Appendix ‘All muscle pair’ coherence calculations

The calculation used to combine muscle pair coherence values after they were normalized was

where M is the number o f muscles used in the recording (i.e. 4) and P is the number of muscle pairs combined (on the majority o f occasions 6).

This combination calculation is different from that used by Kilner et al. (1999; 2000).

where P is the number of muscle pairs combined.

A comparison of both methods is shown in table 1. With regards to calculations using 6 muscle pairs, the combination calculation used in this thesis resulted in slightly larger final coherence values (e.g. for this subject a frequency area of 204 Hz) than would have been calculated by the previously reported method (frequency area of 166 Hz). Note that no comparisons on absolute coherence values have been made to previous work by Kilner et al. (1999; 2000).

In two cases in this thesis (chapter 6 and chapter 7), only 5 muscle pairs were combined to given an overall muscle pair coherence score. In some subjects, the FDS/EDC muscle pair coherence spectra was contaminated with white noise from an unknown source, and so this muscle pair had to be excluded from each subject’s data. In the combination calculation used in this thesis, M remained at 4 (still 4 muscles involved in the analysis), but P was now 5. This resulted in a lower final score for coherence (frequency area of 184

Hz) compared to when 6 muscle pairs were combined (frequency area of 204 Hz), indicating that one muscle pair less was used for analysis.

The combination calculation used by Kilner et al. (1999; 2000), however served to equal out coherence scores regardless o f the number o f muscle pairs used in the analysis. Note that using this method, both final coherence values were very similar (frequency area of 166 Hz for 6 muscle pairs; 165 Hz for 5 muscle pairs).

In this thesis all results presented concern changes rather than absolute values of

coherence. All conclusions were made after statistical comparisons between tasks or conditions, using a paired t-test. With regard to all studies in which all muscle pair coherence was calculated, comparisons were only made on coherence calculated using the same number of muscle pairs.

Both methods of combination are valid, and gave the same overall result, as shown by confirmation in this thesis o f observations made by Kilner and colleagues.

1 B C D E F G H 1 J K 2 C O H E R E N C E V A L U E S - S E E E Q U A T IO N 6 3 F re q u en c y 1 4 .3 9 1 6 .4 5 1 8 .5 0 2 0 .5 6 2 2 .6 2 2 4 .6 7 2 6 .7 3 2 8 .7 8 3 0 .8 4 4 M uscle p airs 5 1 DI/AbPB 0 .1 2 0 . 0 3 0 .0 6 0 .2 8 0 .1 6 0 . 1 4 0 .1 1 0 .0 8 0 .0 9 6 1DI/FDS 0 .0 2 0 .0 1 0 .0 1 0 .0 4 0 . 0 5 0 .0 6 0 . 0 6 0 . 0 3 0 . 0 5 7 1DI/EDC 0 .0 0 0 .0 0 0 . 0 2 0 . 0 4 0 .0 1 0 .0 1 0 .0 1 0 . 0 2 0 . 0 2 8 A bP B /FD S 0 .0 0 0 .0 1 0 .0 1 0 . 0 2 0 . 0 2 0 . 0 2 0 . 0 5 0 . 0 4 0 . 0 3 9 A bPB /ED C 0 .0 1 0 . 0 0 0 .0 1 0 . 0 3 0 .0 1 0 . 0 3 0 . 0 0 0 . 0 2 0 .0 2 1 0 FD S/E D C 0 .0 2 0 .0 0 0 .0 1 0 .0 0 0 .0 0 0 .0 2 0 . 0 0 0 .0 4 0 .0 1 11

1 2 TRANSFORMATION - S E E EQUATION 4 e .g . for 1 DI/ABPB a n d 14.39 Hz SQRT(2*240)*A TA NH(sqrt(C5)) 1 3 N ote 24 0 is n u m b e r of s e c tio n s of d a ta (4 w indow s * 6 0 trials)

