New technological tools for the evaluation and training of postural control and its validation with the "gold standard" systems in a biomechanics laboratory.
REPORT 1. Study of the State of Knowledge and scientific-technical analysis
1. Presentation
The general objective of the BABEN Program is the research of new technological solutions for the assessment and training of postural control aimed at the early detection of the risk of falls and fragility in the elderly, as well as the training or exercise of balance to prevent the risks of falling. This research includes two projects:
- Project 1: with the main goal of developing the postural control evaluation and training system.
- Project 2: with the main goal of validating the functioning of the system developed in project 1, as well as its evaluation and training functions, in comparison with the standard gold systems of kinematics and dynamics of equilibrium and postural regulation in humans.
BABEN aims to respond to the existing demand for new solutions or devices for assessing and training balance or postural control that provide quantitative measures that are correlated with clinical functional scales. We seek to generate solutions that overcome the limitations that the devices currently available in the market present, in terms of:
- reduced cost,
- portability, ease of installation and commissioning,
- quantitative measure of postural stability or control,
- that is contrasted or validated with standard gold equipment.
In light of the gradual ageing of our populations and the consequent increase in the number of elderly users, the BABEN programme offers new validated solutions that will provide professionals and therapists with a more functional assessment of the balance and stability of patients. Solutions that make it possible to increase the number of patients assessed in the primary care centres themselves, favouring the early detection of loss of functional capacity and risk of falling and therefore making possible an early intervention to reduce these risks. All this will result in a better maintenance of functional capacity in older patients and therefore an improvement in their quality of life and ability to perform activities of daily living.
The equipment available on the market that allows the simultaneous study of COM and BOS (such as motion capture systems based on optical technology or inertial sensors) is far from being democratised in a clinical or paraclinical and sports environments. In fact, even for scientific research spaces, they are high-priced devices.
Project 1 of the BABEN programme aims to develop a solution that responds to these needs. Starting from a first prototype developed by TECNALIA, called EQUIMETRIX, the main objective of project 1 is to generate an evolved version of a new type of device for balance assessment and training (Equimetrix) based on the results of the assessment carried out in project 2. The existence of a system such as Equimetrix, duly validated in relation to the technological gold standard, is essential to extend the in-depth evaluation of balance and postural regulation; an evaluation that is decisive in the context of prevention and health promotion in the elderly, reducing fragility and preventing the occurrence of falls.
2. Motivation. The importance of postural control and balance in the elderly: fragility and falls
Falls are a major cause of disability, morbidity and mortality among older people. Approximately 30% of people over the age of 65 and 50% of those over the age of 80 suffer one fall per year (American Geriatrics Society 2010). Of the elderly who fall, half have recurrent falls, 50% fall again in the same year. One falling is therefore a risk factor for further falls.
Falls in older people have serious consequences. As reflected in the injury pyramid in the figure below (Fig. 4), more than 70% have clinical consequences such as fractures, wounds, sprains, etc. and more than half have sequelae afterwards (American Geriatrics Society 2010); 50% of people who suffer a fracture from a fall do not regain the previous functional level. In addition, one in ten falls causes serious injuries, including a hip fracture.
.
Figure 1: Injury pyramid. Consequences of falls in over 65s. Source: (Ministry of Health, Social Services and Equality, 2014)
An estimated 40 per cent of cases of long-term institutional care are due to falls. Age is the greatest risk factor for fall injuries. Older adults are admitted to hospital for injuries related to this cause five times more frequently than for injuries due to other reasons, and their injuries tend to be more severe, while the possibilities for intervention are reduced. Disability and mortality are common consequences.
With deaths secondary to falls being of interest, other consequences of falls have, from the general health perspective of the population, a far greater impact. Based on the data in the previous figure (Fig. 1), it can be calculated that for each person who dies as a result of a fall, 24 have been admitted to hospital for a femoral neck fracture (hip fracture), almost 100 will have suffered a fall with serious consequences and nearly 1000 elderly people will have suffered a fall with consequences.
