PubMed, Scopus, SPORTDiscus, and IEEE Xplore electronic databases were searched for the period from 2000 to November 2023, using the specified terms combined with the Boolean operators outlined in Table 1. Additionally, relevant studies were identified by reviewing bibliographies in academic articles. The titles, abstracts, and full texts of the retrieved documents were meticulously evaluated to determine their relevance. Only papers published in English that specifically measured TA/tibial loading and GRF in the context of running were considered. Exclusion criteria included papers that exclusively assessed GRF signals, those with sensor placements other than the tibial region, and studies involving participants using any form of aid or equipment during running.

In accordance with the Participants, Intervention, Comparisons, and Outcomes (PICO) criteria, information was extracted from thirteen included studies. This extraction focused on participant details, correlation variables, and data-driven approaches. The participant information encompassed the number of participants, their gender, age, height, weight, and running speed during data collection. The Pearson correlation coefficient was used for the correlation evaluation in included studies. The correlation variable included data calculated by the acceleration sensor and/or the force plate, as well as running conditions (speeds and surfaces) for data collection. Machine learning including deep learning were extracted from the included studies. The calculation of the Vertical Average Loading Rate (VALR) is based on the gradient of the initial impact transient, specifically over its linear section, typically spanning from 20% to 80% of the vertical impact peak. In contrast, the Vertical Instantaneous Loading Rate (VILR) is determined by identifying the maximum slope between any two consecutive data points within the same region of interest (Davis et al., 2015).

Two independent reviewers (Z.G. and L.X.) conducted the selection process. Disagreements between these authors regarding article inclusion were resolved through further discussion. In cases where consensus was unattainable, a third reviewer (J.F.) was consulted for resolution. Studies were excluded if they met the following criteria: 1) Participants exhibiting physical injuries during testing; 2) TA measured from the proximal tibia or medial aspect of the distal tibia; 3) Absence of correlation or data-driven approaches; 4) Studies that scored below 75% in the quality assessment. The collation of articles and the removal of duplicates were carried out using EndNote X9 (Thomson Reuters, Carlsbad, California, United States).

The assessment protocol for appraising the quality of the included articles was based on a modified version of established scales in the fields of sports science, healthcare, and rehabilitation. This approach, commonly used in analyzing studies in an exercise-based training context, adopted the study quality scoring system developed by Black et al. (2016). Two assessors, Z.G. and L.X., independently employed this scoring system to evaluate the quality of the graded articles. The results were then reviewed and confirmed by a third reviewer (J.F.). The evaluation included nine distinct criteria, each contributing to a cumulative score (range: 0–18). The criteria were as follows: (1) inclusion criteria stated (score: 0–2); (2) appropriate assignment of subjects (random/equal baseline); (3) description of intervention; (4) definition of dependent variables; (5) practicality of assessments; (6) practicality of training duration (acute vs. long term); (7) appropriateness of statistics (variability, repeated measures); (8) detailed results (mean, standard deviation, percent change, effect size); (9) insightful conclusions (clear, concise, future directions), with each criterion graded from 0 (no) to 1 (maybe) or 2 (yes). To maintain impartiality in the quality assessment of the included studies, the scores were converted to a percentage scale, ranging from 0% to 100%.

A total of 503 articles were identified via electronic databases retrieve (PubMed = 81, SPORTDiscus = 149, Scopus = 120, IEEE Xplore = 2, ScienceDirect = 151). Of these, 182 duplicate records were removed, and a further 294 articles were excluded based on the title and the abstract screening. Twenty-seven full-text articles were then evaluated, with seven being excluded. Reasons for exclusion included four articles not applying a correlation or data-driven approach, two focusing on jumping and walking studies, and one not addressing vertical direction. Five articles were not included in the quantitative synthesis due to data ineligibility for meta-analysis. The details of the search strategy are presented in Figure 2.