1 4 1 5 1DI/AbPB 7 .8 0 3 .7 3 5 .5 2 1 3 .0 0 9 .1 8 8 . 5 3 7 .6 9 6 . 2 5 6 . 8 2 1 6 1DI/FDS 2 .8 3 2 .2 2 1 .6 6 4 . 3 6 4 .9 8 5 .6 8 5 .4 4 3 . 7 4 4 . 8 4 1 7 1 DI/EDC 1 .4 9 0 .9 9 2 .7 2 4 . 2 6 2 .5 3 2 .4 5 2 . 5 8 3 .4 3 3 .3 0 1 8 A bP B /FD S 1 .0 7 2 .4 9 1 .7 6 3 . 3 7 3 .2 0 3 .2 7 4 . 9 5 4 .3 1 4 . 0 3 1 9 A bPB /ED C 1 .7 6 0 .2 8 1 .6 9 4 . 1 3 2 .6 4 4 . 1 0 1 .5 3 3 .4 3 3 .1 3 2 0 FD S/E D C 3 .3 0 0 .3 9 2 .1 7 1 .4 7 1 .2 3 3 .1 9 0 . 5 5 4 . 4 2 2 .2 8 21

2 2 COMBINATION CALCULATION U SED IN TH IS T H E SIS- S E E EQUATION 7

2 3 e .g . for 14.3 9 Hz a n d 6 m u sc le p airs SU M (C 15;C 20)/SQ R T(4); for 5 m u sc ie p a irs SU M (C 15:C 19)/SQ R T (4) 2 4 6 m u sc le p airs 9 .1 2 5 .0 5 7 .7 6 1 5 .3 0 1 1 .8 8 1 3 .6 1 1 1 .3 7 1 2 .7 9 1 2 .2 0 2 5 5 m u sc le pairs 7 .4 7 4 .8 6 6 .6 7 1 4 .5 6 1 1 .2 7 1 2 .0 1 1 1 .1 0 1 0 .5 8 1 1 .0 5 2 6

2 7 SUM BETW EEN 1 4 -3 1 Hz MULTIPLY BY 2 .0 5 5 9 Hz FO R C O H E R E N C E AREA 2 8 6 m u sc le p a irs 9 9 .0 8 S U M ( C 2 4 :K 2 4 ) 2 0 4 Hz

2 9 5 m u sc le p a irs 8 9 .5 8 S U M ( C 2 5 :K 2 5 ) 1 8 4 Hz

3 0 1

31 COMBINATION CALCULATION U SED BY KILNER et al 1 9 9 9,2 0 0 0 - S E E EQUATION 8

3 2 e .g . for 14 .3 9 Hz a n d 6 m u sc le p a irs SU M (C15:C20)/SQ R T{6): for 5 m u sc le p airs SU M (C 15:C 19)/SQ R T (5) 3 3 6 m u sc le p a irs 7 .4 5 4 . 1 3 6 .3 4 1 2 .4 9 9 .7 0 1 1 .1 1 9 . 2 9 1 0 .4 4 9 .9 6 3 4 5 m u sc le p a irs 6 .6 8 4 . 3 4 5 . 9 7 1 3 .0 2 1 0 .0 8 1 0 .7 5 9 . 9 3 9 .4 6 9 .8 9 3 5

3 6 SUM BETW EEN 14 -31 Hz MULTIPLY BY 2 .0 5 5 9 Hz FO R C O H E R E N C E AREA 3 7 6 m u sc le p a irs 8 0 .9 0 S U M ( C 3 3 :K 3 3 ) 1 6 6 Hz

3 8 5 m u sc le p a irs 8 0 .1 2 S U M ( C 3 4 :K 3 4 ) 1 6 5 Hz

1

T ab le 2.1: Sum m ary o f c o h e r e n c e calcu lation s u se d in this th e sis. Data from a sin g le su bject is sh ow n . C o h e r e n c e w a s calcu lated for all

fr e q u en c ie s b e tw e en 2 Hz and 4 0 Hz for e a c h m u sc le pair. C o h e ren ce ca lcu lation s for freq u en cie s b e tw e en 1 4 .3 9 Hz and 3 0 .8 4 Hz only are sh o w n h ere. In order to ca lcu la te an all m u sc le pair c o h e r e n c e s c o r e for e a c h su bject, c o h e r e n c e v a lu e s for e a c h m u scle pair w e re first

transform ed. T ransform ed v a lu e s w ere then com b in ed o v er m u sc le pairs for e a c h freq u en cy. N ote that in s o m e c a s e s only 5 m u sc le pair v a lu e s w ere u se d . T h e com bination calculation u sed in Kilner e t al. (1999; 2 0 0 0 )

is provided a s a com p arison . Final c o h e r e n c e v a lu e s calcu lated using e a c h m ethod are highlighted in bold.

CHAPTER 3: TWO PHASES OF INTRACORTICAL INHIBITION EXPLORED