The medical consequences of falls, including the so-called fall syndrome (fear of falling), are often the beginning of disability in the elderly (Abizanda Soler et al. 2010). In Spain, the consequences of falls also represent a high cost for the health system. Specifically, one of the most serious consequences is a hip fracture. In the elderly, hip fractures are the most frequent cause of hospital admission to traumatology and orthopaedic services. It is an injury of growing importance in society, both in economic and social terms. It is estimated that 90% of cases are due to falls. In recent years, the evolution of hospital discharges due to this cause has undergone a constant increase, especially among women, reaching an increase of up to 50% in those over 74 years of age in less than 15 years, from 1997 to 2011.
Women have a higher risk of falling than men and also suffer more serious consequences, with a higher percentage of hip fractures, three times more than men. In a 2008 study, the average cost per patient (discharge) for this cause was estimated at 8365€ (Instituto de Información Sanitaria 2010).
Given the impact that falls have on individual health and the health system, and their close relationship to disability and pre-dependency fragility syndrome, the new consensus protocols for health intervention treat them as a whole. Thus, the new intervention proposal of the National Health System (SNS) detailed in the "Consensus Document on the prevention of fragility and falls in the elderly person" mentioned above (document approved by the Interterritorial Council of the National Health System on 11 June 2014) aims to "detect and intervene on fragility and the risk of falls in the elderly person, as a way to avoid and/or delay functional deterioration, as well as to promote health in the population aged over 70" and also in the field of Primary Care and the community environment, in coordination with the appropriate specialized geriatric and hospital resources, through the early identification of people at risk of suffering falls and the development of strategies for their prevention.
The general description of this intervention indicates that the first essential preventive component to be included in a possible intervention plan and individualised monitoring of fragile patients consists of multi-component physical activity programs that focus, among other aspects, on balance. The preferred test to be used for functional limitation/fragility screening will be the Short Physical Performance Battery (SPPB) performance test which combines balance, walking speed and getting up from the chair. This prioritisation is based on its good validation to detect fragility and high reliability in predicting disability, as well as its feasibility for use in Primary Care (Cabrero-García et al. 2012; Freiberger et al. 2012).
For the prediction of fragility and the risk of falls it is useful to determine if there is a problem of postural balance. Currently, to assess the risk of falls, health professionals use static tests such as the Romberg test, usually combined with other dynamic tests such as the Berg balance scale and some general questionnaires. As mentioned above, functional performance tests such as the SPPB and the LAC/TUG test (Timed Get Up and Go) are the simplest and shortest tests that detect functional problems and are considered reliable because they are based on a quantitative measures, such as the time used to perform tasks and not on a discrete scale, such as those used in other tests.
These methods have been proven reliable in identifying the risk of falls, although they are not tools that quantify the patient's level of stability and allow differentiation between different balance or stability problems. For clinical practice, the viability and usefulness of the use of technological solutions and computer systems that allow an objective measure of the control of the person's postural balance is now widely recognised. A quantitative assessment tool should have the following 4 characteristics (Mancini and Horak 2010): 1) Carry out measures that reflect both the capacity and quality of postural strategies, 2) Sensitivity to detect postural control anomalies, 3) Reliability and validity, 4) Practicality, simplicity of use and low cost. And it is in this field that the project focuses, new quantitative tools for postural balance evaluation; tools that provide quantitative measures that are correlated with clinical functional scales.
3. State of knowledge
3.1 Postural control
The human ability to maintain equilibrium is a complex function that can be analysed from multiple points of view. Three of them are particularly interesting:
1. static equilibrium versus dynamic equilibrium;
2. the ability to maintain a stable equilibrium when faced with different challenges; and
3. the basic strategies for maintaining equilibrium.
At the higher level, the balance can be contextually divided between static and dynamic, depending on whether you want to maintain a body posture or avoid falls during movements such as locomotion. Static equilibrium occurs when the resultant of the forces acting on the body causes it to be at rest or not to move, while dynamic equilibrium occurs in non-uniform movements by the intervention of inertial forces, where a body appears to be in apparent imbalance but does not fall [1]. On the other hand, the control of equilibrium in the stationary, anticipatory and reactive state is related to the types of equilibrium challenge that are counteracted. These challenges can in turn be classified as internal or self-generated disturbances, such as voluntary outreach, and external, such as a push. Finally, equilibrium control is achieved through movements that are composed of basic strategies or coordinated fundamental actions of the lower limbs, aimed at maintaining or regaining equilibrium. For example, foot balance is maintained by strategies using the ankle, hip and steps, while walking balance uses foot positioning strategies. Evaluations may address different aspects of balance, according to these distinctions, for example:
1. evaluation while standing or walking,
2. evaluation with or without external disturbances or anticipation movements.
