The use of optical flow to characterize muscle contraction
Introduction
Muscle contraction is commonly measured by force and displacement transducers (Joyce et al., 1969, Burke et al., 1970, Stuart, 1970, Mason and Kristan, 1982, Kristan, 1982, Norris and Calabrese, 1987). These transducers are small, cheap and convenient to use. They provide a direct measure of the force along a given direction, i.e. a scalar quantity. However, muscle contraction induces in the tissue a displacement field, i.e. a vector field, which cannot be precisely characterized by using these sensors, which provide only scalar quantities. This problem can be circumvented by using recent advances obtained in computer vision for the analysis of time varying sequence of images.
Research into computer vision has developed many tools for the analysis of image sequences (Horn and Schunck, 1981, Lucas and Kanade, 1981, Aggarwal and Nandhakumar, 1988, Anadan, 1989), such as those taken by a CCD camera monitoring traffic at street intersections (Giachetti et al., 1995) or by a CCD mounted on a moving vehicle (Giachetti et al., 1998). Some of these algorithms identify important features of the viewed scene and track them from one frame to the next (Aggarwal and Nandhakumar, 1988). Other algorithms aim at computing the vector field of the image motion on the CCD sensor, usually called optical flow, by differential methods, requiring the computation of various temporal- and spatial-derivatives of the original image sequences (Horn and Schunck, 1981, Lucas and Kanade, 1981). Once optical flow is obtained, i.e. a two-dimensional vector field describing the image motion, it is possible to recover from it important information of motion (Verri et al., 1989) and deformations (Giachetti and Torre, 1996) of viewed objects. These algorithms, which have been extensively studied and tested in a large variety of image sequences, provide reliable data and accurate measurements in specific cases. Indeed, performances and reliability of all these algorithms depend crucially on the presence of enough textures on the images: the absence of textures and landmarks makes very difficult any analysis of motion and deformation based on image sequences.
Conditions for the success of the algorithms developed by research into computer vision are met in some relevant neurobiological cases. They are met, for instance, when deformations of a piece of skin or of an almost flat tissue with enough texture or landmarks are imaged with a CCD camera. In this manuscript, the use of video miscroscopy and tools of computer vision to measure and characterize the displacement field induced on the skin of a leech by muscle contraction is described. The approach is based on the presence of natural landmarks on leech skin: indeed the whole body of the animal is covered by a rich texture, ideal for the computation of the optical flow.
The manuscript is divided in three sections. In Section 3, the tracking algorithm is discussed and explained step by step. Section 4 shows how to compute a reliable and dense optical flow from a sequence of images of the leech skin during muscle contraction induced by tactile or electrical stimulation. In Section 5, the linear deformation theory is used to characterize and describe skin deformations induced by different stimuli.
The proposed method, here demonstrated for the characterization of muscle contractions in the leech skin, is expected to provide good results for the analysis of all contractions evoked in almost flat tissues with enough landmarks. In this case, the proposed method provides a complete characterization of the induced deformations, which cannot be obtained with usual force transducers.
Section snippets
Preparation
Leeches (Hirudo medicinalis) were obtained from Ricarimpex (Eysines, France) and kept at 5 °C in tap water dechlorinated by aeration for 24 h.
Fig. 2(A) shows a typical skin preparation used to monitor muscle contractions. A hemisection of leech skin, three segments in length (15 annuli), was isolated from the rest of the body, of which one boundary was formed by the dorsal midline of the animal (top of Fig. 2A). The other boundary (bottom of Fig. 2A) was between the lateral line (longitudinal
The tracking algorithm
One of the most useful computer vision techniques for recovering the three-dimensional motion of objects viewed by a CCD camera, is the computation of optical flow. This is a planar vector field, which is the perspective projection on the image plane, of the original three-dimensional field of displacements occurring on the surface of the viewed object (Horn and Schunck, 1981, Verri and Poggio, 1989). Different approaches have been proposed to compute the optical flow (Horn and Schunck, 1981,
Tracking features on the leech skin
Fig. 2(A) illustrates an image of a piece of leech skin taken with a dissecting microscope at a low magnification before passing a depolarizing current step, lasting 3 s, in motoneuron 8, which is an excitor of the ventral longitudinal muscles. Panel A illustrates the skin at rest, before the stimulus application, while panel B illustrates the portion of skin enclosed in the white rectangle of panel A, at the time of the maximal contraction and at a higher magnification. The spike discharge
Processing of the optical flow
Once the optical flow is obtained, how can the deformations on the leech skin be characterized? Is it possible to obtain an accurate and possibly simple characterization of muscle contraction? By using well-known results of the theory of deformable bodies, (Sommerfeld, 1974) a simple answer to these questions is provided in the following sections.
Discussion
The results presented in this manuscript show that usual tools of image processing developed in computer vision can be used to analyze image sequences of a contracting piece of skin and to quantify muscle contraction in a new and useful way. The proposed method can be applied to characterize contractions and deformations of any biological tissue with enough landmarks or visual texture. The analysis of elementary deformations (see Section 5) will be successful with almost flat tissues where
Acknowledgements
We thank Marco Cappello (http://www.e-magine-it.it) for help in developing the software to compute the optical flow. We thank Alessandro Bisso for help in developing the Matlab application for the vector field analysis. We thank Jane Wolfe for editing the text. This work was funded by EU grant Parallel 960211.
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