2.4.1. Children with CP.

The main inclusion criteria for the children with CP are as follows: age between 18 months and 5 years and 6 months; ability to walk without aids for 7 meters (GMFCS level I or II) [63]; ankle dorsiflexion range of motion of at least 5° with knee extended (measured with goniometer, average of three trials); and presence of soleus spasticity defined as Modified Tardieu Scale R2-R1 ≥ 10° with knee flexed, assessed by trained physiotherapist with established inter-rater reliability (κ > 0.75) [64].

The main exclusion criteria are as follows: botulinum toxin injections in the lower limbs in the 6 months preceding the study; lower limb surgery in the 12 months preceding the study; any changes in physical or orthopedic therapy within the previous 2 months; minimum hip flexion greater than 20°; pain in the lower limbs when standing or walking; Inability to follow simple 1-step commands or severe behavioral disturbances preventing assessment completion, as judged by assessing clinician.

2.4.2. Children with TD.

The children with TD will be age-matched with the children with TD. They must be able to walk independently at 18 months of age, to have sufficient cognitive level and cooperation to perform the evaluations, with no history of neurological or orthopedic disease, no history of lower limb surgery, and no pain.

2.5.1. Gait analysis.

Gait analysis is threefold: analysis of trunk accelerations using IMUs, analysis of temporospatial gait parameters and centers of pressure using a walkway equipped with pressure sensors, and analysis of the Edinburgh visual gait score using video recording.

2.5.1.1 Trunk dynamics: Trunk accelerations are measured by Inertial Measurement Units (mTest3 system, mHealth Technologies Srl, Bologna, Italy), validated for trunk postural assessment during gait in adults and children [39]. Each IMU contains a tri-axial accelerometer (±16g range, 100 Hz sampling frequency, adequate for capturing peak accelerations during weight acceptance which occur at 5–8 Hz [26]. Units are attached to skin using hypoallergenic double-sided adhesive tape (3M™ Tegaderm™, 3M Health Care, St. Paul, MN, USA) at sternum, L5 level, and bilateral feet. Data are processed using a custom-made script on Matlab R2022b (MathWorks, Inc., Natick, MA, USA). The raw data are filtered using a 10 Hz low-pass filter and averaged over all gait cycles.

Peak anterior deceleration of the sternum during WA is the primary outcome of the study. High value of this variable is suggested to reflect the higher need to break the upper trunk forward progression during WA in order to compensate for insufficient postural control of the trunk [54]. Peak downward deceleration of L5 during WA is a secondary outcome: high value is suggested to reflect the higher need to break the downward movement of body center of mass during WA in order to compensate for insufficient balance and trunk control [21,54].

2.5.1.2 Temporospatial parameters and trajectory of CoP: Gait pattern related to balance disorder and to toe walking are obtained by a Zeno Walkway Gait Analysis System ®) equipped with pressure sensors positioned on its surface (427 cm x 122 cm, sampling frequency of 120 Hz). These sensors detect plantar pressures during walking, allowing to assess foot prints, trajectory of CoP and temporospatial parameters, processed by PKMAS software (ProtoKinetics Movement Analysis Software). The children are asked to walk barefoot back and forth along the 7 meters-long track several times, at spontaneous speed. Series of successive gait cycles during which the child is not distracted and walks in line with the treadmill are selected in order to obtain a total of more than 17 gait cycles for each side. Zeno Walkway (ProtoKinetics LLC, Havertown, PA, USA; 1.22 × 4.27 m active area, 18,432 sensors, 120 Hz sampling), validated for temporo-spatial analysis in children aged 2–18 years with excellent reliability (ICC > 0.90) [65].

The enhanced gait variability index (eGVI) is hypothesized to be increased. It is a composite score based on 9 temporospatial parameters that quantifies the distance between the amount of variability observed in an asymptomatic reference group and the amount of variability observed in the patient [66,67]. Indeed, this index that assesses instability during gait and the risk of falling is usually high in children with CP, as they are impacted by balance disorders [68,69].

Step width is hypothesized to increase. Indeed, this variable reflects a strategy for reducing the risk of falls in unstable gait and is usually high in children with CP [70].

Center of pressure location normalized to foot length during WA, on the affected side(s), is hypothesized to be excessively anterior (>0.70 of foot length from heel) in children with CP compared to children with TD (<0.60). This will be calculated as the mean anterior-posterior CoP position during the first 20% of stance phase, expressed as a proportion of total foot length. CoP calculation employs center-of-pressure algorithm in PKMAS software (v3.8.8), with foot segmentation based on pressure threshold of 5 N/cm² to distinguish loading phases.

2.5.1.3 Visual evaluation of the gait kinematic pattern: The Edinburgh Visual Gait Score, a kinematic gait pattern score based on two cameras recording front and side view, is hypothesized to be decreased as the gait pattern in CP children, including toe walking, is different from children with TD [58].

