BioSignals - Resolution

Understanding the spatiotemporal events that occur in biological tissue often requires acquisition of multi-channel signals, that is, signals from multiple regions throughout the region of interest (ROI). For a given surface area or volume of tissue, if signals were to be acquired from sites at infinitesimally small distances from one another, then the number of signals acquired would be infinite. Since this is not practical, we settle on acquiring signals from some finite number of locations. The notion of resolution is an important concept relating to both single and multi-channel signals (or images).

Now the distance in space of one recording site to the next in the XY space can be the same or it can be different. For example, site 1 could be distant from site 2 by 1cm in the X direction and by 1cm in the Y direction. If the same spacing was used between all recording sites, then it can be said that the spatial resolution is 1cm in the X and in the Y directions. Another way to describe the resolution is to say that the surface area is 1cm x 1cm = 1cm². If as another example, site 1 were distant from site 2 by 3cm in the X direction and 5cm in the Y direction, and these same distances separated all of the recording site locations, then the spatial resolution in the X direction would be 3cm and in the Y direction it would be 5cm. The surface area encompassed by each recording site would be 3cm x 5cm = 15cm².

It is often desirable to increase the spatial resolution, which will then provide increased information content concerning any events that might occur in biological tissues. However, a tradeoff is that the greater number of acquired signals means that proportionally more recording medium is needed during any give experiment. Also, as the number of multi-channel signals increases, it may approach the limit (bandwidth) to which the equipment has the ability to record data in real-time. A real-time recording is one in which all the acquired data is stored in the recording device continuously and with little delay during the course of an experiment.

There are other types of resolution associated with multi-channel signals. These have to do with the dependent and independent variables that make up any give recorded signal. Consider a typical independent variable, time, which is usually displayed on the abscissa (X axis). If the signal is digitized, the rate of digitization must be specified. This can be done by stating the "sampling rate". A "sample" is a single digitized point of the original continuous, or analog, signal. The sampling rate is either specified as a frequency, for example 100 samples per second, which can also be referred to as 100 cycles per second or 100Hz, or in terms of the period between samples, which in this case would be 1/100 of a second or 10 milliseconds. The choice of sampling rate depends in part on the storage capacity of the system. A signal stored at 2x any given rate will fill up the recording buffer in half the time. This means, practically, that an experiment that can be recorded for two hours at the nominal rate can only be recorded for one hour at the double data rate.

The choice of the sampling rate also depends in part on the characteristics of the signal. Signals with low frequency components only are smoother in appearance and can be sampled at lower rates. Whereas, signals with much high frequency content have sharp edges and require sampling at higher rates. An example of a low frequency signal is the blood pressure pulse. Generally 7 Fourier harmonics is all that is needed to reconstruct ~90% of the signal. This means that if the heart rate is 60 beats per minute (1Hz), then storage of frequencies 1-7Hz will provide a digital representation of the analog signal with 90% accuracy. Whereas, a more random signal such as that acquired from skeletal muscle has many jagged peaks which may require sampling at the kilohertz level for accurate storage and reproduction of the signal.

Lastly, in terms of resolution, we must consider the dependent variable, which is by convention usually plotted on the last alphanumeric axis (ordinate (Y) for signals and Z axis for 2D images). For bioelectric signals, the dependent variable will be some measure of the electrical property of the signal, such as voltage, current, or resistance. For mechanical signals, the dependent variable will specify a mechanical function. For example, for blood pressure the dependent variable is the pressure unit, which is typically given in millimeters of mercury (mm Hg). A unit of force, such as the Newton, might be used to specify the pressure occurring on the surface of the foot during contact with a hard surface.

Typically the dependent axis is divided into a number of equally spaced (discrete) ranges. For example, if a bioelectric signal can vary from 0-8 volts, and there are 8 ranges along the dependent axis, then the digital resolution is 8 volts/8 = 1 volt. Practically, this will mean that whenever a sample point is digitized, it will be assigned to one of the eight ranges. If for example the actual signal voltage at the sampled point was 0.4 volts, it would be assigned a digital value of 1 volt. If the actual sample was 3.3 volts, it would be assigned a value of 4 volts. Hence, for this arrangement a real-numbered value of actual signal voltage will be assigned to one of 8 integer values when the sample point is digitized. By increasing the resolution along the dependent axis the signal appears less "blocky", however the digitization process usually requires more time, which in turn may require limiting the digital resolution of the independent variable(s).

The process is illustrated in the figure below. Here, a blood pressure waveform is shown in analog form (black).

The digitized waveform is shown in blue with 1 and 2 bits voltage, or pressure, resolution (top and bottom of figure, respectively). At one bit digital resolution, the resulting digital signal can take one of 2¹ = 2 levels, labeled 0 and 1. At two bits digital resolution, the resulting digital signal can take one of 2² = 4 levels, labeled 00, 01, 10, and 11. At n bits digital resolution, the resulting digital signal can take one of 2ⁿ levels. The maximum error in digitization is ± D /2, where D is the range between digital levels in volts of mmHg in this case. This figure underscores the reason for boosting the amplitude of the signal as much as possible within the limits of accepted voltages. If the amplitude of the signal above to be digitized were halved, then the conversion process using a 2-bit resolution would be no better than using a 1-bit converter (see below). In this case, the possible levels of the signal are 01 and 10. Hence, it is very important to use a process of automated gaining of the signal prior to digitization, so that the full compliment of digital levels is used during conversion of the signal.

Multi-channel signals were once only acquired simultaneously in very specialized laboratories throughout the United States. However, with the advent of fast digital computers and commercialized acquisition boards, it is becoming typical to find multi-channel recording setups both in the laboratory as well as in clinical settings. Examples of multi-channel recordings are the electrical patterns acquired from the scalp. These patterns reflect the electrical activity of the brain. Although the signals imparted to the recording transducers are low-level in this case (microvolts), with appropriate noise reduction technology, filtering, and amplification, they are readily recorded for analysis of the pattern of electrical activity in the brain. Examples of other tissue types in which multi-channel electrical activity is recorded includes heart, gut, and skeletal muscle. From the heart and smooth muscle in the gastrointestinal system, biosignals can be used to determine the electrical conduction pattern at the surface of even within the interior. Acquisition of multichannel biolelectric signals are important to track abnormal electrical conduction processes in patients, such as irregular heart rhythms and irregular bowel motility. From skeletal muscle multichannel recordings, one can gain an understanding of muscle function in health and disease using multi-channel recordings.