Suresh R. Devasahayam

Time-Frequency and Wavelet Analysis

We have already noted some of the limitations of Fourier decomposition. The assumption of periodicity in the calculation of the DFT is one main limitation. Another more subtle limitation is the unavoidable compromise between time resolution and frequency resolution. This is due to the fact that the DFT is computed on a block of data. This fixes the time window or resolution as ΔT r=N/F s, where N is the block size and F S is the sampling rate. It also fixes the frequency resolution as ΔF r=F s/N. The product of the time resolution and frequency resolution, ΔT r•ΔF r is constant, which means that improvement in time resolution can be obtained only at the expense of frequency resolution and vice versa.

Wavelet decomposition of the blink reflex R2 component enables improved discrimination of multiple sclerosis

OBJECTIVES The blink reflex R2 component was subjected to wavelet decomposition for time feature extraction in order to classify the functional status of patients with multiple sclerosis. METHODS The blink reflex was recorded bilaterally with unilateral stimulation of the supra-orbital nerve in 37 normal subjects and 9 patients with multiple sclerosis (MS). The late component, R2, was subjected to time-frequency decomposition using the Daubechies-4 wavelet. Using the time-frequency coefficients, the mean time of the R2 wave as well as the standard deviation of the R2 interval were calculated in each trial. The wavelet transform enables noise reduction by allowing selective use of frequency bands with high signal-to-noise ratio for time feature extraction; therefore automatic estimation of time parameters is robust. The distribution densities of the mean and the standard deviation of the R2 wave duration for the set of trials for each subject were computed. RESULTS An appreciable difference in the densities of the two parameters extracted in the wavelet domain was seen between normals and patients. This is in contrast to the onset latency of R2 which poorly discriminates MS patients from normals. CONCLUSION The results suggest that the mean and standard deviation of the R2-time robustly estimated using wavelet decomposition can be used to support clinical diagnosis in tracking the functional status of patients with diseases like multiple sclerosis.

Modeling the Cardiovascular System

As seen in the previous chapters every physiological system requires a modeling approach that is unique, either on account of the experimental constraints or the biophysical characteristics. In the case of complex systems like the cardiovascular system several different models are used to look at different aspects of the system and to serve different end uses. A brief look at some of these different modeling approaches to this one system will serve to illustrate the broad range of modeling approaches that are possible for any system.

Continuous Time Signals and Systems

The goal of physiological measurement is to understand the working of a particular physiological system — like the cardiovascular system, the muscular system, the nervous system, the urinary system, etc. — and in the case of diseases, diagnose it with reference to that in healthy individuals. It is useful to regard the physiological system as a process (or set of processes) in which one or more physical parameters are amenable to measurement.

Modeling Myoelectric Activity

The electromyogram (EMG) is a recording of the electrical activity of muscles (also termed myoelectric activity). The EMG is recorded by placing biopotential electrodes close to the muscle of interest. The EMG is usually recorded during voluntary action of the muscles; the signal evoked from muscles by artificial electrical stimulation is called the compound muscle action potential (CMAP). The recorded signal depends upon the anatomy of the muscle and the recording electrode arrangement as well as the physiological activity. It is important to understand the effect of the recording arrangement in order to discount the peculiarities of the recording setup during analysis. Different analytical techniques focus on the anatomical structure (e.g., distribution of the neuromuscular junction, size and distribution of motor units, etc.), or on the physiological behavior (e.g., degree of activation, neuronal firing patterns, the fiber conduction velocity, muscle fatigue, etc.). We shall develop a model of the recorded electromyogram which can be used for understanding the different components in its generation; this will, we hope, lead to a logical understanding of analytical techniques for EMG processing. We shall deal mainly with the voluntary EMG since it is the more general signal. The compound muscle action potential is simply a special case where the neuronal firing pattern is replaced by a simple deterministic function, usually the unit impulse, δ(t).

Modeling Skeletal Muscle Contraction

Skeletal muscles in amphibians and mammals have been subjected to extensive investigation due to their relatively easy access and simple structure compared to other physiological systems. Consequently fairly detailed models exist for skeletal muscle behavior. Several competing models have been proposed that succeed to varying extents in explaining skeletal muscle behavior. Although abundant experimental data exists, no existing model is sufficient to explain skeletal muscle behavior under all conditions.