The quality appraisal ratings for each article are presented in Table 2. Overall, the risk of bias was moderate. Methodological quality scores ranged from 14 to 17 out of a possible 18. The average quality assessment rate for the selected articles in this systematic review was 86.75%. The highest average quality assessment among the quality scores was 1.92 (Q2, Q4, and Q9), and the lowest was 1.38 (Q7). Additionally, seven articles were included in the meta-analysis (Laughton et al., 2003; Greenhalgh et al., 2012; Zhang et al., 2016; Cheung et al., 2019; Van den Berghe et al., 2019; Tenforde et al., 2020; Bradach et al., 2023).

As indicated in Table 3, seven studies included in this review assessed the relationship between TA and GRF metrics (Laughton et al., 2003; Greenhalgh et al., 2012; Zhang et al., 2016; Cheung et al., 2019; Van den Berghe et al., 2019; Tenforde et al., 2020; Bradach et al., 2023). Four studies (Zhang et al., 2016; Cheung et al., 2019; Tenforde et al., 2020; Bradach et al., 2023) were conducted on a treadmill, while three studies (Laughton et al., 2003; Greenhalgh et al., 2012; Van den Berghe et al., 2019) involved overground running. Two studies employed tri-axial accelerometers (Greenhalgh et al., 2012; Van den Berghe et al., 2019), one used a bi-axial accelerometer (Cheung et al., 2019), and one used a uniaxial accelerometer (Laughton et al., 2003), while two other studies utilized IMU sensors (Tenforde et al., 2020; Bradach et al., 2023). The frequency of IMU sensors was 1000 Hz in four studies (Greenhalgh et al., 2012; Cheung et al., 2019; Tenforde et al., 2020; Bradach et al., 2023), followed by 960 Hz in one (Laughton et al., 2003), 400 Hz in one (Zhang et al., 2016), and 100 Hz in another (Van den Berghe et al., 2019). Furthermore, the variable from IMU sensors was peak TA (in 7 studies), and the most common GRF variables were VILR (in 6 studies) (Greenhalgh et al., 2012; Zhang et al., 2016; Cheung et al., 2019; Van den Berghe et al., 2019; Tenforde et al., 2020; Bradach et al., 2023) and VALR (in 4 studies) (Laughton et al., 2003; Zhang et al., 2016; Cheung et al., 2019; Tenforde et al., 2020). Extremely strong (3 occurrences), strong (3 occurrences), medium (4 occurrences), weak (1 occurrence), and extremely weak (1 occurrence) correlations between peak TA and GRF metrics were reported in the seven collected literatures.

As shown in Table 4, two studies included in this review assessed the relationship between TA/GRF and tibial bone load (Matijevich et al., 2019; Zandbergen et al., 2023). Both studies were conducted on treadmills with participants wearing self-selected running shoes. Only one study reported the foot strike pattern as RFS (Zandbergen et al., 2023). In this study (Zandbergen et al., 2023), an IMU sensor, specifically the Xsens model with a sampling frequency of 240 Hz, was used to measure peak TA. Moreover, both studies utilized the Pearson correlation coefficient for correlation analysis. These studies explored correlations between GRF variables (weak correlations) and peak TA (extremely weak correlations) in relation to tibial load.

As presented in Table 5, three studies employed data-driven approaches to predict GRF metrics using acceleration data (Komaris et al., 2019; Derie et al., 2020; Tan et al., 2020), and one study used this approach to predict tibial loading force using IMU signals (Komaris et al., 2019). Additionally, three studies were conducted on treadmills (Komaris et al., 2019; Matijevich et al., 2020; Tan et al., 2020), and one was conducted overground (Derie et al., 2020). One study utilized IMU sensors (Tan et al., 2020), one used tri-axial accelerometers (Komaris et al., 2019), and two used virtual accelerometers (Derie et al., 2020; Matijevich et al., 2020), where the acceleration data were derived from kinematic measurements. Various data-driven methods were applied: gradient boosted regression trees (XGB) (Derie et al., 2020), artificial neural networks (ANN) (Komaris et al., 2019), convolutional neural networks (CNN) (Tan et al., 2020), and LASSO regression (Matijevich et al., 2020). The studies consistently showed high predictive accuracy: mean absolute percentage error (MAPE) was below 10% in two studies (Derie et al., 2020; Matijevich et al., 2020), normalized root mean square error (NRMSE) was under 10% in one study (Tan et al., 2020), and RMSE remained less than 0.2 BW across all (Komaris et al., 2019).

