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Sources and Properties of Biomedical Signals

1.1Introduction

Before describing and analyzing the electronic circuits, amplifiers, and filters required to condition the signals found in clinical medicine and biomedical research, it is appropriate to describe the sources and properties of these signals (i.e., their bandwidths, distribution of amplitudes, and noisiness). Broadly speaking, biomedical signals can be subdivided into two major classes: (1) endogenous signals that arise from natural physiological processes and are measured within or on living creatures (e.g., ECG; EEG; respiratory rate; temperature; blood glucose; etc.) and (2) exogenous signals applied from without (generally noninvasively) to measure internal structures and parameters. These include but are not limited to ultrasound (imaging and Doppler); x-rays; monochromatic light (e.g., two wave lengths used in transcutaneous pulse oximeters); fluorescence from fluorophore-tagged cells and molecules stimulated with blue or near UV light; optical coherence tomography (OCT); laser Doppler velocimetry (LDV) used to measure blood velocity; and applied magnetic fields used in NMR). Other examples of exogenous signals can be found in the text by Northrop (2002).

The following section examines the properties of endogenous bioelectric signals used in medical diagnosis, care, and research.

1.2Sources of Endogenous Bioelectric Signals

The sources of nearly all bioelectric signals are transient changes in the transmembrane potential observed in all living cells. In particular, bioelectric signals arise from the time-varying transmembrane potentials seen in nerve cells (neuron action potentials and generator potentials) and in muscle cells, including the heart. The electrochemical basis for transmembrane potentials in living cells lies in two phenomena: (1) cell membranes are semipermeable,

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2	Analysis and Application of Analog Electronic Circuits

i.e., they have different transmembrane conductances and permeabilities for different ions and molecules (e.g., Na+, K+, Ca++, Cl−, glucose, proteins, etc.) and (2) cell membranes contain ion pumps driven by metabolic energy (e.g., ATP). The ion pumps actively transport ions and molecules across cell membranes against energy barriers set up by the transmembrane potential and/or concentration gradients between the inside and outside of the cell. In the steady state, ions continually leak into a cell (e.g., Na+) or out of a cell (e.g., K+) and ongoing ion pumping restores the steady-state concentrations.

In squid giant axons, the steady-state, internal concentrations are [Na+]i = 50 mM, [K+]i = 400 mM, [Cl−]i = 52 mM. The steady-state external concentrations (in extracellular fluid) are [Na+]e = 440 mM, [K+]e = 20 mM, [Cl–]e = 560 mM, and [A–]i = 385 mM (Kandel et al., 1991). [A–] is the equivalent concentration of large, impermeable protein anions in the cytosol. Ion concentration data exist for the neurons and muscles of a variety of invertebrate and vertebrate species (Kandel et al., 1991; West, 1985; Katz, 1966).

The steady-state transmembrane potential can be modeled by the Gold- man–Hodgkin–Katz equation (Guyton, 1991):

RT

[Na

+

]

P

+

+ [K

+

]

P

+ + [Cl

−

]

P

÷

= −

™

− ™

Vmo

ln

i

Na

i

K

i

Cl

˝

(1.1)

F

[Na+ ]

+ [K+ ]

P

+ + [Cl− ]

P

™

P

+

− ™

©

e

Na

e

K

e

Cl

˛

where T is the Kelvin temperature; R is the MKS gas constant (8.314 J/mol K); F is the Faraday number, 96,500 Cb/mol; and PX is the permeability for ion species, X. The resting transmembrane potential of neurons, Vmo, varies with species, neuron type, ionic environment, and temperature; it can range from 60 to 90 mV (inside negative with respect to outside). Muscle fibers, too, have a transmembrane potential of approximately 80 < Vmo < 95 mV, inside negative.

1.3Nerve Action Potentials

Nerve action potentials (APs) are in general the result of transient changes in specific ionic conductances and permeabilities induced electrically (or chemically by neurotransmitters) in the nerve cell membrane. In excitable neuron membranes, an increase in sodium permeability leads to a depolarization of the transmembrane potential (i.e., sodium ions flow rapidly into the neuron down a concentration gradient and electric field). The inrush of Na+ causes the Vm to go positive, which is a depolarization.

When the excitable nerve membrane voltage reaches a depolarization threshold on the order of a few millivolts, the permeability events that lead to a propagating action potential or nerve spike occur. First, there is a further, “all-or-nothing,” large transient increase in sodium permeability causing a

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Sources and Properties of Biomedical Signals

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strong transient inrush of Na+ ions. This inrush causes a large, fast depolarization so that Vm actually goes positive by tens of millivolts, generally in less than a millisecond. Immediately, permeability to K+ ions also increases, but at a slower rate, which causes an outward JK+, making Vm decrease from its positive peak to its negative resting value after a slight, transient undershoot (hyperpolarization). The total duration of the positive nerve action potential spike is on the order of 2 MS.

