**6. Frequency and time-frequency analysis**

EMG power spectrum estimation methods can be categorized into parametric and nonparametric techniques. The spectral methods include fast Fourier transform (FFT), multitaper analysis and short-time Fourier transform (STFT) and wavelet transform. The difference between FFT and Wavelet Transformation is that FFT is localized to the frequency domain whereas the latter is localized to time-frequency analysis. Hu [53] recorded cortical and spinal somatosensory evoked potential (CSEP and SSEP), cortical motor evoked potential (CMEP) and spinal cord evoked potential (SCEP). The short time Fourier transformation was applied to the CSEP signal with a Hanning window [53]. The results revealed that the time-frequency analysis is a better marker for spinal injury than time domain analysis. The peak power after spinal injury had lesser energy with more dispersion in time-frequency scale.

The EMG time series signal can be analyzed in the frequency domain for the diagnosis of gait disorders. The frequency spectrum for EMG signals is in range of 0–500 Hz [54]. The FFT algorithm [55] computes the discrete Fourier transform (DFT) of EMG signal more efficiently. The FFT decomposes the EMG signals into periodic sine and cosine waves. We computed the FFT of EMG signal recorded from the Vastus Medialis (VM) during walking (**Figure 4**).

#### **Figure 4.**

*(A) sEMG signal from VM during walking in time domain; (B) frequency domain representation of the signal using FFT.*

**27**

signals [61, 62].

*A Review of EMG Techniques for Detection of Gait Disorders*

The FFT allows computation of power spectra by squaring of FFT's magnitude [56]. In Parkinson disease, the spectral power of the signal has lower amplitude for the usual tremor than for the unusual tremor, which has peak amplitude of 4–6 Hz during an atypical tremor [15]. The signals associated with nonperiodic tremors are differentiable with FFT [57]. The EMG signal from neuropathic patients with SCI also exhibited distinct power spectrum density and amplitude in comparison to healthy individuals [58]. The application of FFT to the EMG envelope revealed muscle burst discharge in frequency domain ranging from 4 to 7 Hz [15]. Average power spectra computed from fractionated EMG of ALS mice by FFT was significantly higher than the control group. In the ALS group the spectra were skewed towards higher frequency content but single unit recordings revealed the absence of higher motor neuron (MN) frequencies or shortening of MN frequency in ALS mice [32], due to small type firing neurons improperly increasing firing frequency. This phenomenon results in co-contraction thus producing fractionated EMG. Co-contraction in muscles can also be observed in spinal cord injured patients [32]. In a study, EMG signals from lower limbs of dystonic and nondystonic participants while walking were recorded. The non-dystonic participants were also patients suffering from other gait disorders. The power spectral density was computed using FFT with the Welch method of 50% overlap. The median power frequency (MdPF) and total power in low frequency were calculated for each muscle. The results revealed that MdPF for dystonic muscles had shifted to low frequencies and a concurrent increase in total power percentage in low-frequency range was observed [59]. Thus, frequency analysis of EMG signal not only provides us with distinction between normal and abnormal gait behavior but also specific

Short-time Fourier transformation (STFT) is used to analyze a nonstationary signal in the frequency-domain. The signal is sliced and subjected to Fourier transform. Segmenting the signal is called time domain windowing, and the time

> √ \_\_\_ 2*n*

(τ) = *S* (τ)*h*(τ − *t*), where *h*(*t*) is the window function

. *d* (2)

∫*S* (τ)*h*(τ − *t*) *e*−*it*

Mitchell et al. [60] used cross time-frequency analysis to diagnose hypertension of the GM muscle. The study included 57 elderly people with 10 younger adults. Reduced Interference distribution (RID) was utilized to remove cross terms implementing time smoothing window and frequency smoothing window. A Hanning frequency smoothing window was chosen. In the study of gait, it is necessary to consider a time-localized cross-correlation between two signals, such as left and right muscle groups responsible for gait [60]. Hence, cross Wigner distribution (CWD) was selected to preserve the phase information. The results revealed statistical significance for several time-frequency parameters of sEMG between control group and persons with neuropathy, diabetes, osteoporosis, and arthritis patients [60]. STFT does not adopt an optimal time window or frequency resolution for non-stationary signals [7]. For the implementation of FFT and STFT the signals are considered to be stationary [8]. The problem or resolution can be overcome by continuous wavelet transform (CWT) [8]. Multitaper analysis is another and perhaps more efficient method for power spectral analysis to deal with non-stationary

*DOI: http://dx.doi.org/10.5772/intechopen.84403*

gait abnormalities can be distinguished.

*St*(ω,*t*) = \_\_\_1

centered at time t. The equation for STFT is given by (2).

**6.1 Short-time Fourier transform**

localized signal is defined by *St*


Preface

Chapter 10 **Special Rehabilitation Treatment Methodology: INFINITY**

Elisa Edi Anna Nadia Lioce, Matteo Novello and Caterina Guiot

Chapter 11 **Therapeutic Ultrasounds: Physical Basis and Clinical**

**method® 205** Michaela Tomanova

**VI** Contents

**Assessment 213**

Physical therapy, also known as physiotherapy, is a physical medicine and rehabilitation specialization that, by using mechanical force and movements, remedies impairments and promotes mobility, function, and quality of life through examination, diagnosis, prognosis, and physical intervention. In addition to clinical practice, other activities encompassed by the physical therapy profession include research, education, consultation, and administra‐ tion. Physical therapy services may be provided alongside or in conjunction with other med‐ ical services. They are performed by physical therapists (known as physiotherapists in many countries) with the help of other medical professionals.

