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Previous Article | Next Article
The Journal of Neuroscience, March 15, 2002, 22(6):2283-2298
Using Optical Flow to Characterize Sensory-Motor Interactions in a Segment of the Medicinal Leech
Davide Zoccolan and Vincent Torre Scuola Internazionale Superiore di Studi Avanzati and Istituto Nazionale di Fisica della Materia, Unita' di Trieste, c/o Scuola Internazionale Superiore di Studi Avanzati, 34014 Trieste, Italy
ABSTRACT
TOP
ABSTRACT
INTRODUCTION
Activation of motoneurons innervating leech muscles causes the appearance of a two-dimensional vector field of deformations on the skin surface that can be fully characterized using a new technique (Zoccolan et al., 2001
) based on the computation of the optical flow, the two-dimensional vector field describing the point displacements on the skin. These vector fields are characterized by their origin (i.e., the singular point) and by four elementary components that combine linearly: expansion (or compression), rotation, longitudinal shear, and oblique shear. All motoneurons can be classified and recognized according to the components of the deformations they elicit: longitudinal motoneurons give rise almost exclusively to longitudinal negative shear, whereas circular motoneurons give rise to both positive longitudinal shear and significant negative expansion. Oblique motoneurons induce strong oblique shear, in addition to longitudinal shear and negative expansion. Vector fields induced by the contraction of longitudinal, circular, and oblique fibers superimpose linearly. Skin deformations can therefore be attributed rather reliably to the contraction of distinct longitudinal, circular, and oblique muscle fibers. We compared the deformation patterns produced by touching the skin with those produced by intracellular stimulation of P, T, and N cells: vector fields resulting from the activation of P cells were almost identical to those produced by mechanical stimulation. Therefore, motor responses triggered by light or moderate touch are almost entirely mediated by excitation of P cells, with minor contributions from T and N cells.
Key words: sensory-motor interaction; motoneurons; optical flow; videomicroscopy; leech; mechanosensory neurons; computer vision
INTRODUCTION
A major goal of neuroscience is describing the neuronal pathways linking sensory input and motor output. Exhaustive analysis of these pathways is difficult in higher vertebrates, but is possible in invertebrates (Nicholls and Baylor, 1968
We characterize here skin contractions of a segment of the leech Hyrudo medicinalis by using videomicroscopy and computing optical flow from these images (Zoccolan et al., 2001
We show that motor responses initiated by light or moderate mechanical stimulation are almost entirely mediated by P cells. Mechanical stimulation and electrical excitation of P cells induce contractions with an almost identical shape and sustained by coactivation of both longitudinal and circular fibers. T cells, when individually activated, induce a much weaker skin contraction, with a different shape. They have a minor role in mediating local motor responses, although when coactivated with P cells, they can potentiate the contraction (Kristan, 1982
MATERIALS AND METHODS
Animals and preparations. Hirudo medicinalis were obtained from Ricarimpex (Eysines, France) and kept at 5°C in tap water dechlorinated by aeration for 24 hr. Three preparations were used.
The first preparation consisted of a hemisection of the leech skin, approximately three segments in length (15 annuli), isolated from the rest of the body. One boundary of this preparation was formed by the dorsal midline of the animal; the other boundary was between the lateral line and the ventral midline of the animal. The skin was flattened and fixed with small pins to the bottom of the recording chamber, but allowed to deform during muscle contraction. The middle segment was kept innervated by its ganglion. The connective and the roots emerging from the opposite side of the ganglion were pinned to allow easy intracellular recordings from the cell bodies of motoneurons and mechanosensory neurons in the ganglion.
A second preparation was used to more precisely study the dependence of motor response on the region of skin touched during mechanical stimulation. In comparison with the previous preparation, the differences were: (1) the inferior boundary coincided precisely with the ventral midline of the animal body and (2) the ganglion innervating the central segment was not exposed. This preparation offered two main advantages: (1) the skin could be stimulated near the ventral midline and (2) the roots innervating skin and muscles were perfectly intact because they had not been cleaned and exposed. For these reasons this preparation was used to verify that motor responses observed in the first kind of preparation were not affected by some dissection induced abnormality in muscle and skin innervation.