The body segment acceleration is shaped by GRF and dampening from bodily shock absorbers. Capturing peak positive acceleration at distal locations allows measurement before attenuation as the shock wave propagates proximally. Notably, vertical acceleration correlates directly with vertical GRF: higher vertical GRF load rate leads to increased vertical axial acceleration prior to attenuation (Lafortune et al., 1995). This findings from the data synthesis analysis showed only moderate correlation of coefficient between peak TA and GRF loading rate, which does not support with the general hypothesis under many studies that peak TA is an indicator of impact loading rate (Bigelow et al., 2013; Lucas-Cuevas et al., 2017; Raper et al., 2018; Cheung et al., 2019; Van den Berghe et al., 2019; Johnson et al., 2021; Ryu et al., 2021; Bradach et al., 2023; Johnson et al., 2023; van Middelaar et al., 2023; Zandbergen et al., 2023). This aligns with findings from the meta-analysis in this study, particularly for overground running.

The prevailing hypothesis in gait retraining research posits a robust positive correlation between the vertical GRF load rate and TA (Cheung et al., 2019; Tirosh et al., 2019; Sheerin et al., 2020; Van den Berghe et al., 2020; Derie et al., 2022). This assumption underpins studies suggesting that mitigating peak TA could be instrumental in reducing overuse injury risks by concurrently diminishing the load rate (Milner et al., 2006; Huang et al., 2019; Tavares et al., 2020; Warden et al., 2021). However, reliance on this correlation as a foundation for gait retraining strategies may result in oversimplified approaches that overlook the complexities of individual gait patterns and the multifaceted nature of injury risk factors (Pohl et al., 2008; van Gelder et al., 2023).

TA is often used as a proxy for impact forces during running because it's relatively easy to measure, especially with the advent of wearable technology (Ryu et al., 2021; Xiang et al., 2022c; Xiang et al., 2022d; Bradach et al., 2023; van Middelaar et al., 2023; Xiang et al., 2023). However, the relationship between external forces (such as GRF and TA) and internal stresses (such as bone loading) is not always straightforward (Matijevich et al., 2020). Several factors can influence this relationship. Individual biomechanics, such as gait patterns, muscle strength, and joint stability, can significantly alter how external forces are translated into internal stresses (Baggaley et al., 2022). Moreover, the body’s adaptive responses to running, such as increased bone density or changes in soft tissue properties, can also affect this relationship. These adaptations can provide a buffering effect, reducing the impact of external forces on internal structures. A more holistic approach that considers both external forces and individual biomechanical factors could be more effective in understanding and preventing running-related injuries.

Concerning the relationship between GRF and internal bone loads, it is pertinent to note that recent studies, including those by Zandbergen et al. (2023); Matijevich et al. (2019), have provided compelling evidence challenging the traditionally assumed strong correlation. Zandbergen et al. (2023) found no significant correlation between acceleration and internal bone loads in the tibia, nor between GRF features and tibial bone load during running. Consistent with these findings, our meta-analysis demonstrates that peak TA does not directly correlate with the external loading rate. Further, Matijevich et al. (2019) substantiated that GRF metrics are not consistently correlated with tibial bone load across varied running speeds and slopes, thereby questioning the reliability of GRF as a predictor of internal bone stress in different running conditions. Considering that tibial compression forces encompass both external and internal forces, internal biomechanical adaptations may impact internal forces, even in the presence of external overload, thus influencing the prevention of related injuries (Baggaley et al., 2022). This is supported by recent studies (Milner et al., 2006; Van der Worp et al., 2016; Milner et al., 2023). These insights necessitate a reconsideration of existing biomechanical models and wearable technology applications in running injury prevention. It also highlights that the strategy of reducing peak TA or GRF to mitigate tibial stress fracture risk may be misleading (Van der Worp et al., 2016; Zandbergen et al., 2023).

