The underlying hypotheses which may account for the synchronization o f m otor unit firing and the changes which occur following stroke are now discussed.
branched common stem pre^naptic fibre inputs
Adrian & Bronk (1928) were the first authors to suggest that synchronization o f m otor activity could be due to some com m on input to m otoneurones innervating those muscles. Sears & Stagg (1976) subsequendy advanced this theory, based on their investigations o f the organisation o f inputs to motoneurones innervating the intercostal muscles o f the cat. O ne o f the key results was that m otor unit synchronization was detected between the firing o f intercostal m otoneurones o f the same and o f adjacent segments. These authors hypothesised that m otoneurone synchronization, represented by a narrow cross- correlogram peak centred around time zero, arose from the joint occurrence o f unitary EPSPs evoked in m otoneurones by branches o f com m on stem presynaptic fibres.
Kirkwood (Kirkwood & Sears 1978) then developed a theoretical model which was based on this hypothesis, in order to predict the time course o f the cross-correlogram peak and
theory assumed that, to a first approximation, an EPSP increased the firing probability in a
post-synaptic neurone, f t (primary correlation kernel), which was given by the first two terms o f the Hnear differential o f the EPSP shape, f(t), where t=tim e and the coefficients a and b were associated respectively with the two terms o f the equation:
f t = a.f(t) + b.df/dt(t)
The relationship between f t and f(t) was designated the primary correlation operator.
Kirkwood & Sears (1982) then investigated the effects o f single afferent impulses on the firing probability o f external intercostal m otoneurones in the cat. By simultaneously measuring the EPSPs generated in external intercostal muscles and the increased probability o f m otoneurone firing arising from discharges in muscle spindle afferents, it was shown that the increased probability o f m otoneurone firing was observed mainly during the rising phase o f the EPSP but also extended into the tail o f the EPSP. Therefore, both the total time course o f the EPSP and its differential were necessary in order to fully account for the time course o f the increased probability o f m otoneurone discharges.
The cross-intensity function (cif) which is the function measured by the cross-correlogram was also expressed to a first approximation by the first two terms o f the linear differential o f the A C E potential, where the coefficients a and b were similarly associated with the two terms o f this equation. Thus the same primary correlation operator that transformed the EPSP shape to the raised firing probability o f firing in a cell also related the A C E potential to the cif.
Therefore, collective evidence from both the experimental recordings and from theoretical
m o d e l l i n g led Kirkwood and Sears to suggest that a central peak in a correlogram could be
due to activity in branched inputs to the m otoneurones innervating intercostal muscles in the cat. In order to investigate whether this theoretical m odel could be used for predicting the time course o f m otor unit synchronization in hum an muscle recordings, D atta & Stephens (1990) com pared the time course o f synchronization o f m otor unit firing observed from ID I using single m otor unit recordings. These authors showed that the
the joint occurrence at the m otoneurone o f EPSPs derived from com m on presynaptic stem fibres.
Additional experiments were performed by Fetz & G ustaffson (1983) and G ustaffson & McCrea (1984) in order to investigate w hether the theoretical time course o f the raised probability o f firing produced in a m otoneurone by EPSPs was similar to that observed using experimental recordings. Fetz & Gustaffson (1983) used electrically evoked EPSPs and showed that the duration o f the correlogram peak was related to the duration o f the rise time o f the EPSP and that EPSPs with longer rise times produced wider correlogram peaks. H owever this relationship also depended on the size o f the EPSPs; larger EPSPs produced correlograms which tended to m atch the duration o f the rise times, but smaller EPSPs tended to exceed the rise times. The total duration o f the EPSPs was also related to the total duration o f the correlogram peak; larger EPSPs produced correlogram peaks which were narrower relative to the width o f the EPSP. It was concluded that the correlogram shape was usually related to the derivative o f the synaptic potentials but smaller EPSPs closer to the level o f synaptic noise produced correlograms which were broader than the derivative. Given that electrically evoked EPSPs have a steeper rise time than naturally evoked EPSPs, Gustaffson and McCrea (1984) used stretch evoked EPSPs to investigate the relationship between the synaptic potential and resultant correlograms. They found that for small EPSPs in high levels o f synaptic noise the correlogram shape was described by the linear combination o f the shape o f the EPSP and o f its derivative. In summary therefore, the EPSP shapes predicted from theoretical cross-correlogram modelling studies were consistent with the shape and time course o f the EPSPs generated by spindle afferent fibres and provided further support to the D atta & Stephens’ argument (1991b) that hum an m otor unit synchronization could be accounted for using the branched com m on stem hypothesis.
Thus far, discussion has only considered m otor unit synchronization using single m otor unit recordings. W e will now consider m ore closely the time course o f the cross- correlogram peaks constructed from multi-unit E M G recordings obtained from different hand muscles following stroke in the present study, in order to examine w hether activity in branched inputs to m otoneurones/m otoneurone pools could account for central correlogram peaks obtained.
The peaks in correlograms constructed between multi-unit recordings obtained from STh:LTh in the stroke patients had a mean duration o f 28ms on the stroke side, and 24ms on the non-stroke side and for control subjects mean duration was 25ms. Similar values were obtained for the mean duration o f peaks from correlograms constructed between ID LA D M (stroke side 32ms, non-stroke side 25ms and control subjects 24ms). In comparison, the mean duration o f peaks obtained from single m otor unit recordings when perform ing cross-correlation analysis between different hand muscles in the study by Bremner et al. (1991b) was 14ms. Multi-unit EM G recordings from the 1®*^ and 4* dorsal
interossei muscles in the study by Gibbs et at. (1995) showed that mean central peak
durations were 14ms and a later paper, they showed that the mean duration o f central correlogram peaks constructed from the m otor unit firing o f short and long thumb
abductors was 17ms (Gibbs et at. 1997). Therefore, could the durations o f central
correlogram peaks in the present study be accounted for by the branched com m on stem hypothesis?
Kirkwood & Sears (1991) performed further analysis in order to examine the limits o f the time course o f the correlogram peaks which they believed could confidently be accounted for by activity in branched stem inputs, and concluded that only peaks with a half width o f
<2.1ms duration could be solely due to activity in the last order branched inputs to the m otoneurones (Kirkwood & Sears, 1991) w hen using single m otor unit recordings from cat intercostal muscles. They therefore suggested that some wider cross-correlogram peaks may no t necessarily be due to activity in branched last order presynaptic inputs.
W hen using multi-unit EM G recordings to construct cross-correlograms, Harrison et al
(1991) pointed out that the resultant correlogram was the “sum o f the individual correlograms that would be produced by cross-correlating each possible pairing o f m otor units” and that the variation in the central peak durations could be partly accounted for because the m otor units which are included in the analysis show a range o f different conduction times from the spinal cord to the muscles. D atta & Stephens (1990) showed that the central point o f the correlogram peak was n ot always positioned at time zero but