DATA ANALYSIS

Detailed analysis of rhythmic sympathetic discharges recorded from

sympathetic fibres or whole nerves is performed using time domain or

frequency domain analytical techniques. Time domain analysis involves the

detection of a discharge and plots the occurrence of an event (e.g. sympathetic

discharge) following an event (e.g. sympathetic discharge, phrenic nerve burst

discharge, R-wave on ECG) on a correlogram. This approach is ideal for

revealing the rhythmicity of discriminated action potentials (e.g. Johnson &

Gilbey, 1996; Yusof & Coote, 1988a). However, it is not suitable for whole nerve

recordings in which the sympathetic discharges cannot be discriminated using a

spike processor or interface (e.g. sympathetic activity recorded VCNs, DCNs

and saphenous nerves; see Figures 3.2, 4.1, 4.4). Thus, sympathetic activity

recorded from whole nerves is often subjected to frequency domain analysis

(e.g. Kenney e t at, 1991; Kocsis e t a/., 1990; Taylor & Schramm, 1987). When nerve activity is analysed in the frequency domain, the frequency components

in the nerve recording are separated by fast Fourier transformation (FFT); the

amount of nerve activity occurring at a particular frequency is then quantified

(voltage squared) and plotted on an autospectrum (Chatfield, 1996). Cross-

spectral calculations can also be performed to produce coherence spectra that

indicate constant phase and amplitude ratios of frequency components between

paired nerve recordings (Chatfield, 1996; Christakos 1986 & 1994; Rosenburg

e t at, 1989).

6.1 Time domain analysis of ongoing discharges recorded from single PGNs

300 8 data sets of TTL pulses generated from discriminated PGN action

potentials and rhythmic phrenic nerve activity were sampled by the computer

using Spike2 computer software (see above, Figure 2.3). Autocorrelograms (50

ms bin width) were used to reveal the periodicity of PGN and phrenic nerve

burst discharges. Autocorrelograms are self triggered histograms that plot the

occurrence of TTL pulses following a TTL pulse. The dominant frequency of

rhythm revealed on autocorrelograms was calculated from the reciprocal of the

modal time of the first peak, as shown in Figure 2.5.

6.2 Frequency domain analysis of the sympathetic discharges recorded from whole nerves

300s of integrated whole nerve activity were sampled at 100 Hz by the

computer, using Spike2 computer software (see above). The Spike2 data file

was then converted to a text file and analysed using Matlab computer software

(Maths Works). The Matlab scripts used to analyse data in the present study

were purpose written by Dr. H.-S. Chang (Physiology Department, Royal Free

and University College Medical School, London, UK).

(i) Autospectra

FFT (size 2048, 50% overlap) was performed on 286 72 s of integrated

whole nerve activity (sampled at 100 Hz). This separated the frequency

components in the nerve activity and divided the data set into 28 half­

the spectrum a frequency resolution of 0.049 Hz. Do components and linear

trend were then removed from the data set. An autospectrum was averaged

from these subsections according to the Welch Method (see Chatfield, 1996).

(ii) Definition of a peak in an autospectrum

The term “peak” was allocated to frequencies with discrete spectral

density (> 50% of background power density) where the “rising phase"

occurred within 0.3 Hz. During central apnoea renal nerve autospectra were

considered to lack “peak” frequencies, since remaining power density on such

autospectra were similar to the broad power under the peaks in autospectra

seen during periods of rhythmic phrenic nerve activity, see Figure 2.6.

(iii) Allocation of dominant nerve discharge frequency

Dominant nerve discharge frequency (or T-peak frequency for VCN,

DCN and saphenous nerve recordings) was allocated to the frequency of the

highest peak. However, when the frequency of the highest peak coincided with

the 1®* harmonic frequency of phrenic nerve burst discharge frequency and

there was another peak which was more than 50% of its size (9/102

“sympathetic nerve” autospectra), dominant nerve discharge frequency was

allocated to the 2"^ highest peak. This criterion was applied to insure that

dominant nerve discharge / T-peak frequency was not allocated inappropriately

to a harmonic frequency of rhythmic phrenic nerve activity (Application of

frequency domain analysis to sympathetic nerve activity (which is not a

sinusoidal waveform) generates spectral density at harmonic frequencies of

rhythmic nerve discharges (Chatfield, 1996)).

(iv) Coherence spectra

A coherence spectrum was used to reveal linear correlations between

rhythmic sympathetic discharges at T-rhythm frequency recorded from the VCN

and this activity recorded simultaneously from another nerve (e.g. contralateral

VCN, ipsilateral saphenous nerve, DCN or renal nerve). Assuming that

synchrony between discharges on two nerve recordings is regular and stable,

then a coherence value significantly different from 0 would indicate that

discharges at that particular freauencv were linearly related.

Coherence spectra were averaged from the same 28 half-overlapped

subsections used to generate autospectra (see above). The squared coherence

coefficient (referred to as coherence value) at each frequency was estimated by

normalising the cross spectrum between two nerve activities (see Chatfield

1996; Christakos, 1986 & 1994).

The upper 95% confidence limit for coherence at a particular frequency

to be significantly different from 0 was calculated using the following equation:

---riTi:^---

Upper 95% Confidence Limit = 1-0-05

where: L = number of subsections in the spectrum (Rosenburg e t a/., 1989)

Figure 2.7 shows the upper 95% confidence limits for coherence spectra

constructed from different numbers of subsections. The coherence spectra

generated in the present study were constructed using 28 subsections. Thus,

the upper 95% confidence limit used in the present study was 0.1.

6.3 Calculation of mean arterial blood pressure

equation:

MAP = diastole pressure + / (systolic - diastolic pressure)

Diastolic and systolic blood pressure values were averaged from 6

values taken from the data set at 60 s intervals.

6.4 Linear regression analysis

Linear regression analysis was performed to test if dominant nerve

discharge, T-peak or T-rhythm frequency displayed a linear 1:1 relationship

with phrenic nerve burst discharge frequency. Least square linear regression

analysis was performed using Microcal Origin 3.54 (Microcal Software Inc). The

slopes of regression lines were compared to 1 using a Student t-test (Glantz,

1996).