The third preparation was an intact leech. The head and the tail of the animal were pinned on a Sylgard dish, and the body was stretched. Two or three central segments were flattened and secured to the Sylgard dish with four pins. This portion of body wall and various free segments along the body were mechanically stimulated to verify the consistency of the motor responses in the intact animal and reduced preparations.
All preparations were kept in a Sylgard-coated dish at room temperature (20-24°C). During dissection the preparation was bathed in a Ringer's solution with the following composition (mM): 115 NaCl, 1.8 CaCl2, 4 KCl, 12 glucose, and 10 mM Tris maleate, buffered to pH 7.4 with NaOH (Muller et al., 1981
Imaging. One standard CCD camera (640 × 480 pixels) was mounted on a dissecting microscope. Images of the contracting leech skin were acquired at 5 or 8.3 Hz and stored on a personal computer using a frame grabber DT3155 (Data Translation, Marlboro, MA) and the acquisition software Axon Imaging Workbench 2.2 (Axon Instruments, Foster City, CA).
Electrical recordings. The electrical activity of motoneurons and mechanosensory neurons was monitored by intracellular recordings with sharp electrodes (input resistance 30 M
filled with 4 M potassium acetate) using Axoclamp-2b amplifiers (Axon Instruments). Depolarizing current pulses were passed through the electrodes into the cell bodies to evoke a spike discharge. Intracellular and extracellular voltage recordings were digitized at 10 kHz, stored on a personal computer, and analyzed with the program Clampex 8 (Axon Instruments). Axon Imaging Workbench 2.2 and Clampex 8 can run simultaneously on the same computer, allowing the synchronized acquisition of images and electrical signals.
Mechanical stimulation. In some experiments a brief (200-400 msec) mechanical stimulus was delivered to the skin. The stimulus consisted of a poke with a nylon filament driven by a solenoid (347-652 RS components), as previously described (Lewis and Kristan, 1998a
Analysis of the skin deformations. Muscle fiber contraction evokes in tissue a two-dimensional force field. Force or displacement transducers, providing a single scalar measure, cannot properly quantify this vector field. As described in Zoccolan et al. (2001)
Computing the optical flow. A window-matching algorithm that searches for the most similar patterns of gray levels in consecutive images is used to track points from one image to the next one (Aggarwal and Nandhakumar, 1988
= (x, y) on the image plane, the optical flow Ti( ) = (uTi( ), vTi( )) is the total displacement of the features centered on from image 1 to image i. uTi( ) and vTi(
To monitor the time evolution of a deformation, a sequence of instantaneous optical flows
i can be computed, where each flow i is the instantaneous displacement, i.e., the displacement from image i 1to image i, of the features
Linear deformation theory. The obtained optical flows can be further analyzed by linearizing them. In the case of a planar deformation, the optical flow
Ti( D( ), where is the stationary point of the deformation (referred to in the following as singular point) and L is the matrix describing the linear planar deformation. It is well known (Sommerfeld, 1974
where
(1)
are the elementary deformation components: expansion, rotation, and shears, respectively (Giachetti and Torre, 1996
(2) D is simply the sum of four elementary deformations, defined by the four matrixes in which matrix L is decomposed. The coefficients E, , S1, and S2 determine which is the relative weight of each elementary deformation of
