T H E O C U L O M O T O R S Y S T E M A S A M O D E L F O R T H E S T U D Y O F N E U R O N A L Í N T E R A C T I O N P R O C E S S E S
F . del P o z o ; S e n d r a , A . ; D e l g a d o - G a r c í a , J . M . and P o r t a e n c a s a , R .
D e p t . de C i b e r n é t i c a y A n á l i s i s N u m é r i c o . F a c u l t a d de Informática. U n i v e r s i d a d P o l i t é c n i c a , M a d r i d and D e p t . de F i s i o l o g í a . F a c u l t a d
de M e d i c i n a . S e v i l l a . S p a i n . A B S T R A C T
Identified neurons that control eye mo~ vements offer an e x c e l l e n t e x p e r i m e n t a l t a r g e t f o r the study of information coding and neuronal í n t e r -action p r o c e s s e s w í t h i n the cetitral nervous system. H e r e a r e p r e s e n t e d some p r e l i m í n a r y r e s u l t s of the rhotoneuron behaviour during steady eye f í x a t i o n , obtained by r e g r e s s í o n and analysis of v a r i a n c e techniques. A f l e x i b l e information system intended for the systematic acquisitíon and analysis of s i -multaneous r e c o r d s of neuronal a c t i v i t y and both eyes angular position in a g r e a t amount of c e l l s , o r i e n t e d to the d e f í n i t i o n of mathematical models, is a l s o b r i e f l y outlíned.
nal a c t i v i t i e s be explained by an adequate s e l e c tion of the individual p a r a m e t e r s of a common m a -thematical model ?.
T o cover these o b j e c t i v e s a system was developed f o r the automatic ánd s i mu Itaneous r e -cord ing of neuronal a c t i v i t y , angular position of the eyes and s e l e c t e d e x p e r i m e n t a l inputs. E x p e r í ments w e r e c a r r i e d out in a l e r t cats. A n i m á i s w e -r e p -r e v í o u s l y implanted w i t h s i l v e -r balI e l e c t -r o d o s to r e c o r d t h e í r e l e c t r o o c u l o g r a m (both in the h o r i -zontal and v e r t i c a l planes) and also with a holding system to r e s t r a i n the ir heads d u r i n g r e c o r d ing sessions* R e c o r d i n g s w e r e c a r r i e d out with glass micropipettes in selected a r e a s of the b r a i n stem through a t r a n s c e r e b e l l a r approach.1 A more d e
-tai led account of the e x p e r i m e n t a l set has beeri published e l s e w h e r e ( l ) .
A p r o m i s h i n g new approach to the study of information coding and neuronal i n t e r a c t i o n p r o cesses within the c e n t r a l n e r v o u s system has a p p e a r e d r e c e n t i y due to a major f a c t o r : the i m p r o
-vement in the techniques for r e c o r d i n g the a c t i v i t y of functional identified neurons in a l e r t behaving animáis. A f u r t h e r improvement has been obtained
with the application of these techniques to systems such as the neurons that control eye movements, w h e r é the output and some of the inputs a r e e a s t l y measured under v e r y d i f f e r e n t e x p e r i m e n t a l s i t u a -tions. (see 4, 6 and 7).
N e v e r t h e l e s s , even r e s t r i c t e d to such a class of systems, complexities a r í s e from: T) T h e wide r e p e r t o r y of n a t u r a l eye movements ( p u r s u i t , s a c c a d i c , v e r g e n c e , v e s t i b u l a r ) , and ii) T h e quajj t a t i v e l y d i f f e r e n t behaviour that can be observed from the a c t i v i t y r e c o r d s of neurons involved in the oculomotor control system. Both d i f f i c u i t i e s have f o r c e d the questions that a r e the main c o n -c e r n s of this -commun i -catión: Do s i m i l a r dynami-cal p r o p e r t i e s of eye movements, r e g a r d l e s s of t h e i r o r i g i n , c o r r e s p o n d to equaf coding p r i n c i p i e s ?and, can the d i f f e r e n c e s o b s e r v e d in oculomotor n e u r o
T h e a c t i v i t y of ¡nsolated motor or p r e -motor neurons was r e c o r d e d d u r i n g spontaneous and v e s t i b u l a r or visual induced eye movements in the a l e r t behaving animal. Only eye movements r e -lated neurons w e r e r"ecorded. T o f u r t h e r impróVé the r e l i a b i l i t y of the r e s u l t s , only identified n e u -rons w e r e c o n s í d e r e d f o r a n a i y s i s .
