Table 1 The 16 common features of complex systems adapted for return-for-sport

1. Feedback

Units in a complex system are mutually interacting and output is fed back and becomes a new input [70]. The feedback could be positive or negative. For example, positive feedback increases the rate of change while negative feedback works by reversing the direction of change.

Rehabilitation training leads to tissue adaptations, which improves physical fitness and performance (positive feedback). However, maladaptation can occur (e.g., alteration in neuromuscular control and muscle damage), leading to suboptimal response which may delay progress (e.g., delayed onset of muscle soreness). This acts as negative feedback for the systems, signalling the training intensity was too high.

2. Emergence

Emergent properties arise from the interactions of its units. The units serve as the building blocks for patterns to arise at higher levels [71].

After an ACL injury, injured athletes often train separately from the squad and have a different training regime. During this time of relative isolation and hardship, the athlete may build up a high level of resilience.

3. Self-organisation

Systems may order themselves spontaneously to form patterns and achieve an optimal or stable state [14].

ACL is a key sensorimotor system for postural control, which helps to maintain and control upright posture [72]. Following an ACL injury, the brain activation profile will be affected and shifts toward a visual-motor strategy, as opposed to a sensory-motor strategy. Instead of relying on movement and spatial awareness, people with ACL deficiency may rely more on the visual system, especially under challenging dynamic task constraints [73]. This is an example of how the sensorimotor system self-organises to compensate for the loss of ACL.

4. Levers and hubs

Levers and hubs are key structures in the systems that play a crucial role in how the systems will behave. Identifying them could allow interventions in the systems effectively [27].

There are exceptional factors that are influential in the RTS process and altering them may lead to rapid gain. In ACL rehabilitation, intense rehabilitation and patient motivation are established levers and hubs that may underpin a positive outcome following ACL rehabilitation [74].

5. Non-linearity

Outputs are not always proportional to the inputs. Small changes may lead to a large change in the systems and vice versa [14].

The same training stimulus can create a large recovery response (e.g., delayed onset of muscle soreness) on the first training session, but not subsequent training. This is because the body can non-linearly adjust to the training stimulus after the first session. The response exhibits a non-linear behaviour where the outcome (i.e., training response) is not proportional to the input (i.e., training stimulus).

6. Domains of stability

Many systems are dynamic however may eventually converge to a stable state. This stability will be maintained unless there is a significant perturbation [70].

Balance and proprioceptive training are often included in the ACL rehabilitation protocol. However, balance and technique training may not be effective in changing an athlete’s knee joint kinematics or decreasing external knee moments during pre-planned and unplanned side-stepping [75]. Similarly, gait mechanics are also difficult to modify even after completion of rehabilitation training and restoration of muscle strength [76]. This may be because the systems have achieved a domain of stability and the parts of the systems are well-entrenched, making it very difficult or near impossible to change. Once the systems have achieved a state of stability, they could only be altered when the stimulus is strong enough to push them through the tipping point [70].

7. Adaptation

Components or actors within the systems are capable of learning and evolving in response to the changes in the environment [70].

Some people with ACL deficiency may exhibit increased knee flexion at early stance and reduced extension in mid to late stance [77]. This is an adaptation that allows hamstrings to be efficient synergists to the ACL in walking [78, 79] and to reduce the anterior translation force of the tibia [77]. This represents how the body adapts to ACL deficiency by bringing changes within the systems. The adaptation appears to happen autonomously, unconsciously, and without explicit programming.

8. Path dependency

Events and actions that occurred previously influence future states and decisions [27].

ACL rehabilitation usually follows a path and one can only progress to the next stage by meeting a set of criteria. For example, in the early rehabilitation phase, progressive weight-bearing allows the knee joints to acclimatise to increased load and assist in the development of a normal gait pattern [80, 81]. Plyometric training is only incorporated if full range of motion (ROM), sufficient strength base, and flexibility are demonstrated. For on-pitch rehabilitation, activities should begin with simple drills and advance to more complex exercises [80]. A control-chaos continuum (CCC) could be followed on-field, where rehabilitation training constraints progress from high control to high chaos [82].

9. Tipping point

If the perturbation of a system goes beyond a certain threshold, there will be a phase transition in the system's behaviour which may not be reversible [70].