Human beings, possessing two legs, standing or walking, and humanoid robots, are examples of bipeds that as a mechanical system are characterised by a relatively high position of their center of mass compared to a relatively small support area (support polygon, support base), and that combined create a normally stable delimited mechanical system with respect to the upright posture. This system has a limited ability to cope with disturbances without falling. A biped is, in a first approximation, similar to an inverted pendulum. This is the simplest and most common model used to study human walking and to extract the parameters necessary to observe equilibrium [2]. It is a dynamic model that is often used to characterise the basic dynamics of a standing biped, where the inverted virtual pendulum connects the Center of Mass (the virtual point where the body mass would be concentrated), with the Center of Pressure (the virtual point through which the vector of the Ground Reaction Force passes, see figure 2).
Figure 2: red line showing the inverted pendulum as a model of a walking biped. (illustration from http://www.mi.ams.eng.osaka-u.ac.jp/member/sugihara/research2009-e.html)
In current clinical practice the assessment of balance is based on several well-accepted clinical trials requiring an expert physician and at least half an hour of trial time. These clinical trials usually start from a functional perspective and typically assess a patient's ability to perform specific activities while maintaining balance (using ordinal scales), or measure the speed or duration of task completion (e.g., walking a specific distance or for a specific time). Some examples are: tests for static tasks, such as the Performance Oriented Mobility Assessment (POMA) - Balance Tests or the Tinetti[3] test, the Leg Posture [4] and the Berg Balance Test (BBT)[3], or tests that also include dynamic tasks such as Timed Up and Go (TUG) [5], and BESTest [9]. Extensive reviews of clinical evaluation procedures can be found at [6][7].
Research is currently underway to conduct similar assessments at home using non-intrusive body sensors [8]. The fact that so many procedures exist and are used is due, on the one hand, to the fact that there are many functional tasks that involve balance and, on the other hand, to the fact that there is no clear advantage between scales. A general limitation of such assessment procedures is that reduced ability to perform a functional task (e.g., walking) may be the result of a wide range of sensory, motor, and cognitive impairments that are not necessarily related to balance skills alone [7] and thus also provide little functional diagnostic information about a balance disorder.
Apart from these function-oriented clinical procedures, "posturography" is a set of quantitative methods that use proportion scales to quantify the performance of postural balance in an upright position, whether in static or dynamic conditions. Extensive reviews can be found in [9], [10] and [11].
Posturography measures the ability to maintain the body's Center of Mass (CDM), i.e., its projection on the ground surface, within the Base of Support (BDS) (Figure 3), which is a formal and physical definition of static equilibrium. The movements of the Pressure Center (COP) reflect the subject's active control to maintain the vertical projection of the body's CDM within the lift base [12], and thus provide related but complementary information. In static conditions, the BDS remains stationary and only the CDM moves.
Posturography measures the ability to maintain the body's Center of Mass, i.e., its projection on the ground surface, within the Base of Support (Figure 3), which is a formal and physical definition of static equilibrium. The movements of the Pressure Center reflect the subject's active control to maintain the vertical projection of the body's Center of Mass within the lift base [12], and thus provide related but complementary information. In static conditions, the Base of Support remains stationary and only the Center of Mass moves.
Figure 3. Illustration of the most commonly used biomechanical indicators (COM, COMv, COP, BOS, GRF) that describe or contain information on equilibrium conditions. The characteristics of one or a combination of these indicators are used to describe the performance of the equilibrium in the current posturography.
However, in dynamic conditions both BOS and COM are in motion [44]. Therefore, dynamic posturography, unlike static posturography, involves facing external disturbances applied by the movements of the supporting surface, and is related to "reactive equilibrium control". The planar movements COM and COP are specified by different metrics to describe the equilibrium response [13]. Several metrics used in the literature are included in Table 1.
