The characteristics of the body mass frequency index in dysmobility syndrome: A pilot study

Background: With the advancement of global aging, there has been an increase in patients with dysmobility syndrome (DS), often accompanied by osteoporosis, sarcopenia, and sarcopenic obesity. The objective of this study was to evaluate the application value of the body mass frequency index (BMFI) in older patients with DS by comprehensively analyzing the differences in BMFI between community-dwelling older subjects using medical and engineering methods. Methods: A cross-sectional study was conducted to recruit community-dwelling older subjects aged 60 – 90 years. Various assessments and measurements were performed, including basic information collection, gait analysis, bone mineral density (BMD) and body composition measurement, fall and fracture risk et al. Gait analysis and body mass index (BMI) are in the established model to calculate BMFI. Analysis of BMFI was performed in community-dwelling older subjects, and the specificity and threshold of BMFI in predicting dysmobility syndrome (DS) were further analyzed. Results: Significant differences in BMFI were observed between older adults with DS and those without DS. BMFI in older people was associated with bone quality, fracture risk, body fat percentage, appendicular skeletal muscle mass index (ASMI), grip strength, and speed. The odds ratio (OR) and 95 % confidence interval (CI) for BMFI in the non-DS and DS groups were 0.823 (0.743 – 0.901), respectively. Receiver operating characteristic (ROC) analysis demonstrated that BMFI had predictive value in distinguishing non-DS from DS (AUC = 0.669) ( P < 0.05). The optimal threshold for predicting non-DS and DS was found to be 16.04 (sensitivities = 0.483, specificities = 0.774). Conclusion: The measurement of BMFI has demonstrated disparities in musculoskeletal status among older adults with and without DS. Notably, BMFI exhibits a unique predictive capacity for DS among the elderly population.