D. A sketch of these four elementary fields is provided in Figure 1.
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Figure 1. A sketch of the elementary deformations. A, Expansion (E). B, Rotation (
The parameters E,
, completely determine every linear planar vector field D. In the following, the set of parameters E, The singular point coordinates px and py are measured in pixels. The elementary deformation components E,
RESULTS
Characterization of the contractions induced by leech motoneurons
The first preparation described in Materials and Methods was used to characterize the leech skin contractions induced by excitatory motoneurons. Individual leech motoneurons were stimulated to obtain a strong, sustained contraction of the corresponding muscles. The resulting skin movements were viewed with a CCD camera mounted on a dissecting microscope. Image sequences of the contracting skin were acquired at 5 Hz and analyzed as described in Zoccolan et al. (2001)
Figure 2 shows the optical flows obtained during maximal contraction produced by the stimulation of nine motoneurons: longitudinal L (A); dorsal longitudinal excitatory (DE) 3 (B); DE 5 (C); DE 107 (D); ventral longitudinal excitatory (VE) 8 (E); VE 108 (F); oblique excitatory (OE) 110 (G); circular ventral (CV) (H); and flattener excitatory (FE) 109 (I). In each panel the arrowheads indicate movement direction and the arrow length indicates displacement. The optical flows are drawn on a gray background showing pieces of body wall whose contractions were analyzed.
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Figure 2. Optical flows associated with nine different leech motoneurons. A-I show the optical flow computed on a 30 × 20 grid for the skin deformations caused by intracellular stimulation of motoneurons L, 3, 5, 107, 8, 108, 110, CV, and 109, respectively. The data were obtained from seven different preparations. Each motoneuron was stimulated with a depolarizing step of current causing a spike discharge between 30 and 40 Hz and lasting from 1 to 6 sec. Optical flows were obtained as described in Zoccolan et al. (2001)
These flows are in excellent agreement with the deformations expected from previous descriptions of these motoneurons (Stuart, 1970
The optical flows shown in Figure 2 can be approximated with linear vector fields. Figure 3A-I illustrates the best linear vector fields approximating the corresponding optical flows reported in Figure 2. For each deformation, the linear approximation was computed in a region surrounding the stationary point. This linearization region is indicated by the window drawn in each panel of Figures 2 and 3 (the position of the stationary point is indicated by the X). Comparison of corresponding panels in Figures 2 and 3 shows that the linear approximation is satisfactory in the area of skin where the original optical flow (Fig. 2) is large and poor outside it. This is not surprising because almost all leech motoneurons innervate selectively just a narrow region of muscles in a half segment. For this reason, in almost all the panels of Figure 2 the contraction is restricted to a small area of the skin. By definition, the amplitude of a planar vector field increases linearly while moving away from the singular point (Fig. 3). This explains why linear approximations have large amplitude in areas where corresponding real optical flows are almost zero. For example, in cell 3 (a dorsal excitor) the linear approximation is good not only inside the linearization region but also in a wider dorsal area of the skin where the deformation amplitude is significantly greater than zero (compare Figs. 2B and 3B). On the contrary, in the ventral region the deformation is almost zero and a comparison with the linear approximation is not appropriate. In summary, the contraction induced by each motoneuron is approximately linear in the skin area that is being functionally innervated. In this area, the optical flow and its linear approximation are highly repeatable from preparation to preparation, allowing a precise classification of the different classes of motoneurons (Fig. 5). Outside this area the optical flow is almost null, and its shape is variable from preparation to preparation. This is because the observed deformation is passively driven by the active part of the skin and it is significantly influenced by the location of pins holding the preparation.
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Figure 3. Linear approximations of the optical flows. A-I show the vector fields obtained by linearly approximating the optical flows shown in the solid boxes in the corresponding panels of Figure 2. In each, the X indicates the position of the singular point. The drawings of the segment annuli are the same as Figure 2. The agreement between the original optical flow (Fig. 2), and the linear approximation (Fig. 3) is good within the box and in the skin area mainly involved in the contraction and poor outside.