2.5.2. Evaluation of gross motor function by clinical scores.

The Item Set of the Gross Motor Function Measurement 66 (GMFM-66-IS) is hypothesized to be reduced with CP. Compared to the standardized 66-items used to assess gross motor function [71] the item set version (GMFM-66-IS) which has the same validity is faster to realize (around 20–30 minutes versus 60–80 minutes) since it uses 15–39 items selected according to the achievement of 3 main items [72]. Thus, the GMFM-66-IS by saving time is of great interest for the young children of this study. An experienced assessor, who has initially completed the standardized GMFM-66-IS training (CanChild online modules), is responsible for conducting this assessment as part of the study.

The Early Clinical Assessment of Balance (ECAB) is hypothesized to be reduced in children with CP. This 13-item clinical scale assesses postural stability (balance ability) in children with cerebral palsy, with two subscales: one dedicated to head and trunk postural control, the other to sitting and standing postural control. This scale is validated with high reliability for children, for the different GMFCS levels [60,73,74]. The optimal score is 100.

2.5.3. Evaluation of upper limb function, activity and participation.

Evaluation of upper limb function and child’s activity and participation is made by the Reach Out Questionnaire. This questionnaire filled by the parents ensure a holistic overview of functioning, when a hand and upper limb are affected, including the assessment of activity limitations, participation in activities, attitudes in different environments and satisfaction, according to the domains of the ICF [61]. Rehabilitation by activities involving the trunk is hypothesized to improve hand and upper limb function in case of disorders affecting the upper limb function and the child’s participation, since the trunk appears central in motor activities.

Therefore, by combining neuromuscular assessment, evaluation of overall body and trunk postural control, overall motor function, walking, as well as reaching, grasping behavior, and participation, our study evaluates the effect of RAIT on all ICF domains.

2.6.1. Rehabilitation by activities involving the trunk.

If the physiotherapist providing care for the child with CP agrees to participate in the study, he/she will be initially briefed on the principles of RAIT and given detailed instructions on its content shortly before the start of the RAIT treatment.

Rehabilitation by activities involving the trunk (RAIT) exploits the automatic postural control of body balance, an essential aspect of motor function that enables individuals to maintain balance during static postures or motor activities. It is also noteworthy that our rehabilitation protocol extends over a duration of up to one year, which appears to be an important factor for maintaining improvements in motor function. In our previous study in children with CP aged from 5 to 12 years, the RAIT was applied for 3 months with significant improvement of gait dynamics and pattern [54].

The RAIT program focuses on self-directed exercises actively performed by the child, so that balance is controlled by the child and not by another person, in order to develop and engram balance strategies. These exercises aim to enhance body postural control and balance, including the trunk and affected muscles, rather than focusing rehabilitation on the affected muscles. In fact, RAIT does not only involve the trunk, but the entire body in selected intermediate postures involving the trunk that the child performs on his/her own (Fig 3). These postural activities are less challenging than standing or walking when considering balance control and help eliminate fear of falling. These activities allow automatic recruitment of deficient muscles through their contribution to balance control. For example, children with hemiplegic CP often have limited voluntary control of their affected upper limb: using the latter as support will automatically activate wrist and elbow extension and shoulder control without voluntary control of the affected muscles. Exercise progression follows standardized criteria: (1) child performs posture independently ×3 consecutive sessions, (2) maintains posture >30 seconds, (3) demonstrates correct form per checklist. Physiotherapists receive 2-hour training workshop with video examples and competency assessment before study initiation. Then, one of the first RAIT sessions in the physiotherapist’s office is conducted via videoconference in order to agree on its content.

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Fig 3. Examples of the proposed exercises involving the trunk.

A: “On all fours”, the upper limbs display increased activation of the shoulder muscles, with recruitment of the antigravity extensors, particularly in the elbows and wrists, as well as a tendency for finger extension to allow the hands to lay flat on the ground. These effects are observed in both unaffected and affected upper limbs in children with cerebral palsy, as both contribute to postural balance. B: The transition to “Cobra” posture will promote higher support on the hands with strengthening of the elbow and wrist extensors. Elbow extension is facilitated by cervical extension (symmetrical tonic cervical extension reflex): the child is asked to look up when moving into the “Cobra” position. The Cobra posture is also accompanied by a noticeable extension of the hips.

https://doi.org/10.1371/journal.pone.0334195.g003

Self-exercises are performed by the child, under the guidance of the physiotherapist, in separate small sessions, if possible, for a total of 20–30 minutes a day, 6 days a week, at home under the supervision of a parent and by the physiotherapist in one to two sessions per week. The use of a monitoring log, in which the physiotherapist notes down the exercises to be performed and the parents indicate those that have been completed, will allow for smoother and more regular monitoring of difficulties and progress in rehabilitation (Fig 4). Exercise compliance calculated as: (completed sessions/ prescribed sessions) × 100%. Target compliance ≥75% (≥18/24 weeks). Children <60% compliance will be analyzed separately as per-protocol sensitivity analysis.

