## 1 Introduction  
Understanding the biomechanics of the lower limbs is crucial for preventing injuries and guiding rehabilitation, as even normal gait variations (for example, differences between genders) can alter joint loading and contribute to musculoskeletal disorders [1]. Isometric exercises--muscle contractions performed without joint movement--are widely used in strength training and therapy because they improve muscle performance and joint stability without imposing dynamic strain. Beyond orthopedic benefits, isometric regimens also confer general health advantages such as significantly reducing blood pressure in hypertensive patients (comparable to the effects of medication) [2]. Numerous studies underscore the value of isometric training for musculoskeletal health. For example, in sports medicine, isometric protocols (often combined with isotonic exercise) increase hamstring strength and flexibility, helping to reduce injury risk [3]. Isometric regimens provide effective pain relief in tendinopathies, comparable in the short term to isotonic training,making them integral to tendon rehabilitation [4]. In knee osteoarthritis, targeted isometric quadriceps exercises significantly improve muscle strength and reduce pain and disability, and their effectiveness in enhancing function has been shown to be on par with dynamic resistance training [5; 6]. Researchers often measure muscle activation using surface electromyography (EMG) [7], but this technique has well-known limitations. Surface EMG primarily detects activity in superficial muscles, and the relationship between EMG signal amplitude and actual muscle force is nonlinear and complex [8; 9], making direct force estimation from EMG unreliable. Advanced algorithms (including machine learning) can predict muscle forces from EMG with high accuracy [10], but these complexities underscore the need for computational musculoskeletal modeling to better estimate internal forces. Musculoskeletal modeling enables the estimation of internal forces and muscle contributions during exercise, overcoming some limitations of direct measurement methods. For instance, a detailed shoulder model demonstrated that accounting for muscle architecture and moment arms can predict isometric force-generating capacity across different joint positions [11], illustrating how muscle structure influences functional capability. Experimental findings also help validate models; for example, trunk muscle activation patterns remain remarkably consistent across varying isometric postures [12], providing a valuable basis for verifying model predictions. Modern musculoskeletal simulation software (e.g., the AnyBody Modeling System) supports both static and dynamic analyses [13]. Static optimization methods assume the body is in quasi-static equilibrium at each instant (neglecting inertia) and are computationally efficient [14], making them a cornerstone for analyzing postures or slow isometric tasks. A common approach is to use a min/max optimization criterion to distribute loads evenly among muscles, yielding physiologically realistic recruitment patterns [15]. Dynamic simulations, in contrast, account for inertial forces and time-dependent muscle behavior. They require motion capture data or predefined kinematic inputs and involve solving differential equations of motion, which is more computationally demanding. Careful scaling of a generic model to an individual's anthropometry and strength--using data from both static reference poses and dynamic trials--can improve the accuracy of dynamic simulations [16]. Although more computationally intensive, dynamic analysis is essential for capturing momentum and other time-varying factors in movement (even during nominally \"isometric\" tests). It thus serves as a necessary complement to static modeling approaches. Despite the broad utility of these modeling techniques, direct comparisons between static and dynamic musculoskeletal models during purely isometric exercises are scarce.