F166. Quantifying the tendon hammer tap

Introduction The myotatic reflex is a common neurological test performed at the bedside. This monosynaptic reflex provides a subjective assessment of the central and peripheral nervous system. The assessment of this reflex is based on the clinician’s expertise in performing and interpreting the test. It is difficult for a student or inexperienced clinician to perform and interpret the subtleties of this reflex. Even in expert hands quantification is poor, making it a limited tool for diagnosis and staging of disease. Several factors like the intervening soft-tissue, the exact location of contact and the position of the leg, make it difficult to determine how the administered tap is translated to the stretch of the tendon. We propose a simple addition to a standard tendon hammer that provides feedback to the clinician on the quality of the performed tap. This can be an useful teaching and learning tool. Methods In a freely swinging hammer of known mass, if the acceleration is known, the exact force during the tendon tap can be determined. We used an accelerometer on the head of the hammer to measure the linear acceleration during the tendon tap. Using the data from this we can plot and analyse the entire swing of the hammer along with the deceleration at the point of contact with the tendon. During use, the tendon hammer is held pivoted between thumb and forefinger and the hammer is allowed to freely swing. In this process the only external force on the hammer is the tap on the target tendon. Therefore the force of tap can be calculated accurately. Prior settings can be used for the range of forces that are deemed as adequate to produce a good response. Surface EMG electrodes on the agonist record the electrical response from the muscle which indicates a successful tap. Feedback can be provided to the user to indicate a good tap or a poor tap. Results Using this hammer, we can distinguish a good tap from a poor tap. This is quantified based on the following: magnitude and temporal course of tap force, electrical response from the muscle. Custom written software analyses the characteristics of the hammer accelerometer data to identify strike of the tendon, then confirms an electrical response on the EMG. The force of the tap is then calculated and the software checks if these fall within the preset parameters for the same. A good tap in a normal subject is one where the hammer stretches the tendon of interest with adequate force to elicit an adequate electrical response in the agonist muscle. Preliminary data support such quantitative assessment of the tendon tap. Conclusion Feedback on the quality of a tendon tap will greatly improve the interpretation and reduce the inter-person variability of interpretation of the deep tendon reflexes. Apart from being a tool that can be used for training of students, feedback of quality of tap will help in interpretation of deep tendon reflexes at the bedside.

F189. Reciprocal excitation: A hidden component of the myotatic stretch reflex

Introduction The Myotatic Reflex (MR) and Reciprocal Inhibition (RI) are well documented phenomena. They fit well into the framework of negative feedback control of muscle length and complementary control of movement by opposite groups of muscles. Reciprocal excitation (RE) has been reported intermittently and controversially, only in patients with spasticity of various forms. While using quantitative measures of the MR, we recorded clear and consistent electrical evidence of RE in normal subjects. Our experiments show that the standard textbook model of the MR is in fact incomplete. In this paper we present experimental evidence confirming the presence of RE as a spinal reflex, in normal subjects. Methods Three methods were used to elicit the MR of the quadriceps muscle: the patellar tendon tap, rapid mechanical flexion at the knee, electrical stimulation of the femoral nerve. The electrical response from the agonist and antagonist muscles were recorded simultaneously using surface EMG. Following the stretch of the quadriceps, the reflex excitation from the quadriceps and a smaller excitation from the hamstrings was recorded. Mechanical artefacts and cross-pickup from neighbouring muscles were excluded. Data from 28 normal subjects was processed and analysed with custom programs in Python. The mechanical stretch stimulus was the flexion at the knee lasting roughly 100 ms making it difficult to identify a single time-point of stretch stimulus. On electrical stimulation of the femoral nerve in the femoral triangle it was difficult to separate the reflex wave from the stimulation artefact as most subjects required strong stimulus. Results Excitation of the heteronymous group of muscles as a component of the MR in normal subjects has been clearly observed in our experiments. Though this excitation is around 10% of the primary reflex excitation, its latency and reproducibility confirm its physiological origin as a spinal reflex. The patellar tendon tap latency(ms) and amplitude(mV) ranges averaged over 25 trials for each of the 28 subjects, seen distinct from background noise are, respectively: Rectusfemoris = 15–22, 0.0473–2.1503; Bicepsfemoris = 17–33, 0.0076–0.3462, Semitendinosus = 17–33, 0.003–0.2015. The recordings with mechanical stretch and electrical stimulation of the femoral nerve confirm distinct RE in the hamstrings. Conclusion There are a few reports of RE in spasticity. We have demonstrated its presence in normal subjects. The coexcitation of the antagonist at the same time as the agonist may play an important role in providing stability around a joint to prevent injuries when there is rapid stretch of the agonist. Our data suggests that further studies are required to understand its neuronal pathway, relevance and potential clinical use in normal subjects and pathology.

A Model of the Immune Response to Disease

We shall now take a look at a simple model of the immune response. The immune system is a complex system involving several layers of defense for an organism against external potentially harmful invasions. We shall look specifically at the humoral response of the acquired immune system. In this case the signals are concentrations of antigens and antibodies. Although it is not common to use systems theory in the study of infectious disease, the application of system modeling can be useful to visualize and understand the processes of infection and the immune response. A linear system model is inaccurate in quantitatively describing the immune response, but it serves very well as a first approximation to understanding infection and disease. It is, in fact, rather appealing to regard acute and chronic disease as states of stable immune response and unstable response respectively to infection.

System Identification in Physiology

We shall now discuss some examples of system identification of sensory receptors and control systems in physiology, that is, determination of black box transfer functions. As we have noted earlier such a black box transfer function is useful in understanding the input-output relation and for studying the conditions under which instability is possible. Although such system identification is fairly indifferent to the underlying biophysical processes, an understanding of the relations between the various physiological entities is required to properly understand the feedback mechanism when present. It is also desirable to open the feedback loop if possible and obtain the open-loop transfer function so that the conditions of stability may then be analyzed. Alternatively, individual components of the physiological system in question may be isolated in experimental animals and studied. The experimental methods in these cases is as important as the analytical methods and therefore we shall examine both in some detail.