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Fig 4. Part of a monitoring log in which a series of exercises are suggested.

Part of a monitoring log in which a series of exercises are suggested: the physical therapist selects and adjusts some of them according to the child’s abilities, and the parents indicate which ones have been completed by the child.

https://doi.org/10.1371/journal.pone.0334195.g004

2.6.2. Usual rehabilitation.

The UR corresponds to the type of rehabilitation already received by the child before the study. It variously combines muscle stretching, muscle strengthening (e.g., resistance training), muscle tone reduction (e.g., Bobath concept neuro – developmental treatment), and upper and lower limb motor skill training facilitated by the therapist. These therapies usually involve limited groups of muscles in elementary stretching or actions. In the UR-RAIT group, the physiotherapist is asked to give to the parents an adapted selection of the usual rehabilitation to be achieved at home for a total duration of 20–30 minutes per day, the days without physiotherapist session, for a total of 6 days a week. A monitoring log, as previously described for RAIT, will be used with the exercises prescribed by the physiotherapist.

2.7.1. Sample size.

Sample size was calculated for the primary outcome (peak anterior sternum deceleration during WA) using crossover design framework with Bonferroni adjustment for key secondary outcomes (n = 4 secondary: L5 deceleration, eGVI, step width, CoP location; adjusted α = 0.0125). Between-period correlation: Based on motor development literature in toddlers [75], we conservatively estimate ρ = 0.50 (lower than adult studies due to developmental variability). Variability estimate: Pilot data in 16 children with CP aged 1.5–5.5 years (unpublished) showed sternum deceleration SD = 1.10 m·s ⁻ ². We conservatively use SD = 1.20 m·s ⁻ ². These results are consistent with those of a study reporting maximum vertical acceleration of the pelvis at initial contact in children during the first 5 years of walking, where the standard deviation was < 0.8 m·s ⁻ ² at all times except around 6 months of walking, when it reached 1.5 m·s ⁻ ² [21].

Effect size: Based on prior RAIT study showing 1.20 m·s ⁻ ² reduction in older children, we expect minimum clinically important difference = 1.00 m·s ⁻ ² (30% reduction from baseline mean ≈ 3.30 m·s ⁻ ²) in younger population. Calculation: Two-sided paired t-test (α = 0.0125, power = 0.80, ρ = 0.50, MCID = 1.00, SD = 1.20) requires n = 17 per group. Accounting for 30% attrition (higher than typical due to: young age, 12-month duration, family relocation, illness), we plan n = 25 per group (50 total CP children).

Sample size calculated using G*Power 3.1.9.7, verified with PASS 2024 crossover module. For CP vs TD baseline comparison (independent t-test, d = 1.80, α = 0.05, power = 0.80): n = 12 per group required; we recruit n = 17 TD children for age-stratified matching (1:3 ratio).

2.7.2. Data processing and quality control.

For gait analysis, raw IMU data (.csv) will be extracted from the mTest3 software and processed via a custom MATLAB script (version R2022b, available at [repository link upon publication]). Data relating to the walkway will be exported from PKMAS in.xlsx format and imported into R. The gait cycle will be identified based on the IMU signal from the foot (maximum vertical acceleration > 2 m·s ⁻ ²) = foot contact). The quality criteria for walking are as follows: ≥ 17 cycles per limb, continuous walking (no stopping/starting), and child looking forward (head rotation ± 30°).

2.8.1. Primary analysis (intention-to-treat).

For primary outcome (sternum deceleration), we fit linear mixed-effects model: Y_ijk = μ + α_i + β_j + γ_k + δ_(jk) + π_t + (π_t × β_j) + τ_(period) + λ_(carryover) + ε_ijk. where Y_ijk is the outcome for child i, in sequence j, at assessment k; α_i is a random child effect ~ N(0, σ²_child), accounting for between-subject variability; β_j is the fixed sequence effect (UR–RAIT vs. RAIT–RAIT); γ_k is the fixed treatment effect (UR vs. RAIT), representing the primary parameter of interest; δ_jk is the sequence-by-treatment interaction; π_t is the fixed time effect across the four assessment points (M0, M3, M6, M12); π_t × β_j is the time-by-sequence interaction, capturing potential dose–response patterns; τ_period is the fixed period effect (first 3-month interval vs. later intervals); λ_carryover is the carryover effect, testing the validity of the crossover assumption; and ε_ijk is the residual error ~ N(0, σ²_error).

