Hypothesis regarding the transformation of the intended direction of movement during the production of graphic trajectories: a study of drawing movements in 8- to 12-year-old children

Concurrent and Predictive Validity of a Cycloid Loops Copy Task to Assess Handwriting Disorders in Children

Handwriting disorders (HDs) are mainly assessed using script or cursive handwriting tasks. The most common is the scale for children's handwriting, with a French adaptation (BHK). The present study aims to assess the concurrent validity of a pre-scriptural task (copying a line of cycloid loops) with the BHK for the diagnosis of HDs. Thirty-five primary school children (7 females, 28 males) with HD aged 6-11 years were recruited and compared to 331 typically developing children (TDC). Spatial/temporal/kinematic measures were collected using a digital pen on a paper. Posture and inter-segmental writing arm coordination were video recorded. A logistic regression statistical method, including a receiver-operating characteristic curve, was used to assess the ability of the task to predict HD. Gestural patterns were significantly less mature in HDs than in TDC (p < 0.05), and associated with poorer quality, less fluid, and slower drawing (p < 0.001). Moreover, good correlations between temporal and kinematic measures and the BHK scale were found. Number of strokes, total drawing time, in-air pauses times, and number of velocity peaks showed very good sensitivity (88%) and specificity (74%) to diagnose HDs. Consequently, the cycloid loops task is an easy, robust, and predictive tool for clinicians to identify HDs before the alphabet is mastered.

Phenotyping features in the genesis of pre-scriptural gestures in children to assess handwriting developmental levels

Acquiring writing skills is a long developmental process that is conditioned by both the mastery of the gesture and the spatio-temporal arrangement of characters across the page. While the researches in the literature mainly focused on spatio-temporal and kinematics parameters of tracing letters or words using digitizing tablets, no recent research has previously studied the developmental prerequisites of the organization of handwriting useful for clinical assessment and remediation. Aims of the present study was to investigate and validate the phenotyping of the developmental genesis of pre-scriptural graphomotor gestures among school-aged children in achieving correct handwriting. The subject was examined in depth in an ecological setting similar to school, with the objective of assessing handwriting developmental levels. The pre-scriptural graphomotor task studied was to copy a line of cycloid loops on a paper sheet put on the table. This task was chosen because it reflects the execution of the hand movements from one end of the line to the other and in an anti-clockwise direction, as in handwriting. A new methodological approach was applied incorporating both the maturative evolution of postural-gestural features (video-recorded for analysis in 2D reconstruction) and spatio-temporal/kinematic measures collected with a digital pen connected to an analysis software tool to assess the developmental level and provide an understanding of the phenotypical features of the graphomotor gesture. And we also evidence the concurrent validity of the data in displacements, and the better are the spatio-temporal and kinematic measures. Consequently there are phenotypical features, both postural-gestural and spatio-temporal/kinematic in the developmental genesis of the graphomotor gesture with an easy pre-scriptural task. Typically developing school children from 1st to 5th grade, was collected from elementary schools. Five main patterns of displacement gestures were found for the production of the line of loops with a significant developmental progress from 1st to 5th grade. In addition, significant results in comparisons with spatio-temporal and kinematic age-related normative data were highlighted, associated with the quality of the coordination gesture. Lastly external validity in relation to normative values with the standardized handwriting scale BHK (French adaptation of the Concise Evaluation Scale for Children’s handwriting) showed certain significant correlations with spatio-temporal and kinematic measures and the evolution of the displacement gestures (five patterns) used to draw the loops. The better the motor control of the handwriting gesture, the less variety there is in inter-segmental and joint-scriptural task, enabling handwriting developmental levels to be assessed in screening for handwriting disorders, possibly co-occurring with other learning disabilities, and also useful in clinical decision-making processes for handwriting remediation, or simply to assist handwriting gesture acquisition in elementary school.

The relation between geometry and time in mental actions

Mental imagery is a cognitive tool that helps humans take decisions by simulating past and future events. The hypothesis has been advanced that there is a functional equivalence between actual and mental movements. Yet, we do not know whether there are any limitations to its validity even in terms of some fundamental features of actual movements, such as the relationship between space and time. Although it is impossible to directly measure the spatiotemporal features of mental actions, an indirect investigation can be conducted by taking advantage of the constraints existing in planar drawing movements and described by the two-thirds power law (2/3PL). This kinematic law describes one of the most impressive regularities observed in biological movements: movement speed decreases when curvature increases. Here, we compared the duration of identical actual and mental arm movements by changing the constraints imposed by the 2/3PL. In the first two experiments, the length of the trajectory remained constant, while its curvature (Experiment 1) or its number of inflexions (Experiment 2) was manipulated. The results showed that curvature, but not the number of inflexions, proportionally and similarly affected actual and mental movement duration, as expected from the 2/3PL. Two other control experiments confirmed that the results of Experiment 1 were not attributable to eye movements (Experiment 3) or to the perceived length of the displayed trajectory (Experiment 4). Altogether, our findings suggest that mental movement simulation is tuned to the kinematic laws characterizing actions and that kinematics of actual and mental movements is completely specified by the representation of their geometry.

Movement timing and invariance arise from several geometries

Human movements show several prominent features; movement duration is nearly independent of movement size (the isochrony principle), instantaneous speed depends on movement curvature (captured by the 2/3 power law), and complex movements are composed of simpler elements (movement compositionality). No existing theory can successfully account for all of these features, and the nature of the underlying motion primitives is still unknown. Also unknown is how the brain selects movement duration. Here we present a new theory of movement timing based on geometrical invariance. We propose that movement duration and compositionality arise from cooperation among Euclidian, equi-affine and full affine geometries. Each geometry posses a canonical measure of distance along curves, an invariant arc-length parameter. We suggest that for continuous movements, the actual movement duration reflects a particular tensorial mixture of these canonical parameters. Near geometrical singularities, specific combinations are selected to compensate for time expansion or compression in individual parameters. The theory was mathematically formulated using Cartan's moving frame method. Its predictions were tested on three data sets: drawings of elliptical curves, locomotion and drawing trajectories of complex figural forms (cloverleaves, lemniscates and limaçons, with varying ratios between the sizes of the large versus the small loops). Our theory accounted well for the kinematic and temporal features of these movements, in most cases better than the constrained Minimum Jerk model, even when taking into account the number of estimated free parameters. During both drawing and locomotion equi-affine geometry was the most dominant geometry, with affine geometry second most important during drawing; Euclidian geometry was second most important during locomotion. We further discuss the implications of this theory: the origin of the dominance of equi-affine geometry, the possibility that the brain uses different mixtures of these geometries to encode movement duration and speed, and the ontogeny of such representations.

No existing theory successfully accounts for several amazing properties of biological movements: dependence of movement speed on path curvature, isochrony (movement duration is nearly independent of its size) and the construction of more complex movements from simpler building blocks. Here we present a new theory of movement generation, based on movement invariance with respect to geometrical transformations. Several types of transformations are considered. Euclidian transformations preserve lengths and angles; affine transformations, which are less restricted, preserve parallelisms between lines, while equi-affine transformations preserve both parallelism and area. Each geometry is associated with a different measure of distance along curves. Movement timing is continuously prescribed by the brain by combining different “geometrical times” each assumed to be proportional to the measure of distance of the corresponding geometry. Movements are constructed by using a series of instantaneous (Cartan) coordinate frames. The predictions of the theory compared well with experimental observations of human drawing and walking. Equi-affine geometry was found to play a dominant role in both tasks and is complemented by affine geometry during drawing and by Euclidian geometry during locomotion. The proposed theory has far reaching implications with respect to brain representations of motion for both action production and perception.