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N e u r o n a l I d e n t i f i c a t i o n was achieved by. a n t i d r o -mic activatíon of t h e i r somas from their axona! p r o j e c t í o n s . A c t i v a t í o n was c a r r i e d out by c h r o -n i c a l l y impla-nted stimulati-ng e l e c t r o d e s located
in neuronal p r o j e c t i o n sites: abducens n e r v e , o c u lomotor nucleus, a n t e r i o r v e r m i s of the c e r e b e llum, etc. ( 1 , 8 ) . T h e r e c o r d s of u n i t a r y a c t i v i -ty, eye movements and head position w e r e s t o r e d in a 4 - c h a n n e l s tape r e c o r d e r .
F o r the acquisition, g r a p h i c display and p r o c e s s i n g of the r e c o r d e d data, a system control led by a H P 9 8 4 5 B computer and a set of programs w e r e implemented (see block diagram in f i g u r e 1 . ) . Unit a c t i v i t y of the r e g i s t e r e d neurons
was converted into a point p r o c e s a by f i i t e r i n g , window d i s c r i m i n a t í o n and measuring the i n t e r s p i -ke i n t e r v a l sequence. T h e operation is p e r f o r m e d by a c o m p u t e r - c o n t r o l led counter that t r a n s f e r ta the computer, in a high speed mode, the i n t e r v a l s between neuron action p o t e n t í a l s ; so that, no lost of ¡nformation is guaranteed under the shortest e x -pected i n t e r v a i s with the f a s t e s t p l a y - b a c k rnagne-tic tape speed. Analog data (angular position in both eyes and e x p e r i m e n t a l v a r i a b l e s ) w e r e con-nected to high speed A / D c o n v e r t e r s , w h e r e sam-pling is p r o v i d e d by a c o m p u t e r - c o n t r o l led t i m e r , that also s y n c h r o n i z e the counter operation in o r -der to get exact temporal correspondence between the d i f f e r e n t data channels. D i g i t i z e d analog data
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F i g . 2. A c t i v i t y of ^rt abducens motoneuron (ieft side) d u r i n g espontaneous eye movements of the cat. F r o m top to bottom, the angular position of the Ieft eye in the h o r i z o n t a l plañe ( L . . P O S . ) , the velocity of the s a -me eye in the sa-me plañe ( L . V E L . ) , the I n v e r s e of the i n t e r v a l between spikeg (in sec. - 1) and the spikes
w e r e s t o r e d m o m e n t a r i l y , a f t e r multiplexing, in an a u x i l i a r buffer w h i l e the point p r o c e s s is being a c q u i r e d , and a r e t r a n s f e r r e d into the computer, through the system bus, upon complexión of that operation. F i n a l ly, data a r e s t o r e d in a f l e x i b l e disc together w i t h f i l e codes and acquisitíon v a r h í bles.
In o r d e r to allow the visual ínspection of the t r a n s f e r r e d data and the systematic s e l e c tion of r e c o r d s in a g r e a t amount of c e l l s fór f u r -ther p r o c e s s í n g , the p r o g r a m enabled the d í s p l a y , upon s e l e c t i o n , of the angular position and / o r ve lo city of both eyes w i t h the c e l l u l a r a c t i v i t y point p r o c e s s . E a c h p a r t i a l acquisitíon can be saved or e r a s e d a c c o r d i n g to its r e l e v a n c e for p o s t e r i o r
a n a l y s i s . It was also possíble to select p a r t i a l segments of a given f i l e using a c u r s o r over the C R T s c r e e n and s t o r e them w i t h s e p a r a t e d codes. O r d i n a t e s c a l e s w e r e deflned from c a l í b a t í o n r e -cords of the magnetic tape. H a r d - c o p i e s of the C R T d i s p l a y can be obtained with a therma! p r í n -ter1. A f t e r the p r e s e n t a t i o n of a t r a n s f e r r e d block,
the p r o g r a m automatical ly continué w i t h a new a c -quisitíon.