2.8.2. Model assumptions.

Residual normality will be assessed using Q–Q plots and Shapiro–Wilk tests on residuals; homoscedasticity will be evaluated through residuals-versus-fitted plots and Levene’s test by group; and linearity will be examined using partial residual plots for continuous predictors. If assumptions are violated, log or Box–Cox transformations will be applied, or robust mixed models will be fitted using the rlmer package.

2.8.3. Missing data.

Missing-at-random assumption will be tested using multiple imputation by chained equations (MICE package, m = 50 imputations, following Morris et al. 2014 guidelines for adequate precision). The imputation model will include baseline outcome, treatment allocation, age, sex, GMFCS level, CP subtype, ECAB score, and the number of attended sessions. A sensitivity analysis using complete-case analysis will be conducted to assess the plausibility of the missing-at-random assumption.

2.8.4. Primary hypothesis test.

The primary comparison will test H₀: γ_RAIT − γ_UR = 0 versus H₁: γ_RAIT − γ_UR ≠ 0, using a Wald test on the γ contrast with a Bonferroni-adjusted significance level of α = 0.0125 (two-tailed).

2.8.5 Carryover assessment.

The presence of carryover effects will be evaluated both graphically, using spaghetti plots by sequence showing individual trajectories, and statistically, by testing λ_carryover ≠ 0 using a likelihood ratio test. If p_carryover < 0.10, the analysis will revert to a Period 1 parallel-group analysis as the primary analysis, and the full crossover results will be reported as a sensitivity analysis.

2.8.6. Secondary analyses.

Dose–response. The time-by-sequence interaction will be tested to determine whether the RAIT–RAIT group shows greater M0-to-M12 improvement than the UR–RAIT group, using linear contrasts with sequential Bonferroni correction.

Reproducibility. To assess the reproducibility of the RAIT effect, the first RAIT exposure in both groups will be compared (M0 → M3 in the RAIT–RAIT group vs. M3 → M6 in the UR–RAIT group) using a linear mixed model with a treatment-by-cohort interaction.

Sustained effects. Whether M12 outcomes differ from M6 within the RAIT–RAIT group will be tested using paired contrasts.

Secondary outcomes. The same linear mixed-effects model approach will be applied to L5 deceleration, eGVI, step width, centre of pressure location, GMFM-66-IS, ECAB, and Reach-Out scores, with Bonferroni adjustment (α = 0.0125 for the four gait outcomes).

2.8.7. CP vs. TD comparison (M0).

Between-group comparisons at M0 will use independent t-tests (or Welch’s t-test if Levene’s test indicates unequal variances at p < 0.05). If normality is violated (Shapiro–Wilk p < 0.05), Mann–Whitney U tests will be used. Results will be reported as mean differences with 95% confidence intervals, Cohen’s d (or rank-biserial correlation for U-tests), and exact p-values.

2.8.8. Correlation analyses (exploratory).

Within the CP group at M0, relationships between trunk dynamics, gait instability measures, and clinical scores will be examined using Pearson’s correlation coefficient (or Spearman’s rank correlation if normality assumptions are not met). Results will be reported as r with 95% confidence intervals and p-values, with Bonferroni correction for family-wise error (n = 10 correlations, adjusted α = 0.005).

2.8.9. Software and reporting.

All analyses will be conducted using R version 4.3.0 or later with the following packages: lme4 (linear mixed models), lmerTest (p-values for mixed models), mice (multiple imputation), emmeans (post-hoc contrasts), and effectsize (Cohen’s d with confidence intervals). All estimates will be reported with 95% confidence intervals and exact p-values (e.g., p = 0.03, not p < 0.05). Effect sizes (Cohen’s d or partial η²) will be reported with 95% confidence intervals for all primary and secondary outcomes. Tables will include point estimate, standard error, 95% confidence interval, t/F-statistic, degrees of freedom, and p-value.

3.1.1. Participation.

In longitudinal studies, involving young children can be particularly challenging, as fluctuations in the child’s level of cooperation, alertness or health may prevent regular involvement or completion of the rehabilitation program 6 days per week. Additionally, participation rates may be reduced by time constraints due to parents’ or school schedules.

3.1.2. Developmental variability.

At young age (18 months to 5 and a half years of age), children’s development is highly variable, either for motor, cognitive, emotional, or social development. This natural variability linked to the young age of the children, combined with the variability in the severity of CP and the performance of RAIT, makes it difficult to estimate the number of subjects required for statistical purposes.

3.1.3. Ethical considerations.

When conducting research in children, informed consent must be obtained from the parents or legal guardians, and if possible, from the child. In practice, due to the young age of children, communication with the child is mainly dedicated to the good realization of the rehabilitation content.