Introduction
With the economic development of the country and the improvement of medical levels, the average life expectancy of the Chinese population has been extended.According to the results of the seventh national census in China (2020), about 264 million people have reached the age of 60 years, accounting for 18.70 % (Office of the Leading Group for the seventh National Population Census under the state council and National Bureau of Statistics of China, 2021).Musculoskeletal degenerative diseases are prevalent in older populations (Patel et al., 2013).Agerelated muscle and bone mass declines are strongly associated with fractures and falls (Gomarasca et al., 2020;Hirschfeld et al., 2017) .They impose a huge health and economic burden (Jiang et al., 2015).Studies have shown that about 1/3 of older people fall once a year (Grant et al., 2015), affecting the quality of life of older people (Levinger et al., 2016;Da Beaudart et al., 2017;Gouveia et al., 2018).Older people who have high body fat percentages may have decreased skeletal muscle mass and bone density (Yang et al., 2022) .Absolute and relative fat excess contributes to obesity and sarcopenic obesity and is also a factor in falls and fractures in older adults (Binkley et al., 2013).In 2013, Binkley et al. (Binkley et al., 2013) proposed the disease concept of dysmobility syndrome (DS) combined with osteoporosis, sarcopenia and sarcopenic obesity, and other factors to evaluate the musculoskeletal condition of the older people more comprehensively (Muscle, Bone and Osteoporosis Academic Group of Osteoporosis Branch, and Chinese Geriatrics and Gerontology Society, 2016;Edwards et al., 2013).
The definition of DS involves six conditions, and a diagnosis of DS can be made if three or more of these conditions are met.(1) The bone mineral density (BMD) at the lumbar spine, femoral neck, or total proximal femur is less than or equal to − 2.5.(2) The appendicular skeletal muscle mass index (ASMI) is less than or equal to 7.26 kg/m 2 for men and 5.45 kg/m 2 for women.(3) The body fat percentage is >30 % for men and 40 % for women.(4) The gait speed is <1 m/s.(5) The grip strength is <30 kg for men and 20 kg for women.(6) The number of falls in the past 12 months is more than or equal to one time (Binkley et al., 2013).
Current research indicates that the prevalence of DS among the older population ranges from 10.1 % to 27.0 %, as reported in various studies (Looker, 2015;Hong et al., 2021;Hong et al., 2018;Clynes et al., 2015;Santos et al., 2019;Lee et al., 2017).While a cross-sectional study conducted using data from the Bushehr Elderly Health Cohort suggests a higher prevalence rate of approximately 54 % for DS (Khaleghi et al., 2023).DS is positively associated with fracture risk (Hong et al., 2021;Hong et al., 2018), fall risk (Clynes et al., 2015), and mortality in the older people (Looker, 2015;Lee et al., 2017), indicating that DS is an important cause of decreased physical function and quality of life or even death in the older people.Diagnostic screening of older adults for DS helps identify their high fracture and fall risk and is essential for their quality of life (Iolascon et al., 2015;Nasimi et al., 2019).Dual-energy Xray absorptiometry (DXA) is often employed for DS diagnosis.DXA can distinguish bone, muscle, and fat, thus enabling the determination of BMD and ASMI.However, both BMD and ASMI are limited by body mass index (BMI).On the other hand, the unit of measurement is a mass index, but it cannot scientifically evaluate the status of the relevant muscles and bones in the whole body.Thus, neither BMD nor ASMI, which rely on BMI, can provide a comprehensive and accurate condition of the health status of the muscle-bone unit in less active older adults.
Mechanically, the body system can be represented by its center of mass.The center of the body mass in the distribution space usually moves when the body segments are relatively displaced.During walking gait, the body is in a state of continuous imbalance, and each subsequent step requires the maintenance of gait balance by regulating the center of mass (Lugade et al., 2011).The ability to control the center of mass motion may decline in individuals with gait imbalance.Therefore, 3D motion trajectories of the center of mass are commonly employed to assess the center of mass in clinical studies (Tesio and Rota, 2019).The curvature peaks of the center of mass trajectory and their lateral oscillations are closely related to balance, and balance defects may lead to falls (Robert et al., 1994).Age-related gait disturbance is a common risk factor of fall (Campbell, 1990).Meanwhile, visual system degenerative changes in older adults, decreased motor control, weakness or asymmetry of muscle strength, and external factors include drug reactions are the factors of fall (Gouveia et al., 2018).A focus on research about the center of mass is therefore beneficial to further reveal the biomechanical mechanism of movement imbalance.
In the fields of biomechanics, traffic engineering, and civil engineering, it is often required to establish a spring-mass-damper (SMD) model to study the mechanical properties of the human body to study human movement (such as walking), the effect of vehicle vibration on passengers, and the effect of a large number of people on the dynamic properties of engineering structures (Edwards et al., 2013;Zhang et al., 2016;Chen et al., 2014).To comprehensively evaluate the general musculoskeletal status and behavioral gait of the older population, combined biomechanical and engineering analysis methods were introduced to propose the concept of the BMFI.The BMFI is a novel evaluation index established based on the trajectory of the center of mass, combined with the SMD model of human mechanics for detecting the overall musculoskeletal system of the human body.It integrates the quality, quantity, and distribution characteristics of muscle-skeletal units and reflects the mechanical characteristics of the mass and stiffness of the human musculoskeletal system.The establishment of this concept helps to distinguish the population with DS at high risk of fractures and falls because of reduced function of the musculoskeletal system.It has important guiding significance for clinical practice.Therefore, this study describes the characteristics of BMFI and assesses the diagnostic significance of the BMFI for DS in community-dwelling older adults.

Subjects
This cross-sectional study was based on community-dwelling older adults.All subjects were examined and documented between 2020.Data from young adults aged 20-29 were used as normal controls.Inclusion criteria: (1) 60 to 90 years old of either sex; (2) older people who walk independently and have no cognitive impairment.Exclusion criteria: (1) severe spinal and hip bone deformity; (2) taking medications known to affect the musculoskeletal system in the past six months, such as antiosteoporosis drugs, corticosteroids; (3) suffering from chronic diseases affecting bone metabolism, such as rheumatoid arthritis, chronic renal insufficiency; (4) metal implants in the body, such as joint replacement devices.Informed consent for participation was obtained from all subjects.