Note that the use of linear approximations in characterizing motoneuron contractions was primarily suggested by the finding that almost all optical flows induced by leech motoneurons had only one singular point, i.e., only one stationary point. This is the first requirement for a vector field to be linear (Sommerfeld, 1974
Approximating skin deformations with linear vector fields is a powerful tool, because, as recalled in Materials and Methods, every planar linear field is uniquely characterized by a set of six parameters (Giachetti and Torre, 1996
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Figure 4. Distribution of the location of the singular points for the skin deformations induced by individual motoneurons in different preparations. A, The singular points of longitudinal motoneurons L ( ), 3 (X), 5 (
), 107 (
), 8 (
), and 108 (
) in nine, seven, five, six, three, and seven, different preparations, respectively. B, The singular points of the oblique motoneuron 110 (
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Figure 5. The average relative weights of the elementary deformations for different leech motoneurons. A-I show the mean relative weight of expansion (E), rotation (
Figure 4 shows the singular point positions of the various motoneurons in different preparations. The gray background reproduces the annular margins of a representative body wall preparation; the central annulus is indicated by the arrow. A shows the singular point positions for the contractions induced by longitudinal motoneurons 3, 5, 8, 107, 108, and L. In A six specific regions, in which singular points of each motoneuron aggregate, are apparent. The size of these regions varies from 1.5 to 3 mm in the longitudinal direction (2-4 annuli) and from 1 to 2.5 mm in the transverse direction. As shown in B, singular points of oblique, circular, and flattener motoneurons aggregate in clusters of slightly wider area (the singular points of motoneuron 110 span approximately five annuli).
Figure 5 summarizes the relative weights of the four elementary deformations E,
Figure 5 shows that the contractions induced by single motoneurons can be classified on the basis of their main elementary deformations. This classification is highly reliable because the uncertainty of the relative weight of the main elementary deformations is low (see the error bars in Fig. 5). Moreover, this classification is in strict agreement with the anatomical arrangement of the leech muscle fibers (Stuart, 1970
Table 1 summarizes these properties for nearly well characterized excitatory motoneurons of the leech segmental ganglion. In addition to the nine motoneurons previously described, the classification of other longitudinal (cells 4 and 106), circular (cells 12 and 112), and oblique (cell 111) motoneurons is provided on the base of: (1) the area of skin involved in the contraction, (2) the location of its singular point, and (3) its major elementary deformations. The number of preparations used to validate the classification presented in Table 1 ranges from 3 to 10, depending on the analyzed motoneuron.
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Table 1. Properties of excitatory leech motoneurons Time evolution of the contractions induced by single motoneurons
Figure 6 shows the time evolution of the elementary deformations for the contractions induced by motoneurons 107 (A), 110 (B), and 12 (C), chosen as representative of the three possible classes of motoneuron contractions. The instantaneous values of the elementary deformations for cells 107 and 110 were obtained by computing and linearizing a sequence of 19 optical flows every five frames of the original image sequence (100 images). In the same way, nine optical flows were computed and linearized from the sequence of 50 images describing the contraction induced by cell 12. The bar in the top of each panel gives the duration of the spike discharge induced in each motoneuron. Note that the ordinate values are velocities; these plots show how the rates of change of each elementary deformation proceed throughout the contraction that each motoneuron induces.
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Figure 6. Dynamics of the deformations induced by three different classes of motoneurons. The time course of the elementary deformations for the contractions induced by motoneurons 107 (A), 110 (B), and 12 (C) were obtained from the sequence of instantaneous optical flows. The motoneurons were stimulated to fire at a frequency between 20 and 40 Hz for 6 (cell 107 and 110) or 1 (cell 12) sec. The bar at the top of each panel shows stimulation duration. The units in which the time varying deformations are expressed in seconds 1 because the data were calculated from every fifth image and the images were acquired at 5 Hz. Each panel shows the time evolution of expansion E (
Motoneuron 107 is an excitor of the ventral longitudinal muscles. Its main elementary deformation was a negative longitudinal shear S1 (Fig. 5D). The contraction phase lasted from second 2 to second 6; the relaxation phase started at second 9, 2 sec after the cessation of the stimulus. From second 7 to second 8 the skin reached a stationary phase with not appreciable movements. Figure 6A shows that the relative amplitude of the four elementary deformations did not appreciably change during the whole deformation. S1 was consistently the main component of the deformation, simply reversing its sign in the transition from the contraction to the relaxation phase. Figure 6A also shows that, for cell 107, the contraction phase was much shorter and faster (high and narrow negative peak of S1) than the relaxation phase (smaller and broader positive peak of S1).
The time course of the deformation of motoneuron 110 was similar; the deformation consisted of a short and rapid contraction, a stationary phase, and a long slow relaxation. The main elementary deformations (S2, S1, and E), had an almost identical time course.
