**Abstract**

Modified detrended fluctuation analysis (mDFA) is a novel method to check abnormality of heartbeat which is developed recently by the author. mDFA can characterize any oscillation such as heartbeat by the scaling exponent (scaling index, SI). Healthy heartbeat shows SI = 1. Dying heart's SI sifts toward 0.5. Ischemic sick heart experimentally showed an SI way over 1.0 approaching 1.5. Random vibration, such as FM-radio noise and idling car-engine, shows SI = 0.5. Quietly running motor generates an SI almost equal to zero. Using mDFA, it is possible to check potential risk based on SI values. This chapter shows empirical results quantifying various signals from heartbeat to material vibration.

**Keywords:** mDFA, heartbeat rhythm, material vibration, quantifying risks, scaling exponent

### **1. Introduction**

System failure—ischemic disease of the cardiac system (CS), highway bridge crash, earthquake, space rocket launch failure, and so forth—leads to catastrophic consequences. Watching abnormality by testing toughness is important for preventing disasters. We want to detect early warning sign. But how? We have an idea. The method is modified detrended fluctuation analysis (mDFA).

In this chapter, we show examples of mDFA computation. First, we show mDFA results on the CS, then results on the nonliving, material system.

The CS is composed of the heart and the brain, that is, a pump and a controller. Evolutionally, all creatures have evolved from a common ancestor. If the CS was innovated long ago, "hearted" animals follow fundamental laws of physics (and chemistry and biology). In fact, it is known that all "hearted" animals carry the same DNA for making the heart: development of vertebrate heart is controlled by a common genetic code (a DNA sequence called Nkx, a homeobox, and a cardiacspecific homeobox). However, not only vertebrate heart but also invertebrate heart is controlled by the same genetic code: development of insect heart is regulated by "tinman DNA," which is Nkx family gene. Surprisingly, Hydra, a simple animal, that exhibits "pumping movement," has Nkx-like gene (see [1]). Therefore, the pumping-heart design is evolved since Hydra [2]. If we find a primordial basic rule in a simple creature, it is applicable to humans.

In this chapter, we first show experimental results on crustacean animals (crabs and lobsters), on which we have long worked [3]. In the second place, we present human heartbeat analysis, and lastly mechanical vibration analysis. Throughout

the study, we use an analytical method, mDFA, which is recently developed by our group [1]. We explain mDFA in the later section.
