but we fixed it 2000 after testing [1]. Long data, such as 1 or 2 h data, does not have significant benefit for interpretation of physiological meaning of results. The reason is simple. The cardiac system (CS) never becomes a stable state. The CS is an ever-changing dynamic system, which is our temporary interpretation and we have had consistent results. Currently, we use 2000 beat data. A 2000 beat time period length is about 30–40 min [1].

#### *5.3.2 Second procedure*

Mean value from 2000 data is Xave. By removing Xave from each data (X), one can get a time series of pure fluctuation [X − Xave] (**Figure 6B**).

#### *5.3.3 Third procedure*

A computation <sup>∑</sup><sup>1</sup> <sup>2000</sup>*x* makes a random-walk like temporal sequence [yi] (**Figure 6C**). Important concepts in mDFA are "averaging" and "sigma (summation of data, **Figure 6C**)."

## **5.4 Trend**

**Figure 6** demonstrates diagrammatically that the fluctuation property is expressed in connection with the average value. The sequence [xi] is heart rate time series in beat per min (**Figure 6A**). The sequence [Xi − Xave] expresses pure fluctuation (**Figure 6B**), some larger and some smaller than the average value. One can see that the seventh beat in **Figure 6A** shows a very small value. The seventh beat makes [yi] trace jump down (see the seventh dot, i = 7, in **Figure 6**). It is catastrophic happening; thus, this event is an arrhythmic heartbeat. This kind of event becomes a matter of life or death if extremely unlucky. In fact, a single event is not only life threatening but also not so happy of course. Therefore, the trait of fluctuation is directly linked to life or death.

In summary, the sequence [yi] expresses sigma (Σ) of each value. This [yi] is "trend." This is an explanation about the "pretreatment" of data before conducting mDFA. This [yi] is the data that mDFA analyzes. Both mDFA and DFA use [yi] for calculation, but the concept is different between them as shown below. See [1] for details.

#### **5.5 Box size**

In **Figure 7A**, 2000 beat long data are broken up into small length data; here it is 10 beat long (see three Boxes in **Figure 7A**). Box-size is freely changeable in program. In **Figure 7**, we show only box-size-10 as an example. We tested smaller box less than10 in box-size. As a result, it is not so useful than we thought. In our program, mDFA's box size ranges from 10 to 1000 [1]. In computing, mDFA automatically changes box-size, starting from box-size 10-beat. Then 11-beat, 12-beat, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, …, 30, 31, 32, …, 40, 41, …, 50, 51, …, 60, 61, …, 70, 71, …, 80, …, 90, …, 100, then 110, 120, and so forth [1].

#### **5.6 Fitting curve**

**Figure 7B** shows a fitting curve. They are linear fitting curves yv(1), yv(2), and yv(3) (**Figure 7B**). This example (**Figure 7B**) is linear fitting, just for the sake of ease. But, in practice, we must use biquadratic fitting [1] (see **Figure 8** caption).

**41**

**5.7 Detrending**

*unvarying SI value. mDFA uses quadratic fitting.*

**Figure 8.**

**Figure 7.**

*See text.*

A fitting yv curve is given by a PC computation as shown in **Figure 7B**. Next computation is making a detrended curve that is given as zi = yi − yv. After this procedure, true fluctuation remains. This is "detrending." The [zi] sequence is important.

*Several kinds of fitting; real human data. The [yi] curve shows raw data. We tested fittings, linear, quadratic, cubic, biquadratic, and further. As a result, less than fourth order computation does not return a stable/*

*Diagrammatical representation of the "detrending" procedure. A series shown in Figure 6C is broken up into 10-beat-long box (A), drawing a fitting curve in each box (B), and thereafter executing detrending (C).* 

*mDFA Detects Abnormality: From Heartbeat to Material Vibration*

*DOI: http://dx.doi.org/10.5772/intechopen.85798*

*mDFA Detects Abnormality: From Heartbeat to Material Vibration DOI: http://dx.doi.org/10.5772/intechopen.85798*

**Figure 7.**

*Noise and Vibration Control - From Theory to Practice*

A 2000 beat time period length is about 30–40 min [1].

get a time series of pure fluctuation [X − Xave] (**Figure 6B**).