F i g u r e s 2 and 3 show exampies of the graphíc d i s p l a y s obtained w i t h the p r o g r a m . In both caséis, sampling r a t e was selected to l / 4 0 m s e c " ' (this r a t e was used g e n e r a l l y during the stage of ínitial inspection of data, since it allows a convenient 40 sec duratíon of each acquisitíon
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Fig."3. A c t i v i t y of an abducens motoneuron (left side) during sinusoidal r o t a t i o n of the animal. F r o m top to bottom,the instantaneous position of the head ( T A B L . E M O V . ) , the position of the left eye in the h o r i -zontal plañe (l_. P O S . ) , the i n v e r s e of the i n t e r - s p i k e i n t e r v a l s (in s e c . " *1) and the spikes ísolated through
block with adequate time r e s o l u t i o n for this p u r p o -se). T h e data segments shown in both f i g u r e s a r e c u r s o r s e l e c t e d and expanded portions of a 4 0 sec total d u r a t i o n f i l e . T h e data p r e s e n t e d have not been manípulated in any way to show the c l e a r c o r r e l a t i o n that exists between the s t a t i c a l and d y namical behaviour of the eyes and motoneuron a c -t i v i -t y , which has been r e p r e s e n -t e d a-t -the bo-t-tom of the f i g u r e s by the i n v e r s e of the time i n t e r v a l s between spikes, also included ( r e p r e s e n t e d below) as they a r e obtained a f t e r the window d i s c r i m i n a -t o r .
F i g u r e 2 is an example of the typical a c t i v i t y of an abducens (ieft side) motoneuron d u -r í n g spontaneous eye movement of an a l e -r t cat. In this case the angular position ín the h o r i z o n t a l pía ne ( L . POS.) of the Ieft eye and íts c o r r e s p o n d i n g v e l o c i t y have been selected for r e p r e s e n t a r o n . F | gure 3 shows the a c t i v i t y of the same c l a s s of neuron d u r i n g v e s t i b u l a r stimulation (sinusoidal r o t a t i o n of the head ín the h o r i z o n t a l plañe). In thís f i g u r e it has been selected the table angular position ¡n the h o r i z o n t a l plañe ( T A B L E M O V . ) and the angular position in the same plañe of the Ieft eye ( L H P O S ) .
r a c t e r i z a t i o n of the p r o f i l e of motoneuron d i s c h a r -ge r a t e associated to a saccadic movement followed by a f i x a t í o n i n t e r v a l . T h e evaluation of these d i s -charge p a t t e r n s could p r o v i d e some insight into the mechanism involved in the integration of i n f o r m a tion at the motoneuron level of the oculomotor s y s -tem, since according to our p r e l i m í n a r y r e s u l t s (see in f i g u r e 4 A . some typical p r o f i l e s d u r i n g eye f i x a t i o n i n t e r v a l s ) v a r i a b i l i t y d u r i n g steady f i x a -tion does not f i t with r e s u l t s published p r e v i o u s l y . A c c o r d i n g to Robinson's model (6, 7) motoneuron a c t i v i t y shows a p u l s e - s t e p i n c r e a s e in the spike r a t e d u r i n g s a c c a d i c movement in the on d i r e c t l o n followed by a constant valué which c o r r e s p o n d s to the new steady position. A s shown ín the f i r i n g -p r o f i l e s of f i g u r e 4 A . a d i f f e r e n t a-p-proach to the i n t e r p r e t a t i o n of motoneurona} a c t i v i t y , ahd corres; ponding functional system o r g a n i z a t i o n , can' be i n tended. M o r e o v e r , the adecúate d e s c r i p t i o n of -those patterns could e x p l a i n at least, p a r t of the high v a r i a t i o n found in the r e í a t i o n s h i p between the anglevof fixation and the f i r i n g r a t e d u r i n g steady f i x a t i o n . T h i s v a r i a t i o n has been hypothetized d u e t o tw/o main contributions: the level of a l e r t n e s s and a dependency on the d i r e c t i o n of the p r e v i o u s s a c c a de, i . e . a s a r t of h y s t e r e s i s effect ( 2 , 3 ) .