Many of these metrics are linked to the risk of falling or to some of the clinical scales described above, but the exact interpretation of normality and abnormality, as well as its interpretation, remains a subject of research. In order to properly interpret the movements of the COP and COM in their interrelationship, methods that apply well-defined perturbations (external, sensory or motor) in combination with techniques of identification of closed-loop systems are currently used in research [14][15]. These techniques can reveal the causes of abnormal movement and control of COP and COM, identify which of the underlying systems (vestibular system, muscle strength generation, muscle coordination) is impaired, and to what extent [10].
Table 1 contains metrics that quantify equilibrium, as used in posturography and walk analysis. Most of the metrics presented have been validated showing that they are significantly different between groups or conditions with varying equilibrium behaviour, such as the elderly compared to young adults, or open eyes compared to closed eyes. It is recommended to consult the studies indicated for the approaches or methods of calculation and to obtain detailed information on the groups or conditions in which methods have been shown to be indicated.
Table 1. Review of metrics used to quantify balance performance when standing and walking.
3.2 Existing tools for postural control measurement
We are now considering how to simultaneously measure and monitor the relevant parameters indicated (COM, COP and BOS). Traditionally, both the COM and the COP are evaluated in a human motion analysis laboratory that has an optical, magnetic or mechanical system for measuring motion, and one or more force platforms. This infrastructure is not available for doctors and physiotherapists, let alone for use in daily activity. To overcome these limitations and move towards portable solutions, systems have been developed based on:
- body sensor network (Luinge and Veltink 2004; Roetenberg, Baten, and Veltink 2007; Roetenberg et al. 2005; Zijlstra and Hof 2003; Moe-Nilssen 1998)
- and/or portable/wearable force platforms such as sensorized footwear or insoles (Liu, Inoue, and Shibata 2010; Mariani et al. 2010; Martin Schepers et al. 2010; Rouhani et al. 2010; Schepers, Koopman, and Veltink 2007; Schepers et al. 2009)
Using these sensors, various techniques have been proposed in recent years. With a combination of image, inertial (IMUs) and portable/wearable force sensors it will be possible to estimate continuously:
- The relative displacement of the COM with respect to the COP
- and BOS (its size and shape).
For the measurement of the COM position and movement, 3 methods are normally applied to estimate the COM position:
1) segmental analysis based on the movement of segments and an anthropometric model of the human body
2) the double integration of the reaction force of the ground (applying Newton's second law)
3) the movement of the pelvis, assuming that the movement of the COM can be approximated through the movement of the pelvis.
The project chooses this third measurement method, the movement of the pelvis, as it seeks a solution that requires the minimum number of sensors to be placed in the human body.
During the last 30 years, instrumental tools have been proposed to quantitatively evaluate the parameters of postural equilibrium. Measuring stability directly is impossible... it is not a magnitude, but simply an aptitude, allowing the body to return to the equilibrium position when it moves away from it. However, stability has characteristics that can be measured. Force and the stabilometric platform ( Ground Reaction Force, COP) are currently the most commonly used devices. The COM kinematics are now also accessible, but through expensive devices (Figure 4). These are the reasons why currently, in clinics, the tools used for equilibrium assessment use COP or plantar pressure distribution through force platforms and/or sensorized carpets for pressure measurement. These techniques alone do not reflect whether the body posture during the ongoing action is stable or not. They do not take into account the upper body part (or COM), which obviously also participates in the execution of a dynamic task and is essential in daily activities.
As indicated in Table 1, there is scientific evidence to support the paradigm that a joint analysis of COM-COP or COM foot placement reflects better human functional stability during dynamic tasks than COP or COM alone.
Figure 4. Types of products for measuring information related to equilibrium (COP, COM, BOS)
The commercial products used in the valuation of equilibrium can be divided into the following classification (see figure 5):
- Stabilometry Equipment: these products offer postural control evaluation and training methods using only the COP (COP path, COP maximal excursion, Statokinesigram).
- Baropodometric Platforms: provide a measure of the plantar distribution from which we estimate the BDS. However, they do not allow the COM to be measured by themselves.
