Biomedical Engineering Evoked Responses

Transcription

1 Biomedical Engineering Evoked Responses Dr. rer. nat. Andreas Neubauer Tel.: Stimulation of biological systems and data acquisition 1. How can biological systems be stimulated? Visually Acoustically Via drugs 2. How to record the response of stimuli? Distinguishing signal from noise Artifacts and responses 3. Computer aided data analysis AI vs. PI Andreas Neubauer I Slide 2 I

2 Linear Systems Andreas Neubauer I Slide 3 I How to describe linear systems Components behave in a proportional manner e. g. electrical systems mechanical systems Consider a system with Input and output Goal: Find a function to describe the system Andreas Neubauer I Slide 4 I

3 Frequency responses Easiest test for frequency response: function infinitely high and infinitely short Fourier integral of : 1 1 Testing the response of a low pass filter Fourier transform of the input: Andreas Neubauer I Slide 5 I Stimuli Andreas Neubauer I Slide 6 I

4 Neural stimulation I The body is a good conductor Nerves an muscles work electrically neural stimulation with electricity is possible muscle contraction induced by a current between two surface electrodes Andreas Neubauer I Slide 7 I Neural stimulation II Apart from an alternating current, one can apply a short pulse between two surface electrodes Pulse duration is between 50 s "# 2 %& to avoid high amplitudes The stimulation occurs under the electrode which sees the pulse as negative pulse the transmembrane potential will be reduced where the current leaves the nerve R: Rheobase C: Chronaxie Andreas Neubauer I Slide 8 I

5 More about currents and voltages Stimulation of a nerve is achieved if the transmembrane potential is reduced by about 30% Stimulation current must flow for a minimum time generation of an action potential Position of the electrodes Approx. charge required for stimulation Inside a nerve axon 10 ) On the surface of a nerve trunk 10 * ) On the skin several mm from the nerve 10 + ) Andreas Neubauer I Slide 9 I Depolarization with an electrode Charge has to be removed from one node of Ranvier depolarization generation of an action potential Membrane capacitance is approx. 10 Applied polarization potential: Approx /" % ) Andreas Neubauer I Slide 10 I

6 Electrical stimulation a practical example Energy required to stimulate a nerve with electrons placed directly over the nerve: Approx corresponds to 10 %6 flowing for 100 s through an electrical resistance of 10 7Ω Energy stored in a battery with an output voltage of 9 - and a capacity of 500 %6/: : ; 500 % & a small battery is enough to stimulate a nerve more than times if the nerve is not superficial a much larger amount of energy may be required several joules for a human heart Andreas Neubauer I Slide 11 I Strength duration curves The stimulation energy is not the same for different nerves Large fibers need less energy than small fibers Cutting the innervation of a muscle leads to a slow death of the muscle Denervation Electrical stimuli can be used to stimulate the muscle directly threshold will be increased record the threshold current in dependence of the applied pulse length Rheobase R: Minimum current to stimulate the muscle (independent of pulse length) Chronaxie C: Pulse width with threshold current 2 Rheobase Andreas Neubauer I Slide 12 I

7 Which other stimuli can be used? Stimuli can be applied to each of our senses mechanically auditory taste/smell (difficult in practice) Andreas Neubauer I Slide 13 I visually Andreas Neubauer I Slide 14 I

8 Auditory stimuli Auditory equivalent of a function? Very short click containing a wide range of frequencies Mostly used in objective hearing tests What if the audiologist wants to know which frequencies have been heard? Hypothesis: Give an auditory stimulus, record the response, apply Fourier transform to the response obtain transfer function of auditory system Unfortunately the brain and the hearing system are nonlinear systems Andreas Neubauer I Slide 15 I Auditory stimulus in practice Short burst of single frequency Obtain the response of the ear by testing different frequencies Signal equation: = cos 2@f B Fourier transform leads to: = = B C sin 2@ BF C G sin 2@ BG C 2@ B F C 2@ B G C Andreas Neubauer I Slide 16 I

9 Visual stimuli Visual equivalent of a function? Flash of light The eye cannot deal with frequencies above 20 H Pattern recognition is much easier with visual stimuli Fourier transformation may be more useful in the spatial than in the temporal domain Neubauer, AADA 2014 Andreas Neubauer I Slide 17 I Detour to spatial frequencies Courtesy of M. Ruttorf Neubauer, AADA 2014 Andreas Neubauer I Slide 18 I

10 Detection of small signals Andreas Neubauer I Slide 19 I Bandwidth and signal-to-nose ratios Bandwidth: Frequency range over which the gain remains constant F3 I bandwidth: Frequency range over which the gain is not less than 3 I below the maximum gain Signal Bandwidth [1/&] ECG 0.5F100 EEG Arterial pressure wave 0.5 F75 L) F40 Body temperature L) 1 Respiration L) 10 Electromyograph Nerve action potentials O O Smooth muscle potentials 0.05 F 10 Andreas Neubauer I Slide 20 I

11 Choice of the amplifier Which signal should be amplified? Current? Voltage? Noise will also be amplified! The amplifier will contribute some noise to the signal usually quoted in terms of the equivalent noise at the input, Noise Referred to the Input (RTI) noise (RTI) = (noise at output)/(amplifier gain) RTI can be directly compared with the size of the input signal Example: Measurement of an ECG: 1 %- Required signal to noise ratio: 40 I 100:1 RTI < QR BB 10 - Andreas Neubauer I Slide 21 I Input resistance Amplification may be frequency dependent The choice of the input resistance must be related to the recorded signal Source and input resistance form a potential divider If the input resistance is equal to the source resistance the signal will be reduced to half it s value Reducing this error to 1% requires an input resistance 100 times higher than the source resistance => Source resistance must be known! Andreas Neubauer I Slide 22 I

12 Differential amplifier II In practice almost all bioelectric amplifiers are differential amplifiers ability to reject external signals Use operational amplifiers for the design instrumentation amplifier configuration input voltages Rules for analyzing operational amplifier circuits 1. There will be no voltage between the inputs of an operational amplifier 2. No current will flow into the inputs of an operational amplifier Andreas Neubauer I Slide 23 I Differential amplifier II In practice almost all bioelectric amplifiers are differential amplifiers ability to reject external signals Use operational amplifiers for the design instrumentation amplifier configuration input voltages Rules for analyzing operational amplifier circuits 1. There will be no voltage between the inputs of an operational amplifier 2. No current will flow into the inputs of an operational amplifier Andreas Neubauer I Slide 24 I