*5.3.2 Second procedure*

*5.3.3 Third procedure*

**5.4 Trend**

**5.5 Box size**

**5.6 Fitting curve**

A computation <sup>∑</sup><sup>1</sup>

tion of data, **Figure 6C**)."

directly linked to life or death.

For mDFA computation, we use 2000 heartbeat data. Both data shorter or longer than 2000 can be usable but we fixed it 2000 after testing [1]. Long data, such as 1 or 2 h data, does not have significant benefit for interpretation of physiological meaning of results. The reason is simple. The cardiac system (CS) never becomes a stable state. The CS is an ever-changing dynamic system, which is our temporary interpretation and we have had consistent results. Currently, we use 2000 beat data.

Mean value from 2000 data is Xave. By removing Xave from each data (X), one can

(**Figure 6C**). Important concepts in mDFA are "averaging" and "sigma (summa-

**Figure 6** demonstrates diagrammatically that the fluctuation property is expressed in connection with the average value. The sequence [xi] is heart rate time series in beat per min (**Figure 6A**). The sequence [Xi − Xave] expresses pure fluctuation (**Figure 6B**), some larger and some smaller than the average value. One can see that the seventh beat in **Figure 6A** shows a very small value. The seventh beat makes [yi] trace jump down (see the seventh dot, i = 7, in **Figure 6**). It is catastrophic happening; thus, this event is an arrhythmic heartbeat. This kind of event becomes a matter of life or death if extremely unlucky. In fact, a single event is not only life threatening but also not so happy of course. Therefore, the trait of fluctuation is

In summary, the sequence [yi] expresses sigma (Σ) of each value. This [yi] is "trend." This is an explanation about the "pretreatment" of data before conducting mDFA. This [yi] is the data that mDFA analyzes. Both mDFA and DFA use [yi] for calculation, but the concept is different between them as shown below. See [1] for details.

In **Figure 7A**, 2000 beat long data are broken up into small length data; here it is 10 beat long (see three Boxes in **Figure 7A**). Box-size is freely changeable in program. In **Figure 7**, we show only box-size-10 as an example. We tested smaller box less than10 in box-size. As a result, it is not so useful than we thought. In our program, mDFA's box size ranges from 10 to 1000 [1]. In computing, mDFA automatically changes box-size, starting from box-size 10-beat. Then 11-beat, 12-beat, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, …, 30, 31, 32, …, 40, 41, …, 50, 51, …, 60, 61, …,

**Figure 7B** shows a fitting curve. They are linear fitting curves yv(1), yv(2), and yv(3) (**Figure 7B**). This example (**Figure 7B**) is linear fitting, just for the sake of ease. But, in practice, we must use biquadratic fitting [1] (see **Figure 8** caption).

70, 71, …, 80, …, 90, …, 100, then 110, 120, and so forth [1].

<sup>2000</sup>*x* makes a random-walk like temporal sequence [yi]

**40**

*Diagrammatical representation of the "detrending" procedure. A series shown in Figure 6C is broken up into 10-beat-long box (A), drawing a fitting curve in each box (B), and thereafter executing detrending (C). See text.*

#### **Figure 8.**

*Several kinds of fitting; real human data. The [yi] curve shows raw data. We tested fittings, linear, quadratic, cubic, biquadratic, and further. As a result, less than fourth order computation does not return a stable/ unvarying SI value. mDFA uses quadratic fitting.*

#### **5.7 Detrending**

A fitting yv curve is given by a PC computation as shown in **Figure 7B**. Next computation is making a detrended curve that is given as zi = yi − yv. After this procedure, true fluctuation remains. This is "detrending." The [zi] sequence is important.

### **5.8 DFA and mDFA**

In **Figure 7C**, arrows point two values: "entrance value" and "exit value" in each box (**Figure 7**). mDFA uses entrance and exit values obtained by detrending procedures.

In turn, Peng's DFA uses all 10 values in each box (see **Figure 9**). But the detrending procedure is a common concept between mDFA and DFA.