One of the analytical p r o c e d u r e s í m p l e mented w i t h our p r o g r a m was intended f o r the c h a
-T o analyze the temporal evolution of the motoneuron f i r i n g p a t t e r n s it has been used least
CflT RX4/S/MOTONEURON 3*D5/6:F9
F í g . 4. Examples of the a c t i v i t y of abducens motoneurons d u r i n g saccadic movements and fixatíons ¡ h a l e r t behaving cat. A ) F r o m top to bottom the position of the Ieft eye in the orbit (i_. P O S . ), its velocity ( L . V E I ), the i n v e r s e of the i n t e r - s p i k e s I n t e r v a l of an abducens motoneuron (ieft side) and the spike itself
isolated from the rough data s t o r e d on tape a r e shown. Note the i n c r e a s i n g freqüency during saccadic movements in the on d h e c t i o n and the decay d u r i n g the f o l l o w i n g f i x a t i o n . S e e f u r t h e r explanations Ín test. B) L i n e a r , l o g a r i t h m i c , exponential and 2n c l and 3pd o r d e r polynomial r e g r e s s i o n modeís least mean ^
mean s q u a r e r e g r e s s i o n techniques, applied to the i n t e r v a l s between action potential and f r o m data segments c o r r e s p o n d í n g to steady eye f i x a t i o n -states, a f t é r the p r e v i o u s eye saccade e x t i n t i o n . T h i s shoufd be c o n s í d e r e d as a f i r s t stage of a more d e t a i l e d and e f f i c / e n t estimation of the p a r a -méters of d i f f e r e n t p r o b a b i l i s t i c modeis of the sto chastic point p r o c e s s defined by the motoneuron output. F o r this purpose the f i r s t and second o r -der s t a t l s t i c s a r e at p r e s e n t being estimated in our department.
D i f f e r e n t r e g r e s s i o n modeis { l i n e a r , I o -g a r i t h m i c , exponential and polynomial) have been applied to the data ( X , Y ) m a t r i c e s defined as f o l -lows: V i ¡s thé o b s e r v e d time from the f i r s t spike to the r t h one, Y 2 f r o m the r t h spike to the 2 r t h one, and so on.' X ¡ was defined as thé time s c a l e at mid-points of the Y ¡ i n t e r v a l s . T h e par arrié t e r r was selected small enough to assume that the f i -r i n g -r a t e does not change a p p -r e c i a b l y d u -r i n g any of the Y ¡ i n t e r v a l s , p r o v i d i n g on the other hand adequate e f f i c i e n c y of the estimated model p a r a m e -t e r s . In a l I cases -the s i g n i f i c a n c c of -the f i -t -t e d mo-deis was tested by an a n a l y s i s of v a r i a n c e . It should be kept in mind that s i g n i f i c a n c e of a se lee ted r e g r e s s i o n model does only mean that the mo^ del account f o r a sígnificant p o r t i o n of the v a r i a tion o b s e r v e d in the v a r i a b l e along the time. F -s t a t i -s t i c wa-s u-sed for r e j e c t i o n of the modei-s, a t
a 0. 01 s i g n i f i c a n c e l e v e l , and a l s o as a s e l e c t i o n c r i t e r i a of those modeis proved s í g n i f i c a n t .