Cell 12 (an excitor of the ventrolateral circular muscles) showed a similar time course of its main elementary deformations: S1 and E. The main difference from the previous contractions was that the relaxation phase was shorter and faster: the peaks of S1 and E in the relaxation phase were as large as their peaks in the contraction phase. As a general rule, contractions induced by the excitors of circular muscles always relaxed faster than the contractions induced by longitudinal and oblique motoneurons (data not shown).
The elementary deformations of the other longitudinal and circular motoneurons had similar time courses. For each motoneuron the relative amplitudes of the four elementary deformations did not appreciably change during the whole deformation. That is, although the amplitude of the vectors changed with time, according to the intensity of the contraction, the direction of the vectors was substantially constant, simply reversing sign from contraction to relaxation.
Combination of vector fields induced by single motoneurons
The characterization of skin deformations described in the previous sections was obtained when each motoneuron was stimulated individually. We next investigated how skin deformations induced by individual motoneurons add when two or more motoneurons are simultaneously activated.
Let us first consider the case when two longitudinal motoneurons, such as the L motoneuron and the dorsal longitudinal motoneuron 5, were coactivated. Figure 7, A and B, shows the optical flows induced by stimulation of motoneurons L and 5 individually. C shows the optical flow induced by identical simultaneous stimulation of the two motoneurons. D compares the vector field shown in C (black) to the vector field obtained by linear superposition of the vector fields shown in A and B (red). The black and red vector fields are very similar, indicating a simple linear summation of the skin deformations induced by the individual motoneurons. E shows the values of the elementary deformations for the contractions induced by the individual stimulation of cells L (gray histogram) and 5 (white histogram). F shows: (1) in gray, the elementary deformations for the contraction obtained by the simultaneous stimulation of the two motoneurons and (2) in red, the sum of the elementary deformations obtained for the individual stimulation of the two neurons (each red bar in F is the sum of the corresponding gray and white bars in E). E and F show that all three vector fields drawn in A-C are characterized by a large negative value of S1 and negligible values of E, S2, and
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Figure 7. Superposition of the deformations evoked by motoneurons innervating the same class of muscle fibers. A, Optical flow after longitudinal motoneuron L stimulation with a current pulse lasting 5 sec and evoking a spike discharge of ~14 Hz. B, Optical flow after longitudinal motoneuron 5 stimulation with a current pulse lasting 5 sec and evoking a spike discharge of ~34 Hz. C, Optical flow after identical simultaneous stimulations of both longitudinal motoneurons. D, Sum of the optical flows shown in A and B (red) compared with the optical flow shown in C (black). E, Elementary deformations of the optical flows shown in A and B (L, gray bars; 5, white bars). F, Sum of the elementary deformations of motoneurons L and 5 (red bars) compared with the elementary deformations of the optical flow shown in C (gray bars). The width of the annuli in A-D is ~0.8 mm. Equal normalization in E and F.
Let us now consider the case when two motoneurons innervating different muscle fibers are simultaneously stimulated. Figure 8, A and B, shows the optical flows induced by individual stimulation of circular motoneuron 112 and of longitudinal motoneuron 5. C shows the optical flow obtained by identical simultaneous stimulation of the two motoneurons. D compares the vector field shown in C (black) to the linear superposition of the vector fields shown in A and B (red). The black and red vector fields in D are very similar, indicating that simultaneous activation of cells 5 and 112 induces a skin deformation that is an almost perfect linear summation of the deformations the individual motoneurons induced.
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Figure 8. Superposition of the deformations evoked by motoneurons innervating different muscle fiber classes. A, Optical flow after circular motoneuron 112 stimulation with a current pulse lasting 5 sec and evoking a spike discharge of ~28 Hz. B, Optical flow after longitudinal motoneuron 5 stimulation with a current pulse lasting 5 sec and evoking a spike discharge of ~42 Hz. C, Optical flow after identical simultaneous stimulation of both motoneurons. D, Sum of the optical flows shown in A and B (red) compared with the optical flow shown in C (black). E, Elementary deformations computed for the optical flows shown in A and B (112, gray bars; 5, white bars). F, Sum of the elementary deformations of motoneurons 112 and 5 (red bars) compared with the elementary deformations of the optical flow shown in C (gray bars). The width of the annuli in A-D is ~1 mm. Equal normalization in E and F.