General information collection
General information was collected from the enrolled subjects by the dedicated investigators, including the name, sex, age, height, and weight of the subjects.The BMI was then calculated, and the past medical history and the number of falls in the past year were recorded.

Bone mineral density and body composition measurements
Dual-energy X-ray Absorption (DXA) was used to measure bone mineral density, distinguishing bone, muscle, and fat.Bone mineral density at the lumbar spine (L1 -L4) and proximal femoral neck was determined using Prodigy DXA (GE Lunar, Madison, WI, USA).According to the diagnostic criteria for osteoporosis (International Osteoporosis Foundation, n.d.), normal bone mass, − 1.0 ≤ T value; osteopenia, − 2.5 < T value< − 1; osteoporosis, T value≤ − 2.5.
Body composition was measured using DXA, ASMI and fat percentage were calculated.According to the recommendations of the Asian Working Group for Sarcopenia (AWGS) (Chen et al., 2020), decreased muscles of the extremities, ASMI ≤7.0 kg/m 2 in males or ASMI≤5.4kg/ m 2 in females; normal muscle mass, ASMI >7.0 kg/m 2 in males or ASMI >5.4 kg/m 2 in females (Chen et al., 2020).High, fat percentage ≥ 30 % in males and fat percentage ≥ 40 % in females; normal, fat percentage < 30 % in males and fat percentage < 40 % in females.The same physician performed all DXA measurements.

Musculoskeletal mobility
Hand grip strength was evaluated using an electronic dynamometer (EH101; Camry, China) using the standard position of grip strength test recommended by the American Society of Hand Therapists in 1992 and averaged over three repeated measurements.Low grip strength (Chen et al., 2020), males<28 kg, females<18 kg; normal grip strength, mal-es≥28 kg, females≥18 kg.
Gait speed measurements were calculated the time of the walk of 6 m.According to European and Asian recommendations on gait speed standards (Chen et al., 2020), low speed, gait speed <1.0 m/s; normal speed, gait speed ≥1.0 m/s.Repeated measurements were taken three times and averaged.

W. Sun et al.
A quick tool named short physical performance battery (SPPB) was developed by the National Institution Aging, a National Institutes of Health division, to test lower limb muscle strength and assess performance status and includes 2.44 m step speed, standing balance, and five sit-to-stand tests (Phu et al., 2020).Poor performance: total SPPB score < 9; normal performance: total SPPB score ≥ 9.

Fracture risk assessment and fall risk assessment
Fracture risk assessment tool (FRAX), a tool for fracture risk prediction recommended by the World Health Organization, was used to calculate the probability of hip fracture (HF) and any major osteoporotic fracture (MF) in the next ten years (Sheffield Uo, n.d.).Respondents were asked to provide information on various factors, including age, gender, height, weight, past history of brittle fractures, family history of hip fractures (specifically among parents), smoking habits, alcohol consumption, and other relevant risk factors for secondary osteoporosis.MF ≥ 20 % or HF ≥ 3 % is considered high risk for osteoporotic fractures (Lai et al., 2019).
Fall risk for older people-community setting assessment tool (FROP-Com) (Department of Health and Human Services SGoV, n.d.), a scale developed by the Australian National Ageing Research Institute, was used to assess the risk of falls in community-dwelling older adults.A comprehensive tool that encompasses 13 categories and 28 questions.The survey questions covered a wide range of areas, including fall history, current medication usage, number of chronic diseases, sensory loss, footwear and clothing appropriateness, cognitive status, continence, nutritional status, home environment, regular activity level, and balance ability.The scale is graded on a scale of 60, with a score of ≥12 indicating a high risk of falling (Mascarenhas et al., 2019).