In ACL rehabilitation, one of the early goals is to strengthen lower limb muscles to minimise muscle atrophy [83]. Squat exercise may be used as a training stimulus (perturbation) and it may cause micro-tears and inflammation of the muscle fibres (system deviates from the stable state). The neuromuscular system will repair and adapt (system returns to a stable state), leading to muscle hypertrophy [84]. However, if the intensity and volume exceed the capacity of the soft tissue, there will be a loss in stability (e.g., quadriceps muscle strain) and an inability to relax back to the previous stable state automatically. There will be a change in system behaviour (i.e., re-injury [85]).

10. Change over time

Systems are dynamic and can evolve over time. This is because they constantly interact and negotiate with the environment, leading to continuous change [70].

Psychological characteristics of athletes can change during the ACL rehabilitation process and affect how they cope with RTS and future injury [86].

In the physical performance aspect, training capacity evolves and generally declines with age [87]. For example, the heart rate maximum during exercise declines with age [88]. Maximal oxygen consumption is inversely and strongly related to age for active and endurance-trained populations [89].

11. Open system

Complex systems are considered open as it is difficult to define their boundary. The systems interact with the environment and are also being influenced by the environment continuously. In contrast, closed systems are systems where the influence of the environment on them is negligible [14].

The size of the systems could hardly be defined, as things in the environment that are seemingly small may also influence them. For example, a wet training ground affects the ground reaction force and movement strategy for athletes during running [90]. Shoe designs and types of playing surfaces are related to ACL injury risk due to the shoe-surface friction [91]. Playing music during rehabilitation training may reduce the perception of physical effort during training and improve physical performance by delaying fatigue or increasing work capacity [92, 93].

12. Unpredictability

Due to non-linearity and emergence properties, it is difficult to predict how the systems will evolve [9].

Precise forecasting of when an athlete should RTS is challenging. It is difficult to predict the estimated time for recovery as there is unpredictability on how the systems evolve. For example, how will the motivation of the athlete change throughout rehabilitation? How will the change in a personal relationship affect the performance of the athlete? In some cases, it is impossible to gather, store, and use all of the information about the state of complex systems at one point to predict the outcome.

13. Unknowns

There are always units that influence the systems which are either unknown or could not be observed or measured. Therefore, it may seem that the systems evolved unpredictably [9].

There are factors that decisions makers may not be aware of during the ACL rehabilitation due to different reasons, for example, limited knowledge (e.g., how a genetic variant is associated with ACL rehabilitation and injury risk?), technology constraints (e.g., how reliable are the measurement tools?), insufficient resources (e.g., is it possible to measure everything?), bias and issues that stakeholders have been unaware of.

14. Distributed control

Control of a system is distributed across different parties and no one has complete control over the systems [9]. There is no top-down control approach as the process is not controlled by a single factor at a superior level.

The success of ACL rehabilitation is determined by all interacting units, from biological graft healing at the microscopic level, to intra-personal factors (clinical assessment, functional test, and biopsychosocial factors), and inter-personal factors at the macroscopic level. No single factor in isolation could determine the success of the outcome.

15. Nested system

There are nested hierarchies within the complex systems, forming systems within systems [27].

ACL rehabilitation itself exhibits nest hierarchies in the following order:

Cell > muscle > brain > inter-personal > family and friends > organization > environment.

At the cell level, shortly after graft implantation, fibrous scar tissue will be formed between the graft and host bone [94], followed by ligamentization [95]. At the muscular system level, quadriceps muscle atrophy and dysfunction are commonly observed after ACL reconstruction and are often associated with altered movement pattern [96, 97], possibly due to alterations at the brain (motor cortex) level and neurophysiological changes in muscles [98,99,100,101]. At the intrapersonal level, physiological cardiac adaptation [102] and aerobic fitness [103] are all substantially reduced after an ACL injury. At the interpersonal level, social support plays a key role in regaining confidence and eradicating fear of re-injury throughout rehabilitation [104,105,106].

16. Multiple scales and levels

Multiple perspectives are required when viewing complex systems. The systems are three dimensional and interactions within the systems often occur at different scales and levels [27].

Rehabilitation can be considered on the biological level, psychosocial level or performance level. There is more than one domain involved and often the systems have to be understood from multiple perspectives.