The analysis of the elementary deformations shows that the combination of a longitudinal and of a circular motoneuron leads to a vector field characterized by a large negative value of E as the main deformation component. In the following, we will refer to this kind of skin deformation (characterized by large E and smaller values of S1, S2, and
This deduction was supported by simultaneous recordings from different pairs of longitudinal and circular (or flattener) motoneurons, such as: motoneurons 3 and 112 (data not shown); motoneurons 108 and 12 (data not shown); motoneurons L and 109 (data not shown). These experiments clearly showed that when a longitudinal and a circular (or flattener) motoneuron were coactivated, the resulting skin deformation was a compression. Similarly, simultaneous recordings from different pairs of longitudinal motoneurons confirmed the result shown in Figure 7: when two longitudinal motoneurons were simultaneously stimulated, the resulting skin deformation was an almost pure negative longitudinal shear. When motoneurons innervating oblique muscles, such as motoneurons 110 or 111, and a longitudinal or circular motoneuron were simultaneously activated by depolarizing current, vector fields induced on the leech skin similarly added linearly.
In summary, these experiments strongly support the hypothesis that skin deformations induced by different motoneurons, during a light or moderate mechanical stimulation, sum linearly as a general rule. In turn this property of linear superposition enables complex deformations to be decomposed into the muscle types sustaining them. For example, when a skin deformation caused by a mechanical stimulation is indeed a local compression, characterized by a large value of E without a simultaneous large S1 or/and S2, it can be inferred that longitudinal and circular fibers are coactivated.
Note that real skin deformations sum linearly, but in general this is not the true for their linear approximations. The linear sum of linear approximations only holds for pairs of motoneurons innervating skin areas that are at least partially overlapping. This is the case for cells 112 and 5, both innervating dorsal muscles, and cells 5 and L, whose deformations overlap in a wide dorsal area of the skin (Figs. 7F, 8F). On the contrary, when two motoneurons innervating nonoverlapping skin regions are coactivated, their elementary deformations do not add linearly (data not shown). Nevertheless, the skin deformation resulting from their coactivation is still generally linear around the singular point. Its elementary deformations are strictly related to those of individual motoneurons, so that it is still easy to infer which classes of motoneurons sustain the contraction.
Comparison of skin deformations caused by mechanical stimulation and electrical excitation of mechanosensory neurons
As a further example of the ability of optical flow analysis in neurobiology, we analyzed the optical flows induced by mechanical stimulation of the leech skin to identify which muscle fibers are primarily activated and which mechanosensory neurons mediate that activation. In these experiments an intracellular electrode was inserted into an identified mechanosensory neuron to: (1) measure the number of spikes the mechanical stimulation induced in that neuron and (2) characterize the vector fields induced by a controlled number of spikes elicited in the mechanosensory neuron.
Ventral and dorsal P cells
Figure 9 shows data obtained from a preparation in which both the ventral (A and B) and dorsal (C and D) P cells were impaled. Mechanical stimulation of the skin in the ventral side, exerting a force of ~20 mN for 300 msec (touch location is indicated by the circle in A), induced 12 ventral P cell spikes (bottom trace in A), and the vector field of skin deformations shown in the top part of A. Induction of similar P cell firing by current injection (bottom trace in B), induced a very similar vector field and singular point location (top part, B; singular points are indicated by the "X" in A and B). Both vector fields have the characteristic shape of a ventral compression with the arrows pointing toward the center of the deformation. This qualitative observation was confirmed by computing their elementary deformations (Fig. 10A,B); both vector fields have similar large negative E values. On the base of the considerations reported in the previous section (Fig. 8C), we concluded that both deformations were sustained by simultaneous activation of longitudinal and circular muscles.