For convenience, a portion of **Figure 7C** (from the 1st to the 16th) is enlarged in **Figure 9**. Peng's DFA measures vertical differences between fitting curve and real data (**Figure 9**). Thus, Peng's DFA looks at "critical phenomena" according to physicists. But mDFA does not do those measurements: mDFA looks at 10 heartbeats at once (**Figure 9**).

Peng's DFA looks at individual heartbeat one by one (**Figure 9**). What mDFA looks at is how much [zi] sequence has proceeded over time within a box, sometimes up and sometimes down. Therefore, mDFA can see ever changing undulation or fluctuate in each box (**Figure 9**). Fluctuation is not always stochastic noise. Rather, fluctuation carries previously unknown hidden information. It is sometimes hidden threat. It is sometimes high-risk information.

One might think that both, Peng's DFA and mDFA, have a similar calculation concept. But, mathematically, there is a gap between their concepts. According to Peng's paper and successor's publications, there is a tipping point (changing point and critical point) at the box-size11-beat. Peng et al. labeled the scaling exponent as alpha-1 and alpha-2. Alpha-1 corresponds to box-size ranges smaller than 11. In turn, alpha-2 corresponds to box-size range greater than 11. However, mDFA does not detect this tipping point. We found that box-size smaller than 30 (30-beat-box-sise) does not carry physiologically significant information. mDFA program begins computation from 10-beat-box-size and goes to 1000-beat-boxsize (see **Figure 10**) but draws regression lines from box-size greater than 30 (see next section).

#### **5.9 Scaling**

**Figure 10** shows typical mDFA results from heartbeat data of a crab (**Figure 10A**). mDFA makes a log-log plotting graph. Abscissa axis, which is box-size and ordinate is shown in variance (**Figure 10B**). If a clear slope can be seen in the graph, mathematically, the slope represents scaling property buried in heartbeat signal.

#### **Figure 9.**

*Diagrammatic representation of the difference between Pang's DFA and mDFA. Pang's DFA calculates vertical difference between data and zero-line (four small arrows). Peng's DFA computes average of 10 data in a box. Total data length is 2000-beat. There are 200 boxes of 10-beat-box. Peng's DFA thus can get 2000 data in onebox-size-calculation. In turn, mDFA computes the difference between Ent and Exit (Ext − Ent). mDFA thus can get 200 data. After finishing box-10 computation, the program increases box-size and repeats calculations cyclically: box-11, box-12, box-13, and so on.*

**43**

**Figure 11.**

*Standard six box size range.*

*mDFA Detects Abnormality: From Heartbeat to Material Vibration*

By drawing a strait regression line, mDFA computes SI (**Figure 10B**). But the length of the regression line, from where to where, is unsolved. Default mDFA program draws six lines at once in a log-log graph. Each slope corresponds to the respective SI value. In **Figure 10C**, four SIs are computed. Standard six box-size ranges include: [30; 70], [70; 140], [51; 100], [30; 140], [130; 270], and [30; 270] (**Figure 11**). In our studies, unless otherwise specified, the six set is not changed for the sake of NOT to create confusion, while it can be changed infinitely. **Figure 11** is the final style after testing a variety of ranges. We have been using this "unaltered

*An example mDFA. (A) Heartbeat interval time series; Gazami crab. (B) mDFA graph, box size versus variance; slope determines the SI. (C) Four box-size-ranges and corresponding SI. Crossover can be seen at two points, at a box-size of ~30 beat and ~200 beat. Physiological interpretation is under study. In this computation, 20,000-beat data were used, although 2000-beat data produce similar results (not shown).*

Meanwhile, those who have the skill of programing can easily make his/her own program. It is a high school level mathematics. Scaling range can be determined by the person who makes it. Other mathematical procedures, such as averaging, square

So, we can guaranty that any mDFA program surely captures cardiac scaling properties. mDFA works in physiology. Thanks to great names, William Harvey (1628 Circulation), Marcello Malpighi (1653 Medical Dr., Capillary), Ludwig Traube (1872 Alternans pulse), Willem Einthoven (1903 EKG), and Anton Julius

program" made by former master student, Tanaka [7] for over 10 years.

root fitting, and drawing a scaling line, are not complicated tasks.