Once initiated, an action potential propagates down a neuron’s axon at a velocity that depends on a number of physical and chemical factors, including the diameter of the axon. One of the earliest mathematical models for nerve impulse generation was given by Hodgkin and Huxley in 1952. The H–H model now appears to be somewhat oversimplified with its description of a single type of potassium channel, but is still valid and a useful model to teach about the dynamics of nerve impulse generation. Figure 1.1 illustrates the result of a computer simulation of the H–H model using Simnon™ (Northrop, 2001). Shown are the transmembrane voltage, the time-varying conductances for Na+, K+, and “leakage anions.” Readers interested in pursuing the molecular and ionic details of neurophysiology should consult Kandel et al. (1991); West (1985); Guyton (1991); and Northrop (2001).

50

1

2

3

4

5

6

0

−50

−100
0	2	4	6	8	10

>axes v −90 45 >simu−mark

>

FIGURE 1.1

Results of a Simnon™ simulation of the Hodgkin–Huxley 1952 mathematical model for nerve action potential generation. Traces: (1) Jin (μA/cm2). (2) vm(t) (transmembrane potential). (3) gK(t,

vm) mS/cm2. (4) gNa(t, vm) mS/cm2. (5) gnet = gK + gNa + gL mS/cm2. (6) Jin, μA/cm2. (Northrop, R.B. 2001. Introduction to Dynamic Modeling of Neuro-Sensory Systems. CRC Press, Boca Raton, FL.)

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4	Analysis and Application of Analog Electronic Circuits

Most neurons in the vertebrate CNS are too small to record their transmembrane potentials with glass micropipette electrodes directly. However, their action potentials can be recorded over long periods of time with extracellular, metal microelectrodes whose uninsulated tips are in the neuropile within several microns of axons or cell bodies. Action potentials from peripheral nerve bundles can be recorded with simple platinum hook electrodes, saline-filled suction electrodes, or saline-wetted wick electrodes coupled to silver–silver chloride electrodes. All extracellular recording techniques suffer from the problem that the electrodes pick up nerve spikes from active, adjacent, or neighboring neurons. This neural background noise is added to the desired unit’s signal and, unfortunately, has the same bandwidth as the desired unit’s spikes. In dissected peripheral nerve fibers, it may be possible to isolate single axons with hook, suction, or wick electrodes, thus greatly improving the recording SNR.

Because the nerve action potential is a traveling wave, it can be shown that an external electrode in close proximity to the outside surface of an axon will respond to the passage of the AP with an electric potential waveform that is in effect the second derivative of the transmembrane spike waveform (Plonsey, 1969) as shown in Figure 1.2. (The intracellular AP, Vm, is to scale, but its derivatives are not to scale.) The triphasic (second derivative) waveform of the AP recorded at a point near the axon comes from the fact that the AP is traveling along the axon with velocity, v. As the AP approaches the electrode, a weak, net outward JK+ causes a low positive voltage peak. When the AP has moved opposite the electrode, the electrode responds to the strong inward flow of JNa with a large negative voltage peak. Then, as the AP passes the electrode, its potential again goes positive from the outward JK+ in the recovery phase of the AP. (The (−) terminal of the amplifier is connected to a AgΩAgCl reference electrode electrically far from the recorded neuron.)

In the author’s experience, using fine platinum–iridium extracellular microelectrodes, which were glass insulated down to 6 to 12 μm of their conical tips, made it possible to record from single units in insect optic lobes and protocerebrum and frog tectum, with major spike amplitudes ranging from −50 to −500 μV. Midband gain for signal conditioning was 104 and signal conditioning bandwidth was 100 to 3 ∞ 103 Hz (Northrop and Guignon, 1970).

Nerve APs recorded through the neuron membrane (in the cell body, base of dendrites, or axon) using glass micropipette electrodes can be approximately 100 mV or more peak to peak. A capacity-neutralized electrometer headstage used to couple the high-resistance microelectrode generally has a gain of 2 or 3; the second stage may gain from 5 to 30, so the overall gain can range from 10 to 90. Bandwidth is from dc to 3 to 5 kHz. The direct coupling is required because interest is usually in the neuron’s resting potential, Vmo, or slow changes in Vm caused by incoming excitatory or inhibitory signals. If Vmo is not of interest, then it is technically simpler and less noisy to use external microelectrodes and band-pass filtering (e.g., 100 to 3 kHz). More gain will be required with external electrodes, however.

© 2004 by CRC Press LLC