- Optical motion capture systems: these products provide complete information on the kinematics of the subject from which the COM is estimated. They are expensive in cost and maintenance and require a high level of training to be used properly.
- Wireless sensor networks for motion analysis: these products also provide complete information on the kinematics of the subject from which the COM is estimated. Their major drawback is the placement of the sensor in the subject's body. This can take more than 15 minutes, making them unusable for clinical practice.
Figure 5. Characteristics of existing postural control equipment
3.3 Equimetrix: Making progress in the state of the art in postural control measurement
The project will advance in the state of the art by developing a solution, Equimetrix (see diagram in figure 6), that combines both measures in the same system and relates them, with the objective of measuring the relative position of the CDM - BDS (or CDM - CDP) outside a movement analysis laboratory.
- Regarding the stabilometry equipment, the Equimetrix prototype provides the distribution of plantar contacts (from which the BOS is estimated). The vision sensor incorporated in the prototype provides an estimate of the COM.
- Regarding the baropodometric platforms, the prototype also offers information about BOS at a more affordable price.
- Compared to optical systems, the Equimetrix prototype offers data on ODM and BOS (distribution of plantar pressure). The Equimetrix COM estimate is less accurate than optical systems, but it is precisely the aim of the project to quantify this loss of accuracy. This will make it possible to assess the suitability of its use in a clinical environment.
- Equimetrix offers a solution with a much shorter installation and set-up time (around 2 minutes), compared to sensor networks, which offer COM measurements and allow the BOS to be reconstructed.
Figure 6. Components of the Equimetrix prototype
The project is based on a prototype of Equimetrix, the components of which are shown in Figure 6. Equimetrix presents an innovative concept for the analysis of equilibrium and its evaluation based on a single parameter called the "stability index". Compared to stabilometry equipment such as baropodometric, the concept of the stability index the position of the COM in relation to the BOS (and the COP) is known and allows a more reliable and accurate assessment of the equilibrium capabilities of the subject.
However, the concept of "stability index" used needs to be validated against standard equipment used in motion analysis laboratories. Therefore, the use of standard gold systems for the determination of 3D center of mass by optical (Qualisys) and inertial (XSens) means, as well as for the measurement of plantar pressures (Tekscan / Pedar) and dynamometric pressures (Bertec) for the measurement of the plantar support area and the migration of the pressure center, is fundamental. Thus the Equimetrix system will be analyzed by LABIOMEP in their laboratories and the results will serve for the improvement of the system especially in two aspects:
- Refinement of equilibrium parameter calculations based on modifications made to the corresponding algorithms.
- Improvements in the sensors of the baropodometric platform, both in the manufacture and in the processing of the information they provide.
The result will be an advanced version of the Equimetrix prototype, whose measurements will be contrasted with commercially available high-precision devices commonly used in equilibrium laboratories.
The existence of a system such as Equimetrix, duly validated in relation to the technological gold standard, is nuclear to extend the in-depth evaluation of the balance and postural regulation. Such evaluation is decisive in the context of prevention and health promotion in the elderly, reduces fragility and anticipates the occurrence of falls, also in special populations such as patients affected by neurodegenerative diseases with motor implications. In these cases, this evaluation is decisive for the prescription and therapeutic control.
3.4 Abbreviations list
BBT: Berg Balance Test
BESTest: Balance Evaluation Systems Test
BOS: Base of Support
COG: Center of Gravity
COM: Center of Mass
COP: Center of Pressure
IMU: Inertial Measurement Unit
POMA: Performance-Oriented Mobility Assessment
TUG: Timed Up and Go
SPPB: Short Physical Performance Battery
3.5 References
[1] Izquierdo, Mikel. Biomecanica y Bases Neuromusculares de la Actividad Fsica y el Deporte / Biomechanics and Neuromuscular Bases of Physical Activity and Sport. Ed. Médica Panamericana. 2008.
[2] Winter, DA. Human Balance and Posture Control during Standing and Walking. Gait & Posture 3(4): 193– 214. 1995.
[3] Tinetti ME. Performance-oriented assessment of mobility problems in elderly patients. Journal of the American Geriatrics Society. 1986.
[4] Jonsson E, Seiger Ã, Hirschfeld H. One-leg stance in healthy young and elderly adults: a measure of postural steadiness?. Clinical Biomechanics. 2004;19(7):688-694.