*DOI: http://dx.doi.org/10.5772/intechopen.85798*

**5.10 Scaling range**

**Figure 10.**

#### **Figure 10.**

*Noise and Vibration Control - From Theory to Practice*

In **Figure 7C**, arrows point two values: "entrance value" and "exit value" in each box (**Figure 7**). mDFA uses entrance and exit values obtained by detrending

In turn, Peng's DFA uses all 10 values in each box (see **Figure 9**). But the

For convenience, a portion of **Figure 7C** (from the 1st to the 16th) is enlarged in **Figure 9**. Peng's DFA measures vertical differences between fitting curve and real data (**Figure 9**). Thus, Peng's DFA looks at "critical phenomena" according to physicists. But mDFA does not do those measurements: mDFA looks at 10 heartbeats at

Peng's DFA looks at individual heartbeat one by one (**Figure 9**). What mDFA looks at is how much [zi] sequence has proceeded over time within a box, sometimes up and sometimes down. Therefore, mDFA can see ever changing undulation or fluctuate in each box (**Figure 9**). Fluctuation is not always stochastic noise. Rather, fluctuation carries previously unknown hidden information. It is sometimes

One might think that both, Peng's DFA and mDFA, have a similar calculation concept. But, mathematically, there is a gap between their concepts. According to Peng's paper and successor's publications, there is a tipping point (changing point and critical point) at the box-size11-beat. Peng et al. labeled the scaling exponent as alpha-1 and alpha-2. Alpha-1 corresponds to box-size ranges smaller than 11. In turn, alpha-2 corresponds to box-size range greater than 11. However, mDFA does not detect this tipping point. We found that box-size smaller than 30 (30-beat-box-sise) does not carry physiologically significant information. mDFA program begins computation from 10-beat-box-size and goes to 1000-beat-boxsize (see **Figure 10**) but draws regression lines from box-size greater than 30

**Figure 10** shows typical mDFA results from heartbeat data of a crab (**Figure 10A**). mDFA makes a log-log plotting graph. Abscissa axis, which is box-size and ordinate is shown in variance (**Figure 10B**). If a clear slope can be seen in the graph, mathemati-

*Diagrammatic representation of the difference between Pang's DFA and mDFA. Pang's DFA calculates vertical difference between data and zero-line (four small arrows). Peng's DFA computes average of 10 data in a box. Total data length is 2000-beat. There are 200 boxes of 10-beat-box. Peng's DFA thus can get 2000 data in onebox-size-calculation. In turn, mDFA computes the difference between Ent and Exit (Ext − Ent). mDFA thus can get 200 data. After finishing box-10 computation, the program increases box-size and repeats calculations* 

cally, the slope represents scaling property buried in heartbeat signal.

detrending procedure is a common concept between mDFA and DFA.

hidden threat. It is sometimes high-risk information.

**5.8 DFA and mDFA**

procedures.

once (**Figure 9**).

(see next section).

**5.9 Scaling**

**42**

**Figure 9.**

*cyclically: box-11, box-12, box-13, and so on.*

*An example mDFA. (A) Heartbeat interval time series; Gazami crab. (B) mDFA graph, box size versus variance; slope determines the SI. (C) Four box-size-ranges and corresponding SI. Crossover can be seen at two points, at a box-size of ~30 beat and ~200 beat. Physiological interpretation is under study. In this computation, 20,000-beat data were used, although 2000-beat data produce similar results (not shown).*

#### **5.10 Scaling range**

By drawing a strait regression line, mDFA computes SI (**Figure 10B**). But the length of the regression line, from where to where, is unsolved. Default mDFA program draws six lines at once in a log-log graph. Each slope corresponds to the respective SI value. In **Figure 10C**, four SIs are computed. Standard six box-size ranges include: [30; 70], [70; 140], [51; 100], [30; 140], [130; 270], and [30; 270] (**Figure 11**). In our studies, unless otherwise specified, the six set is not changed for the sake of NOT to create confusion, while it can be changed infinitely. **Figure 11** is the final style after testing a variety of ranges. We have been using this "unaltered program" made by former master student, Tanaka [7] for over 10 years.