In f i g u r e 4 A . ' four eye f i x a t i o n i n t e r -v a l s , f o r an identified motoneuron, with d i f f e r e n t angular position have been included.' F i g u r e 4 B . shows the r e g r e s s i o n modeis obtained f o r the s e cond f i x a t i o n i n t e r v a l of f i g u r e 4 A . T h e a p p l í c a tion of analysis of v a r i a n c e to this segment p r o v i -ded the f o l l o w i n g r e s u l t s : l ) A l l four modeis (2nd and 3r d o r d e r for polynomial r e g r e s s i o n ) p r o v e d
to be signifícant and 2) the highest F valué {54. 33; with r - 4 and 19 residual, d e g r e s s of f r ^ edóm) c o r r e s p o n d e d to the togarithmic model. T h e application of the same p r o c e d u r e to a f j r e a t amount of f i x a t i o n i n t e r v a l s provided s i m i l a r r e -sults to those mentioned. H o w e v e r , the c o e f f i c í e n ts of the modeis r e f l e c t impórtant d í f f e r e n c e s that appear to be r e í á t é d to the f i x a t i o n angle and p r e -víous saccade waveshape. T h e c h a r a c t e r i z a t i o n of thís dependences ís at present being studied.
ce of present knowledge on the coding principies and neuronal i n t e r a c t í o n p r o c e s s ínvolved ín highér motor functions.
R E F E R E N C E S
1. D e l g a d o - G a r c í a , J. M . ; B a k e r , R . y Highs"tein, S . M. " T h e a c t i v i t y of i n t e r n u c l e a r neurons identified w i t h i n the abducens nucleus of the a l e r t cat-, " in: " C o n t r o l of G a z e by B r a i n S t e m N e u r o n s " , R . B a k e r and A . B e r t h o z ( e d s . ) , E l -s e v i e r , A m -s t e r d a m , pp. 2 9 1 - 3 0 0 , 1977. 2. E c k m i l l e r , R . " H y s t e r e s i s in the s t a t i c c h a
-r a c t e -r i s t i c s of the e y e position coded neu-rons in the a l e r t monkey, " P f l u g e r s A r c h . , vol. 350, pp. 2 4 9 - 2 5 8 , 1974.
3. G o l b e r g , J. " A c t i v i t y of abducens nucleus units in the a l e r t c a t , " Ph. D . D i s s . U n i v e r s i -ty of C a l i f o r n i a , B e r k e l e y , 98pp. , 1979. 4. K e l l e r , E . L . "Oculomotor neuron b e h a v i o u r " ,
¡n:"Models of Oculomotor B e h a v i o u r and C o n -t r o l , " B . L . Z u b e r (ed, ), C R C P r e s s , ín p r e s s . 5. Kel l e r , E . L . and Robínson, D . A . , "Absense
of a s t r e t c h r e f l e x in e x t r a o c u l a r muscles of the monkey", J. N e u r o p h y s i o l . , vol. 34, pp. 9 0 8 -919, 1971.
6. Robínson, D . A . , "Modeis of the s a c c a d i c eye movement control system", K y b e r n e t i k , vol. 14, pp. 7 1 - 8 3 , 1973.
7. Robínson, D . A . , "Oculomotor control signáis1}
ín: " B a s i c Mechanisms of O c u l a r Motil ity and t h e i r C l t n í c a l Implicatíons, " P . ' B a c h - y ~ R i t a and G. L e n n e r s t r a n d , ( e d s . ) , P e r gamón, O x -f o r d , pp. 3 3 7 - 3 7 4 , 1975.
8. S e r r a , R . ' and D e l g a d o - G a r c í a , J. M. , " E s t u d i o n e u r o f i s í o l ó g i c o de las motoneuronas del n ú -cleo a c c e s o r i o del motor o c u l a r e x t e r n o en el gato d e s p i e r t o ,1 1 R e v . E s p . F i s i o l . , vol. 36,
pp. 4 5 7 - 4 6 1 , 1980.
S U M M A R Y