Three-dimensional gait analysis to detect trajectories of the center of mass and BMFI calculation
Three-dimensional gait analysis system (VICON NEXUS 1.8.5) from the biomechanics laboratory of Shuguang Hospital Affiliated to Shanghai University of Traditional Chinese Medicine with 16 Vicon T40s infrared high-speed cameras (acquisition frequency 100 Hz), 4 AMTI three-dimensional force stations (AMTIOR6Series, USA) (acquisition frequency, 1000 Hz) and NORAXON (Telemyo DTS, USA) were used to record the trajectories of the subject's center of mass during movement.
SMD model of a human (Fig. 1), where M represents the static mass of the human body, the elastic coefficient K represents the elastic characteristics of the human body and the damping coefficient C considers the energy dissipation characteristics during human movement.Biomechanically, K is a measure of the overall stiffness of the human body, and its value reflects the elastic properties of the tendons, ligaments, bones, the density of the muscles, and their tightness to the bones of the human body macroscopically.Because the influential elements are numerous and difficult to test, the SMD model is often described using the self-oscillation frequency f, i.e.
√ BMFI calculation refers to the method proposed by Zhang et al. (2016).The equation of motion of the human body is first expressed as: In Eq. ( 1), M, C, and K are the mass, damping, and stiffness parameters of the human body, u, u and ü are the displacement, velocity, and acceleration of the center of mass of the human body, respectively, and F bio is the internal driving biological force, which can be further expressed in the form of Fourier series.
In Eq. ( 2) ai, bi is the coefficient of the Fourier series, fp is the cadence (not the human body's frequency) when the subject walks, and n is the order of the model.By gait analysis, meanwhile, the trajectories of the subject's center of mass were obtained, and at each moment during the whole walking test, the Eq. ( 1) was satisfied, i.e.
Rewriting Eq. (3) to matrix form, then Where, Because the mass of the human body is known, the stiffness, damping, and biological force coefficients of the human body can be identified by Eq. ( 3) using the least-squares principle i.e.
Finally, the frequency of the human body was calculated from the The self-oscillation frequency f is a parameter that comprehensively reflects the mass and elastic characteristics of the human body and is an inherent characteristic value of the human body.The higher the stiffness K, the higher the frequency value f, and the lower the stiffness, the lower the frequency.The mass of the human body is composed of the weight of the muscle tissue and skeletal system of the human body.In contrast, the stiffness of the human body mainly characterizes the quality, quantity, and distribution characteristics of the muscle-skeletal unit of the body.BMFI is combined with the calculation of human body self-oscillation frequency f and BMI, which can comprehensively reflect the quality, quantity, and distribution characteristics of the muscle-bone unit and the mechanical properties of the quality and stiffness of the human musculoskeletal system.
The BMFI value of the older people can be obtained from the gait trial data using MATLAB software according to the above calculation steps.For the accuracy of the data, the subject's gait examination was performed by an experienced physician.Moreover, the physician for the gait examination performed separately from the physician who assessed DS to prevent learning additional information about the subjects.

Statistical analysis
Data in this study were statistically analyzed using IBM SPSS 23.0 (SPSS, Inc., Chicago, IL, USA).Variables were tested for normality and presented as mean ± standard deviation (x ± s) or median (interquartile range) [M (Q1, Q3)].The independent t-test or Kruskal-Wallis test was performed for differences in indicators between the two groups.Pearson and Spearman correlation analysis was used for data.Logistic regression analysis was performed to analyze the impact of BMFI on the population with DS.The sensitivity and efficacy of BMFI in the diagnosis of DS were analyzed by Receiver Operator Characteristic curve (ROC curve).A Pvalue <0.05 was considered statistically significant.