In the realm of running biomechanics, the interplay between neuromotor control and muscle co-contraction presents a critical avenue for understanding the complex dynamics of tibial acceleration, GRF, and tibial bone loading. The coordinated muscle actions, steered by sophisticated neuromotor control, significantly dictate the force distribution and magnitudes transmitted through the musculoskeletal system during running (Kellis et al., 2011; Di Nardo et al., 2015). Insights from Martelli et al. (2011) shed light on how sub-optimal neuromotor strategies can amplify joint loads, potentially leading to increased tibial bone stress in runners. Furthermore, while muscle co-contraction is crucial for joint stabilization, it's important to note that excessive co-contraction might paradoxically decrease stability by increasing the mechanical loads on the tibia, without proportionally enhancing stability (Benjuya et al., 2004; Cenciarini et al., 2009; Tassani et al., 2019). This highlights the importance of identifying an optimal level of muscle co-contraction that ensures joint stability without contributing to unnecessary stress, aligning with the perspectives offered by Martelli et al. (2011).

The advent of wearable sensor technology, capable of capturing these complex neuromotor and muscle dynamics in real-time, opens up new vistas. By amalgamating this data with traditional measures such as GRF and TA, wearable sensors can offer a more nuanced understanding of running biomechanics. This comprehensive approach not only challenges traditional paradigms but also heralds a new era of integrated strategies in monitoring, preventing, and rehabilitating running-related injuries, emphasizing the shift towards more holistic models in running biomechanics studies.

The ongoing progression in machine learning and wearable technology has facilitated the innovative use of data from inertial sensors, particularly in the prediction of GRF metrics (Higgins et al., 2003; Cheung et al., 2019; Hernandez et al., 2021). This advancement is notable in its potential to offer a more dependable methodology compared to approaches reliant on the correlation between peak TA and impact loading rate. The latter method’s assumption of a strong correlation may not always hold true (Laughton et al., 2003; Greenhalgh et al., 2012; Zhang et al., 2016), underscoring the significance of this novel application of inertial sensor data in biomechanics studies.

Nevertheless, caution is warranted when asserting that reducing the impact loading rate could effectively mitigate musculoskeletal injuries in running, such as tibial stress fractures (Milner et al., 2006; Milner et al., 2007; Matijevich et al., 2019; Milner et al., 2023). The data-driven approach has also yielded favorable outcomes in projecting tibial bone force using wearable sensor data (Matijevich et al., 2020; Elstub et al., 2022). This approach incorporates the muscular forces acting on the tibia, potentially offering a more comprehensive understanding of musculoskeletal injuries (Matijevich et al., 2019). By integrating this data with external impact loading rates, a more holistic view of the biomechanical factors contributing to injury risk can be achieved, enhancing the precision and effectiveness of injury prediction and prevention strategies. Although data-driven approaches using wearable sensors show promise for predicting external loading (Derie et al., 2020; Tan et al., 2020) and internal muscular force (Matijevich et al., 2019; Matijevich et al., 2020), their opaque “black-box” nature presents a challenge in terms of data interpretability or explainable artificial intelligence (XAI) (Halilaj et al., 2018; Uhlrich et al., 2023). This area warrants further investigation to understand how wearable sensor signals correlate with biomechanical forces (Kaji et al., 2019; Schlegel et al., 2019; Jeyakumar et al., 2020; Gandin et al., 2021; Xiang et al., 2024). Therefore, personalized biomechanical adaptation strategies, tailored for precise injury prevention and rehabilitation monitoring, can be more effectively applied once a deeper understanding of these correlations is achieved.

➢ The utility of peak TA as an indicator of GRF, particularly VALR and VILR during running, is subject to skepticism in the context of current literature, especially with respect to overground running.