[5] Berg KO, Maki BE, Williams JI, Holliday PJ, Wood-Dauphinee SL. Clinical and laboratory measures of postural balance in an elderly population. Archives of physical medicine and rehabilitation. 1992;73(11):1073-1080
[6] Deathe AB, Miller WC. The L test of functional mobility: measurement properties of a modified version of the timed “up & go” test designed for people with lower-limb amputations. Physical therapy. 2005;85(7):626-635.
[7] Mancini M, Horak FB. The relevance of clinical balance assessment tools to differentiate balance deficits. European journal of physical and rehabilitation medicine. 2010;46(2):239.
[8] Shumway-Cook A, Woollacott MH. Motor control: translating research into clinical practice. Lippincott Williams & Wilkins; 2007.
[9] Rispens SM, van Schooten KS, Pijnappels M, Daffertshofer A, Beek PJ, van Die. Identification of Fall Risk Predictors in Daily Life Measurements Gait Characteristics’ Reliability and Association With Self-reported Fall History. Neurorehabilitation and neural repair. 2014 1545968314532031.
[10] Prieto TE, Myklebust JB, Hoffmann RG, Lovett EG, Myklebust BM. Measures of postural steadiness: differences between healthy young and elderly adults. IEEE_J_BME. 1996 Sept. ;43(9):956-966.
[11] Pasma J, Engelhart D, Schouten A, Van der Kooij H, Maier A, Meskers C. Impaired standing balance: The clinical need for closing the loop. Neuroscience. 2014;267:157-165.
[12] Visser JE, Carpenter MG, van der Kooij H, Bloem BR. The clinical utility of posturography. Clinical Neurophysiology. 2008;119(11):2424-2436.
[13] Hof A, Gazendam M, Sinke W. The condition for dynamic stability. Journal of biomechanics. 2005;38(1):1-8.
[14] Henry SM, Fung J, Horak FB. Effect of stance width on multidirectional postural responses. J Neurophysiol.
2001 Feb;85(2):559-570.
[15] van der Kooij H, van Asseldonk E, van der Helm FC. Comparison of different methods to identify and quantify balance control. Journal of neuroscience methods. 2005;145(1):175-203.
[16] Engelhart D, Schouten AC, Aarts RGKM, van der Kooij H. Assessment of Multi-Joint Coordination and Adaptation in Standing Balance: a Novel Device and System Identification Technique. IEEE Transactions on Neural Systems and Rehabilitation Engineering. 2015;23(6):973-982.
[17] Brewer L, Horgan F, Hickey A, Williams D. Stroke rehabilitation: recent advances and future therapies. QJM. 2013;106(1):11-25.
[18] Tamburella F, Scivoletto G, Molinari M. Balance training improves static stability and gait in chronic incomplete spinal cord injury subjects: a pilot study. Eur. J. Phys. Rehabil. Med. 2013;49:353-364.
[19] Alahmari KA, Marchetti GF, Sparto PJ, Furman JM, Whitney SL. Estimating Postural Control With the Balance Rehabilitation Unit: Measurement Consistency, Accuracy, Validity, and Comparison With Dynamic Posturography. Archives of physical medicine and rehabilitation. 2014;95(1):65-73.
[20] Allum JH, Adkin AL, Carpenter MG, Held-Ziolkowska M, Honegger F, Pierchala K. Trunk sway measures of postural stability during clinical balance tests: effects of a unilateral vestibular deficit. Gait & Posture. 2001 Dec;14(3):227-237.
[21] Bloem BR, Visser JE, Allum JHJ. Chapter 20 Posturography. In: Hallett M, editor. Handbook of Clinical Neurophysiology. Vol 1. Elsevier; 2003. p. 295-336.
[22] Ruhe A, Fejer R, Walker B. Center of pressure excursion as a measure of balance performance in patients with non-specific low back pain compared to healthy controls: a systematic review of the literature. Eur Spine J. 2011 Mar;20(3):358-368.
[23] Najafi B, Horn D, Marclay S, Crews RT, Wu S, Wrobel JS. Assessing postural control and postural control strategy in diabetes patients using innovative and wearable technology. Journal of diabetes science and technology. 2010;4(4):780-791.