Meanwhile, those who have the skill of programing can easily make his/her own program. It is a high school level mathematics. Scaling range can be determined by the person who makes it. Other mathematical procedures, such as averaging, square root fitting, and drawing a scaling line, are not complicated tasks.

So, we can guaranty that any mDFA program surely captures cardiac scaling properties. mDFA works in physiology. Thanks to great names, William Harvey (1628 Circulation), Marcello Malpighi (1653 Medical Dr., Capillary), Ludwig Traube (1872 Alternans pulse), Willem Einthoven (1903 EKG), and Anton Julius

**Figure 11.** *Standard six box size range.*

Carlson (1904 Heart physiology on model animals), for example, basics of physiology would never change forever.

If two persons have their own mDFA program, then they analyze the same data, and then one can say, "my computed SI is 1.10" and the other can say, "mine is 0.93." This kind of "contradiction" can happen. But it is NOT a big deal. We need to overlook the details. Both are around 1.

Regarding mDFA computation, please see the following sections that show what we calculate from heartbeat data.

EKG signal is generated by the cardiac system. Elements in the system are linked to each other. The system cannot work properly without feedback connections. If one can find a scaling-line in the graph (**Figure 10B**), the heart system is working properly. If a line is bending or winding, something is wrong in the body system. We guaranty so. And if a subject is healthy, mDFA tells you that the SI-value is around 1 (1.0).

As far as we know, this scaling property of the heart system was first documented in 1982 [8] and then in 1990s [9]. They proposed this nice metric theory. They used a well-known mathematical idea. We must say we moved it forward. But mDFA is based on different concepts—this is the novelty of this research—than Peng's concept as shown below. We just use the scaling property that the cardiac system inherently has.

#### **5.11 Physiological interpretation**

After finding the slope, linear fitting is necessary to determine SIs. We draw a regression line from box-size 30-beat to 270-beat as the best range for interpreting physiological meaning of heartbeat data [1]. In our study for more than 10 years, SI is "always" obtained from the regression line ranging from box-size 30-beat to box-size 270 beat (**Figure 10B**).

A 30-beat time length corresponds to about 30 s. A 270-beat time length is approximately 3–5 min. We feel sure that life prefers "3–5 min" period length: boxing round fighting time, for 3 min; hit song one musical performance, for 3 min; instant noodles cooking time, for 3 min; and a pain killer medication, coming on 3 min after taking it. We found that it seems convenient and correct that mDFA draws a line within a box-size range [30; 270] (**Figure 10C**) to check if the body system is alright or not.

## **6. Human general population**

#### **6.1 Ethics**

We try to record EKGs of general population including people in the classroom, in the exhibition hall, company-employees, university-employees, and people at a scientific conference venue [1]. Every experimental subject was treated as per the ethical control regulations of universities (Tokyo Metropolitan University; Tokyo Women's Medical University; Universitas Advent Indonesia, Bandung; Universitas Airlangga, Surabaya, Indonesia).

#### **6.2 SI: reproducibility**

All our data are collected by the author [1, 5, 6]: invertebrate heart study since the 1980s, human data since approximately 2000, and materials data since 2010. The mDFA program was made by a former master student Tanaka [7] in about 2004.

**45**

*mDFA Detects Abnormality: From Heartbeat to Material Vibration*

mDFA results are reproducible and consistent. We found stratification phenomena that provide evidence for the quantitative measure SI links to various physiological phenomena in a one-to-one manner [1, 7, 10–12]. Arrhythmic heartbeat decreases SI [11]. Non-REM sleep decreases SI [12]. Premature ventricular contraction (PVC) decreases SI [11]. Alternans (harbinger of death rhythm) decreases SI [7]. Anxiety, fear, and worry decrease SI [10]. University president, vice president, president-secretary, and dean professor all have a low SI [1] but teaching-only professors have a healthy SI (SI = ~1.0) [1]. A happy content house-

