The need for speed in rodent locomotion analyses

Abstract

Locomotion analysis is now widely used across many animal species to understand the motor defects in disease, functional recovery following neural injury, and the effectiveness of various treatments. More recently, rodent locomotion analysis has become an increasingly popular method in a diverse range of research. Speed is an inseparable aspect of locomotion that is still not fully understood, and its effects are often not properly incorporated while analyzing data. In this hybrid manuscript, we accomplish three things: (1) review the interaction between speed and locomotion variables in rodent studies, (2) comprehensively analyze the relationship between speed and 162 locomotion variables in a group of 16 wild-type mice using the CatWalk gait analysis system, and (3) develop and test a statistical method in which locomotion variables are analyzed and reported in the context of speed. Notable results include the following: (1) over 90% of variables, reported by CatWalk, were dependent on speed with an average R(2) value of 0.624, (2) most variables were related to speed in a nonlinear manner, (3) current methods of controlling for speed are insufficient, and (4) the linear mixed model is an appropriate and effective statistical method for locomotion analyses that is inclusive of speed-dependent relationships. Given the pervasive dependency of locomotion variables on speed, we maintain that valid conclusions from locomotion analyses cannot be made unless they are analyzed and reported within the context of speed.

Keywords: CatWalk; gait; locomotion; mice; mouse; rodent; speed; velocity.

Fig. 1

Variations in speed distributions. A: Total speed distribution across 12 time points n=1,137, mean = 78.73 cm/sec, and SD = 18.85 cm/sec; this distribution approximated normal (K-S P = 0.000, skewness = −0.340). B: Speed distribution for PND 105, n = 111, mean - 78.38 cm/sec, SD = 16.33 cm/sec; this distribution approximated normal (K-S P = 0.195). C: Speed distribution for PND 103, n = 103, mean = 75.44 cm/sec, SD = 16.62 cm/sec; this distribution approximated normal (K-S P = 0.006, skewness = −0.159). D: Speed distribution for PND 111, n = 86, mean = 74.06 cm/sec, SD = 17.75 cm/sec; this distribution did not approximate normal (K-S P = 0.008, skewness = −0.553).

Fig. 2

Average speed ± SEM per day, overall and per animal. A: Average speed for the group of 16 WT animals across 12 time points. Each day is expressed as mean ± SEM. (a) = significantly different from PND 89 (P≤ 0.044). (b) = significantly different from PND 91 (P = 0.005). (c) = significantly different from PND 95 (P = 0.023). B: Average speed ± SEM of each of the 16 subjects across 12 time points. Each colored line represents a different animal.

Fig. 3

Scatterplots of speed-averaged data depicting the relationship between discrete speed (cm/sec) and Paw Statistics variables. Data are color coded: Blue = left front (LF) paw, Green = RF paw, Orange = left hind (LH) paw, and Pink = right rind (RH) paw. A: Step cycle versus speed. LF, RF, LH, RH = inverse, ↓ WIS. B: Stand versus speed. LF, LH, RH = power, ↓ WIS; RF = inverse, ↓ WIS. C: Swing versus speed. LF = inverse, ↓ WIS; RF, LH, RH = power, ↓ WIS. D: Duty cycle versus speed. LF, RH = logarithmic, ↓ WIS; RF, LH = power, ↓ WIS. E: Stand index versus speed. LF, RF, LH, RH = logarithmic, ↓ WIS. F: Single stance versus speed. LF, RF = inverse, ↓ WIS; LH, RH = power, ↓ WIS. G: Swing speed versus speed. LF, RF, RH = power, ↑ WIS; LH = linear, ↑ WIS. H: Stride length versus speed. LF, RF, LH, RH = linear, ↑ WIS.

Fig. 4

Scatterplots of speed-averaged data depicting the relationship between discrete speed (cm/sec) and Paw Statistics variables. Data is color coded: Blue = left front (LF) paw, Green = RF paw, Orange = left hind (LH) paw, and Pink = right rind (RH) paw. A: Max contact at (%) versus speed. LF, LH, RH = linear, ↓ WIS; RF = compound, ↓ WIS. B: Max intensity at (%) versus speed. LF = S, ↓ -WIS; RF = inverse, ↓ - WIS; LH, RH = linear, ↓ WIS. C: Max contact max intensity versus speed. LF, RF = logarithmic, ↑ WIS; LH = inverse ↓ WIS; RH = logarithmic, ↓ WIS. D: Max contact mean intensity versus speed. LF = linear, ↑ WIS; RF = compound, ↑ WIS; LH = inverse, ↓ WIS; RH = compound, ↓ WIS. E: Maximum intensity versus speed. LF, RF = linear, ↑ WIS; LH = inverse, ↓ WIS; RH = linear, ↓ WIS. F: Mean intensity versus speed. LF, RF = compound, ↑ WIS; LH = inverse, ↓ WIS; RH = compound, ↓ WIS. G: Minimum intensity versus speed. LF, LH = S, ↑ WIS; RF = inverse, ↓ WIS; LH = logarithmic, ↑ WIS.