This book consists of 11 chapters written by professionals from all around the world. It in‐ cludes manuscripts on scapular muscle activity, physical function for elderly people, and important points for excise therapy with rhythmic movement. These manuscripts demon‐ strate precious points for physical therapy.

Next, the book includes chapters on physical therapy for cancer, chronic venous disease, and mental health, special physical therapy for back pain, therapeutic ultrasounds, and oth‐ ers. This information should instruct global physical therapists and related experts.

I am very pleased to be the editor of this book, as all manuscripts are excellent and open up new directions for physical therapists.

> **Professor Toshiaki Suzuki, DMSc** Graduate School of Kansai University of Health Sciences, Osaka, Japan


*Article* **Displacement of the Greater Tuberosity in Humeral Head Fractures Does Not only Depend on Rotator Cuff Status**

**Lisa Klute \*, Christian Pfeifer, Isabella Weiss, Agnes Mayr, Volker Alt and Maximilian Kerschbaum**

Clinic of Trauma Surgery, University Medical Center Regensburg, Franz-Josef-Strauss-Allee 11, 93053 Regensburg, Germany<EMAIL_ADDRESS>(C.P<EMAIL_ADDRESS>(I.W<EMAIL_ADDRESS>(A.M<EMAIL_ADDRESS>(V.A<EMAIL_ADDRESS>(M.K.) **\*** Correspondence<EMAIL_ADDRESS>Tel.: +49-941-944-6841

**Abstract:** It is assumed that dorsocranial displacement of the greater tuberosity in humeral head fractures is caused by rotator cuff traction. The purpose of this study was to investigate the association between rotator cuff status and displacement characteristics of the greater tuberosity in four-part humeral head fractures. Computed tomography scans of 121 patients with Neer type 4 fractures were analyzed. Fatty infiltration of the supra- and infraspinatus muscles was classified according to Goutallier. Position determination of the greater tuberosity fragment was performed in both coronary and axial planes to assess the extent of dorsocranial displacement. Considering non-varus displaced fractures, the extent of the dorsocranial displacement was significantly higher in patients with mostly inconspicuous posterosuperior rotator cuff status compared to advanced fatty degenerated cuffs (cranial displacement: Goutallier 0–1: 6.4 mm ± 4.6 mm vs. Goutallier 2–4: 4.2 mm ± 3.5 mm, *p* = 0.020; dorsal displacement: Goutallier 0–1: 28.4◦ ± 32.3◦ vs. Goutallier 2–4: 13.1◦ ± 16.1◦, *p* = 0.010). In varus displaced humeral head fractures, no correlation between the displacement of the greater tuberosity and the condition of the posterosuperior rotator cuff could be detected (*p* ≥ 0.05). The commonly accepted theory of greater tuberosity displacement in humeral head fractures by rotator cuff traction cannot be applied to all fracture types.

**Keywords:** humeral head fracture; greater tuberosity; rotator cuff; fatty degeneration


*<IP_ADDRESS>. Microwave annealing (MW)*

The use of microwave-assisted annealing enabled quick fabrication of ZnO-TFT at 140°C with a *μ* of 1.7 cm2 V−1 s−1, which is improved to three- to sixfolds in comparison with TFTs processed by conventional hot-plate annealing [56]. This enhanced TFT performance is attributed to the improved development of ZnO grains suitable for reducing the length of transport paths across grain boundaries and the shorter Zn-Zn distance enabling better overlap between the Zn s-orbitals, thus creating chemical structures appropriate for high-performance AOS.


• Inhibitor and water molecules interaction

Adsorbed water molecule are removed from the metal surface due to displacement reaction of adsorbed inhibitor molecules and increases the size of hydrocarbon part of inhibitor, which leads to decreasing solubility and increasing adsorption ability. This is consistent with the increasing inhibitive efficiency observed at constant concentrations with increasing molecular size in a series of related compounds.


*2.3. Multiple-Linear Regression*

One of the principal objectives of this study is to quantify the effects of temperature, precipitation, ET, soil moisture at root-zone (NDII), ENSO and DMI on the NDVI as a surrogate for vegetation in the study area. Multiple-linear regression analysis (MLR), which is commonly used to explain the relationship between one continuous dependent variable and two or more independent variables, was employed. The MLR model output of a number *n* observations can be represented as

$$y\_i = \beta\_0 + \beta\_1 \mathbf{x}\_{i2} + \dots + \beta\_p \mathbf{x}\_{ip} + \varepsilon\_i \text{ where } i = 1, 2, 3, \dots, n \tag{4}$$

where *yi* is the dependent variable (NDVI in this case), *xip* represents the independent variables (soil temperature, precipitation, Niño3.4, and DMI in this case), *β*0 is the intercept, and *β*1, *β*2, ... *βp* are the coefficients of the *x* terms. The term ε*i* represents the error term, which the model always tries to minimize.