Meanwhile, we encountered some healthy looking but non-healthy-heart subjects in general population [1]. We found that these subjects have had received cardiac surgery. Their myocardium is indeed injured like the crab specimen shown in **Figure 3**. All of them had a high SI. A person who has an implantable cardioverter had SI = 1.22 [1]. A person who has stent-replacement had SI = 1.26 [1]. A person who had bypass-surgery had SI = 1.38 [1]. A person who had a surgery due to ventricular septal defect had SI = 1.41 [1]. However, until today, we have never met any person, in general population, who keep maintaining a high SI and later

Ergometric exercise increases SI [1]. We think that hard exercise is probably

We would like to declare that mDFA can sense warning sign although mDFA

We learned that mDFA detects abnormality of the heart system. Especially, we learned that a system failure increases SI up from the basic value 1.0. The failure of the heart is generally myocardial cell damage. Myocardial cells are the elementary structure of the system. Analogically, it is like a material that is made by granulated elements [13]. We expected that mDFA might contribute to nonliving system

In **Figure 3**, when a crab heart's cells were damaged by an electrode, the damage caused a significant shift of SI (toward SI = 1.5) (**Figure 3**). In human heart cases, a person who had a surgery due to ventricular septal defect, the cardiac surgery might be a major cause that pushed SI up from normal SI [1] (see a large SI, 1.41, in

Materials have different properties, meaning each has its own quirks when

In nonliving material experiments, we use a piezoelectric sensor for vibration detection. It is a mechanical monitoring device made for a cardiac pulse sensor (ADInstruments, Austuraria). The sampling rate is 1 kHz in our heart experiments. The heart beats at about 1 Hz in rate. In turn, a motor rotates ~3000 times per min.

Heartbeat is repetitive muscle contraction. It is a cyclic behavior. It is oscillation. It is a fluctuating event. SI can quantify these unstable movements. SI can tell us the cardiac system's condition. If SI is around 1, there is no health problem regarding the heart and its control. However, if your SI is high or low, maybe I say, "Better see

*DOI: http://dx.doi.org/10.5772/intechopen.85798*

NOT a healthy behavior for normal humans.

a doctor." But the research has only just begun.

because mDFA works well in the heart.

processing [13] like the hearts.

**7.2 Abnormal vibration**

cannot identify what is wrong or what is going on.

wife has a healthy SI too [1].

passed away.

**7. Nonliving material**

**7.1 Introduction**

Section 6.2).

*mDFA Detects Abnormality: From Heartbeat to Material Vibration DOI: http://dx.doi.org/10.5772/intechopen.85798*

mDFA results are reproducible and consistent. We found stratification phenomena that provide evidence for the quantitative measure SI links to various physiological phenomena in a one-to-one manner [1, 7, 10–12]. Arrhythmic heartbeat decreases SI [11]. Non-REM sleep decreases SI [12]. Premature ventricular contraction (PVC) decreases SI [11]. Alternans (harbinger of death rhythm) decreases SI [7]. Anxiety, fear, and worry decrease SI [10]. University president, vice president, president-secretary, and dean professor all have a low SI [1] but teaching-only professors have a healthy SI (SI = ~1.0) [1]. A happy content housewife has a healthy SI too [1].

Meanwhile, we encountered some healthy looking but non-healthy-heart subjects in general population [1]. We found that these subjects have had received cardiac surgery. Their myocardium is indeed injured like the crab specimen shown in **Figure 3**. All of them had a high SI. A person who has an implantable cardioverter had SI = 1.22 [1]. A person who has stent-replacement had SI = 1.26 [1]. A person who had bypass-surgery had SI = 1.38 [1]. A person who had a surgery due to ventricular septal defect had SI = 1.41 [1]. However, until today, we have never met any person, in general population, who keep maintaining a high SI and later passed away.

Ergometric exercise increases SI [1]. We think that hard exercise is probably NOT a healthy behavior for normal humans.

Heartbeat is repetitive muscle contraction. It is a cyclic behavior. It is oscillation. It is a fluctuating event. SI can quantify these unstable movements. SI can tell us the cardiac system's condition. If SI is around 1, there is no health problem regarding the heart and its control. However, if your SI is high or low, maybe I say, "Better see a doctor." But the research has only just begun.

We would like to declare that mDFA can sense warning sign although mDFA cannot identify what is wrong or what is going on.