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Figure 9. Skin deformations caused by mechanical stimulation and P cell intracellular stimulation. A, Optical flow induced by mechanical stimulation (20 mN for 300 msec; circle) in the ventral side of the segment. The X is the location of the singular point. The bottom traces show stimulus duration and the ventral P cell response. B, Optical flow induced by ventral P cell intracellular stimulation; note marked similarity. C, Optical flow and dorsal P cell response induced by mechanical stimulation (20 mN for 200 msec) in the dorsal side of the segment. Symbols as in A. D, Optical flow induced by dorsal P cell intracellular stimulation; note marked similarity. The width of the annuli is ~0.9 mm.
Mechanical stimulation in the dorsal side of the skin (circle) induced the vector field and dorsal P cell firing shown in Figure 9C. Induction of similar P cell firing induced a very similar vector field and singular point location (Fig. 9D, singular points marked by X). Both contractions are characterized by a similar high negative value of the expansion E (Fig. 10C,D). The higher values of E and S1 in Figure 10C in comparison to those in Figure 10D indicate that the compression induced by the mechanical stimulation was slightly stronger than that induced by dorsal P cell intracellular stimulation, in accordance with the higher number of spikes elicited by the mechanical stimulus.
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Figure 10. The elementary deformations induced by mechanical stimulation and intracellular P cell stimulation. A-D show the elementary deformations of the optical flows in the corresponding panels of Figure 9. The elementary deformations were computed by linearizing the optical flows shown in Figure 9 in the regions indicated by the solid boxes. Equal normalization in all panels.
Monitoring T cells
Figure 11 shows the results obtained when a dorsal T cell was impaled. Mechanical stimulation of the dorsal skin (circle, A) induced an ON discharge of ~4 spikes in the T cell followed by an OFF response of >10 spikes (bottom trace in A). The induced vector field on the leech skin was again a compression, characterized by a high negative value of the expansion E, as is shown in C, which plots the elementary deformations for the optical flow in A. When the same T cell was forced to fire similarly by successive depolarizing current pulses, the induced vector field was qualitatively different and of much smaller amplitude (Fig. 9B) (note that the magnification-gain is fivefold greater in this panel than in A). The large difference in optical flow induced by mechanical stimulation and T cell stimulation is also apparent in the elementary deformation plots (Fig. 11C,D).
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Figure 11. T cell contribution to motor response. A, Optical flow induced by mechanical stimulation (20 mN for 400 msec) in the dorsal side of the segment. Symbols as in Figure 9. The bottom traces show the duration of the stimulus and the spikes that it evoked in the dorsal T cell. B, Optical flow induced by intracellular dorsal T stimulation cell with successive depolarizing current pulses (bottom trace). C, Elementary deformations computed for the vector field shown in A. D, Elementary deformations computed for the vector field shown in B. The boxes in A and B are linearization regions for the corresponding optical flows. The width of the annuli in A and B is ~0.6 mm. Equal normalization in C and D.
Relative contribution of P and T cells
The data presented so far clearly show that motor responses initiated by a localized mechanical stimulation are primarily mediated by P cells. This result is in agreement with previous studies (Kristan, 1982Monitoring N cells
Figure 12 shows data obtained when the medial N cell was impaled. Mechanical stimulation (circle, A) induced in the medial N cell just 1 or 2 spikes or no spikes at all (bottom trace, A). Measurable skin deformation could only be evoked firing at least six spikes in the medial N cell (nine spikes were elicited in the experiment shown in B). Despite this increase in the N cell activity, the deformation vector field induced by N cell firing was much smaller (note magnification change in B) and qualitatively different from that induced by the mechanical stimulation (A). C and D, which report the elementary deformations for the optical flows drawn in A and B, support the qualitative data shown in Figure 12, A and B; mechanical stimulation induced a large negative E and a slightly smaller positive S1, but N cell stimulation evoked equally small negative E and S1. Similar results were obtained by impaling the lateral N cell.
