Figure 1

Determination of digital high-speed videomicroscopy parameters of ciliary beat pattern of a cilium . The three positions of the cilium (base of the cilium, P₀, positions of the tip before the active and recovery strokes, P₁ and P₂ respectively) and the five time-points of beating (start and arrival of the active stroke, t₁ and t₂ respectively, start and arrival of the recovery stroke, t₃ and t₄ respectively, and start of the following cycle, t₅) were measured. Twelve parameters were then determined from these measurements:.

* The cilia length:$L_c\text{=max}\left({\overline{P_{0}P}}_1,\overline{P_0{P}_2}\right)$ where$\overline{P_i{P}_j}$ designates the euclidean distance between the points P_i and P_j. In cartesian coordinates$\overline{P_i{P}_j}=\sqrt{{\left(x_i-x_j\right)}^2+{\left(y_i-y_j\right)}^2}$

*The angle of beating,$\widehat{P_1{P}_0{P}_2},$ is given by the law of cosines:$\widehat{P_1{P}_0{P}_2}\text{=Arcos}\left(\frac{{{\overline{P_{0}P}}_1}^2+{\overline{P_0{P}_2}}^2-{\overline{P_1{P}_2}}^2}{2\cdot {\overline{P_{0}P}}_1\cdot \overline{P_0{P}_2}}\right)$

*The global frequency:$\mathrm{Fg=}\frac{1}{\left(t_5{-t}_1\right)}$ *The power stroke duration: Dp=(t₂ - t₁)

*The recovery duration: Dr=(t₄ - t₃) *The pause after stroke: Ps=t₃ - t₂

*The pause after recovery: Pr=t₅ - t₄ *The total pause: Pt=Ps+Pr

*The distance travelled per${\text{second = L}}_c\cdot \widehat{P_1{P}_0{P}_2}\cdot f_g\cdot 1\text{second}$

*The area swept$\text{per second =}\widehat{P_1{P}_0{P}_2}/2\cdot L_c^2\cdot f_g\cdot 1\text{second}$

*The weighted distance travelled$\text{per second = \% of beating edges}\cdot L_c\cdot \widehat{P_1{P}_0{P}_2}\cdot f_g\cdot 1\text{second}$

*The weighted area swept$\text{per second = \% of beating edges}\cdot \widehat{P_1{P}_0{P}_2}/2\cdot L_c^2\cdot f_g\cdot 1\text{second.}$