Fig. 5

Scatterplots of speed-averaged data depicting relationships between discrete speed (cm/sec) and Other Statistics. A: Run duration versus speed. Power, ↓ WIS. B: Cadence versus speed. Logarithmic, ↑ WIS. C: Base of support (BOS) versus speed. Gray square represents front paws (F), open circle represents hind paws (HP). F = quadratic, ↓↑ WIS. HP = linear, ↑ WIS. D: Regularity index versus speed. Linear, ↓ WIS.

Fig. 6

Diagrammatic depiction of the print positions parameter and scatterplot of speed-averaged data depicting relationships between discrete speed (cm/sec) and print positions. A: Print positions describes the distance between the hind paw (H) and the previously placed front paw (F) ipsilaterally. (+) indicates H was placed behind F, (0) indicates H was placed at F, and (−) indicates H was placed in front of F. B: Print positions versus speed. Reference line at 0 cm. Gray square represents left paws (L), open circle represents right paws (R). R, L = quadratic, ↓ WIS.

Fig. 7

Graphical depiction of two-paw combination categories and scatterplot of speed-averaged data depicting the relationship between discrete speed (cm/sec) and support variables. A: Graphical depiction of the categories used to describe pairs of paws. Solid lines = diagonal, small dashed lines = girdle, and medium dashed lines = lateral. B: Support (%) versus speed, which relays the percentage of a run that a particular number and/or combination of paws were in contact with the glass. Zero = logarithmic, ↑ WIS. Single = logarithmic, ↑ WIS. Three = inverse, ↓ WIS. Diagonal = quadratic, ↑↓ WIS. Girdle = logarithmic, ↓- WIS. Lateral = inverse ↓ WIS.

Fig. 8

Graphical representation of the six normal step sequence patterns (NSSPs) and scatterplot of speed-averaged data depicting relationships between discrete speed (cm/sec) and NSSPs. A: The boxed arrow indicates the first paw placed within the sequence. From top left to bottom right: Ca, Cb, Aa, Ab, Ra, and Rb. B: NSSPs (%) versus speed, which relays the percentage of a run that a particular sequential placement of paws was used. All data points are color coded according to the legend. Aa = quadratic, ↑↓ WIS. Ab = inverse, ↓-. Ca = linear, ↑ WIS. Cb = no dependence (ND), - WIS.

Fig. 9

Scatterplots of speed-averaged data depicting the relationships between Phase Dispersions (PD), Couplings (C), and discrete speed (cm/sec). All points are color coded according to respective legends. A: Normal mean versus CStat Mean for diagonal pairs in Phase Dispersions, reference line at 0%. B: Normal mean versus CStat Mean for lateral pairs in Phase Dispersions, reference line at 50%. C: Reciprocal representations for diagonal pairs in Couplings, reference line at 3.1%; Blue and pink are reciprocals, green and orange are reciprocals. D: Reciprocal representations for lateral pairs in Couplings, reference line at 50%. E: Comparison of diagonal pairs between Phase Dispersions and Couplings versus speed, reference line at 0%. F: Comparison of lateral pairs between Phase Dispersions and Couplings versus speed, reference line at 50%.

Fig. 10

Visual guide to linearizing relationships with speed. A: Scatterplot of curve estimation from raw data of RF swing versus speed; the power model was selected (R² = 0.721, P = 0.000). B: Scatterplot of curve estimation from raw data transformed according to the power model [ln(y) and ln(x)]; the linear model was selected (R² = 0.721, P= 0.000). C: Histogram of residuals from the power model of raw data. D: Histogram of residuals from linear model of the transformed data. E: Scatterplot of residuals versus predicted for the power model of raw data. F: Scatterplot of residuals versus predicted for the linear model of the transformed data.

Fig. 11

Comparison between fast and slow groups, with speed excluded as a covariate in the linear mixed model (LMM). A: Mean speed ± SEM per day between groups. Asterisks denote significance at P≤ 0.035. B: Mean RF swing speed ± SEM per day between groups. Asterisks denote significance at P ≤ 0.047.

Fig. 12

Comparison between fast and slow groups, with speed included as a covariate in the linear mixed model (LMM). A: Mean slope of RF swing speed versus speed per day between groups. No difference existed between groups overall or on any day. B: Scatter-plot depicting group averages of RF swing speed versus speed for PND 99. No significant differences existed between groups regarding slope or intercept. C: Scatterplot depicting the total raw data of RF swing speed versus speed between groups. No significant differences existed between groups regarding slope or intercept.