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Figure 12. N cell contribution to motor response. A, Optical flow induced by mechanical stimulation (20 mN for 200 msec) in the dorsal side of the segment. Symbols as in Figure 9. B, Optical flow induced by intracellular medial N cell stimulation. C, Elementary deformations computed for the vector field shown in A. D, Elementary deformations computed for the vector field shown in B. The boxes in A and B are the linearization regions for the corresponding optical flows. The width of the annuli in A and B is ~0.8 mm. Equal normalization in C and D.
Mechanical stimulation in more intact preparations and in intact leech
The experimental results presented so far were obtained in isolated leech segments. Some of these results, such as the major contribution of the P cells to the motor responses induced by mechanical stimulation, confirm and extend the classical descriptions of the local reflexes in the leech (Kristan, 1982Time evolution of the contraction caused by mechanical stimulation
As shown in the previous section, mechanical stimulation can evoke a complex pattern of skin deformations in which different classes of motoneurons and muscles are involved. The dynamics of this complex deformation, i.e., the timing with which different sets of muscles are recruited, can again be described by analyzing the sequence of instantaneous optical flows
computed for each video frame. Figure 13 shows the dynamics of a deformation induced by touching the skin in the lateral side (the location of the touch is indicated by the circle in A). Every fifth frame of the original image sequence (50 images) acquired at 5 Hz was selected, and a sequence of nine instantaneous optical flows was obtained. A-C show the instantaneous vector fields at three different times during the skin contraction. D shows the time course of the elementary deformations during the first 9 sec of the deformation. The thick horizontal bars on the top of D indicate the time intervals in which longitudinal and circular muscles are supposed to contract (gray) or relax (white). The thin black bar indicates the duration of the mechanical stimulus (20 mN for 200 msec).
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Figure 13. Dynamics of a complex contraction induced by a mechanical stimulation. A-C show the instantaneous vector fields at three different times during skin contraction. The location of the mechanical stimulus is indicated in A by the circle. The Xs represent the positions of singular points. The time interval during which each flow occurred is shown in the top of each panel. D shows the time course of the elementary deformations: expansion E (
Direct observation of the shape of the vector fields reveals at least three different phases of the deformation. The initial phase shown in A is a dorsal local compression. The successive phase (B) is a ventral longitudinal shear. The third phase (C), computed several seconds later when the deformation is in the relaxation phase, looks like a longitudinal shear, but the parallel direction of the arrows suggests the presence also of a strong expansion component. These qualitative observations are confirmed by the time course of the elementary deformations (D). In the initial phase of the contraction, from second 0 to second 2, the main component of the deformation was the negative expansion E. We concluded that in this phase the longitudinal and circular muscles were coactivated to produce the dorsal compression drawn in A. Immediately after (from seconds 2-4), the expansion coefficient vanished, and the contraction was sustained by only negative longitudinal shear S1 (B). Presumably in this phase circular muscles had ceased contracting and the deformation was driven only by the longitudinal muscles. At second 5 the circular muscles started to relax. The expansion coefficient E became positive and increased until it reached the same magnitude as S1, but with opposite sign (compare with the transverse relaxation in C). The longitudinal relaxation began later, after the termination of the acquired image sequence.
Figure 13 shows that the dynamics of a deformation induced by a mechanical stimulation can be complex. The dynamics exhibited some variability from preparation to preparation, but in the same preparation were usually reproducible over 30-40 min. Sometimes longitudinal and circular muscles seemed to contract and relax in clearly distinct phases, as for the experiment described in Figure 13, but other times the longitudinal and circular muscles seemed to contract and relax simultaneously.
DISCUSSION
We have shown here that, by using a recently developed technique based on the computation of optical flow (Zoccolan et al., 2001
Motoneuron classification and optical flow
Table 1 and Figures 4 and 5 show that by analyzing the optical flow of contracting pieces of skin, it is possible to more completely characterize leech excitatory motoneuron actions. This is possible because optical flow provides a two-dimensional characterization of muscle contraction that cannot be adequately measured by conventional force transducers, which measure only scalar quantities. Quantitative properties of the optical flow (i.e., the location of the singular point and its elementary deformations) produced by the excitation of a given motoneuron were highly reproducible in different leech segments and in different leeches. This quantitative two-dimensional description represe
