# External Validation of Accelerometry-Based Mechanical Loading Prediction Equations
## 1 Introduction  
Physical activity and exercise are among the main factors that induce mechanical loading on bones, which is essential for maintaining and enhancing bone health [1, 2]. Engaging in regular weight-bearing activities, such as vigorous walking, running, and jumping [2, 3], stimulates bone formation, increases bone mass, and improves bone geometry and microarchitecture [4, 5], thereby reducing the risk of osteoporosis and bone fractures [1, 6]. These beneficial adaptations occur due mostly to the mechanical forces exerted on bone tissue during physical activity, which are detected by osteocytes and osteoblasts [7] that trigger adaptive signaling responses [8], stimulating bone remodeling and, ultimately, contributing to strengthening bone structure. Accurately measuring these forces is essential for developing effective and safe exercise interventions to enhance bone health and prevent bone loss-related disorders such as osteopenia and osteoporosis [1, 2, 3, 9], but has been a major challenge to address [10].  
Traditionally, mechanical loading has been measured using laboratory-based methods such as force plates, which are considered the gold standard [11]. While these methods provide precise and accurate measurements of ground reaction forces, they are limited by their high cost, the need for specialized equipment and expertise, and their restriction to controlled laboratory environments. More recently, questionnaires have been introducedto estimate mechanical loading [12], but they are subject to recall bias and cannot provide objective data on the intensity and frequency of physical activities [13; 14; 15]. Accelerometer-based prediction equations have emerged as a promising alternative to address these limitations [16; 17; 18; 19; 20; 21], offering the advantages of portability, lower cost, and the ability to collect data in free-living conditions [22; 23].  
Accelerometer-based equations have been developed to predict mechanical loading variables such as peak ground reaction forces (pGRF) and peak loading rate (pLR) from acceleration data [16; 17; 18; 19; 20; 21]. These equations have shown potential in various populations and activities, but they are often validated only within the specific contexts of their original studies. Importantly, factors such as sample characteristics, activity type, and testing conditions can exert a major influence on the performance of these models [24]. Individual variability in characteristics such as age [25], gender [25], and BMI [26] can significantly impact the accuracy of these predictions, as these factors influence biomechanical aspects (e.g., gait patterns, center of mass, balance) that can change how the load is borne by the body. Therefore, it is crucial to evaluate the external validation of accelerometer-based equations by testing them on different populations and in diverse activity contexts. Doing so not only uncovers their limitations but also assesses their reliability in real-world scenarios, guiding their refinement and ensuring their effective application in clinical settings to improve bone health interventions. This study aims to validate mechanical loading prediction equations by testing their prediction accuracy against a different sample and testing conditions than those used in the original validation studies, in order to assess their external validation. We tested all previously published equations that could be applied to our data, specifically those using raw accelerometer data from the right hip, lower back, or right ankle, and designed to predict mechanical loading during walking, running, and/or jumping.