[24] Pai YC, Patton J. Center of mass velocity-position predictions for balance control. Journal of biomechanics,1997;30(4):347-354.
[25] Slobounov SM, Slobounova ES, Newell KM. Virtual time-to-collision and human postural control. Journal of motor behavior. 1997;29(3):263-281.
[26] Riccio GE. Information in movement variability about the qualitative dynamics of posture and orientation. University of Illinois at Urbana-Champaign. 1992.
[27] Hasson CJ, Van Emmerik RE, Caldwell GE. Predicting dynamic postural instability using center of mass time- to-contact information. Journal of biomechanics. 2008;41(10):2121-2129.
[28] Hendrickson J, Patterson KK, Inness EL, McIlroy WE, Mansfield A. Relationship between asymmetry of quiet standing balance control and walking post-stroke. Gait \& posture. 2014;39(1):177-181.
[29] Rougier P, Genthon N. Dynamical assessment of weight-bearing asymmetry during upright quiet stance in humans. Gait \& posture. 2009;29(3):437-443.
[30] Nardone A, Godi M, Grasso M, Guglielmetti S, Schieppati M. Stabilometry is a predictor of gait performance in chronic hemiparetic stroke patients. Gait \& posture. 2009;30(1):5-10.
[31] Roerdink M, De Haart M, Daffertshofer A, Donker S, Geurts A, Beek P. Dynamical structure of center-of-pressure trajectories in patients recovering from stroke. Experimental brain research. 2006;174(2):256-269.
[32] van Asseldonk EH, Buurke JH, Bloem BR, Renzenbrink GJ, Nene AV, van der Helm FC, van der Kooij H. Disentangling the contribution of the paretic and non-paretic ankle to balance control in stroke patients. Experimental neurology. 2006;201(2):441-451.
[33] Hausdorff JM, Peng CK, Ladin Z, Wei JY, Goldberger AL. Is walking a random walk? Evidence for long-range correlations in stride interval of human gait. J Appl Physiol (1985). 1995 Jan;78(1):349-358.
[34] Duarte M, Freitas SMSF. Revision of posturography based on force plate for balance evaluation. Rev Bras Fisioter. 2010 Jun;14(3):183-192.
[35] Amoud H, Abadi M, Hewson DJ, Michel-Pellegrino V, Doussot M, Duchêne J. Fractal time series analysis of postural stability in elderly and control subjects. J Neuroeng Rehabil. 2007;4:12.
[36] Yamada N. Chaotic swaying of the upright posture. Human Movement Science. 1995;14(6):711-726.
[37] Ladislao L, Fioretti S. Nonlinear analysis of posturographic data. Medical & biological engineering & computing. 2007;45(7):679-688.
[38] Liu K, Wang H, Xiao J, Taha Z. Analysis of human standing balance by largest lyapunov exponent. Comput Intell Neurosci. 2015;2015:158478.
[39] Maurer C, Peterka RJ. A new interpretation of spontaneous sway measures based on a simple model of human postural control. Journal of Neurophysiology. 2005;93(1):189-200.
[40] Toosizadeh N, Mohler J, Lei H, Parvaneh S, Sherman S, Najafi B. Motor Performance Assessment in Parkinson's Disease: Association between Objective In-Clinic, Objective In-Home, and Subjective/Semi- Objective Measures. PLoS One. 2015;10(4):e0124763.
[41] Kirtley, C. Cait analysis: theory and practice. Elsevier Health Sciences. 2006
[42] Lord, S. R. (2007), Falls in older people : risk factors and strategies for prevention, Cambridge University Press, Cambridge
[43] Hill, K.; Schwarz, J.; Flicker, L. & Carroll, S. (1999), 'Falls among healthy, community-dwelling, older women: a prospective study of frequency, circumstances, consequences and prediction accuracy', Australian and New Zealand journal of public health 23(1), 41--48.
[44] Horak, Fay B. Postural Orientation and Equilibrium: What Do We Need to Know about Neural Control of Balance to Prevent Falls? Age and Ageing 35(suppl 2): ii7–ii11. 2006.