Baseline analysis of subjects
A total of 204 community-dwelling older subjects were included, including 36 males and 168 females.According to the diagnostic criteria for DS, there were 105 cases in the DS group and 99 cases in the non-DS group.Table 1 presents a comparison of descriptive data between the two groups.Variables differed between older adults with and without DS, except for age and gait speed.There was no significant difference in self-oscillation frequency f between the two groups, while there was a significant difference in BMFI.

Differences in BMFI between community-dwelling middle-aged and young
Sixty-eight young adults aged 20-29 years in the database of Shanghai Tongji University were used as normal controls, including 54 males and 14 females.The BMFI and self-oscillation frequency f of two subjects of different age groups were compared and analyzed.The selfoscillation frequency f was lower than the self-oscillation frequency f in the group of young people.The BMFI was higher in the group of older people than in the group of young people (Table 2, Fig. 2).

Influential factors of f and BMFI in community-dwelling older people
According to the grading criteria for bone mineral density, body fat percentage, ASMI, grip strength, gait speed, fracture risk, and fall risk, different groups were compared for BMFI and self-oscillation frequency f in different groups (Table 3).The results showed that f of the high body fat percentage group and the low-speed group were lower than the normal group, and BMFI was higher than the normal group.The f of the osteoporosis group, low ASMI group, and low grip strength group were not different from the normal group.BMFI was lower than the normal group.The f of the low-performance group was lower than the normal group, and BMFI was not different from the normal group.There was no difference in f between the high fracture risk group and the normal group, and BMFI was lower than that in the normal group.The f and BMFI in the high fall-risk group were not different from those in the normal group.
Logistic regression was used to analyze other BMFI influential factors (normal indicator = 0, abnormal indicator = 1), and models were adjusted for age and sex (Table 4).The results showed that BMFI was a protective factor for bone, and those with high BMFI had a low risk of osteoporosis, with an OR and 95 % CI of 0 0.673 (0.582-0.778), and those with high BMFI had a lower risk of fracture, with an OR and 95 % CI of 0 0.783 (0.701-0.875).Body fat percentage, ASMI, grip strength, and gait speed of the subjects influenced BMFI (p < 0 0.05).Thus, f was associated with body fat percentage, gait speed, SPPB performance score, BMFI was associated with bone quality, fracture risk, and also with body fat percentage, ASMI, grip strength, and gait speed.

Diagnostic analysis of BMFI in community-dwelling older people with DS
BMFI, BMI, f, fracture risk, fall risk, and SPPB score were compared for the prediction of DS, respectively (Table 5), and ROC curves of BMFI for predicting DS were plotted according to the sensitivity and specificity at different cut-off points (Fig. 3).The area under the ROC curve AUC was 0.669, suggesting BMFI had some predictive value for distinguishing non-DS from DS (P < 0.01), the curve cut-off point was 16.04, the sensitivity and specificity were 0.483 and 0.774, the Youden index was 0.273, and the likelihood ratio was 0.645.BMFI had better predictive power for DS than BMI, f, fracture risk, fall risk, and SPPB score.Logistic regression analysis (Table 6) was performed to investigate the effect of BMFI on DS in the community-dwelling older population.The OR and 95 % CI values of BMFI in the non-DS and DS groups were 0.823 (0.743-0.901), respectively.The results showed that BMFI was a protective factor for DS.BMFI was divided into two groups, high BMFI and low BMFI, according to the cut-off point 1 6.04 of the ROC curve.When BMFI <16.04,OR value and 95 % CI value were 2.738 (1.509-4.967),suggesting that low BMFI had a 2.738 times higher risk of DS than high BMFI.

Musculoskeletal status for BMFI ranges
The sensitivity, specificity, cut-off points of BMFI, different performance statuses, fracture risk, fall risk, and DS diagnosis were used to obtain the range of BMFI in different groups of people (Table 7).According to the range of BMFI in different groups, the musculoskeletal status of community-dwelling older subjects corresponding to BMFI was obtained (Table 8, Fig. 4).Older adults may have osteoporosis and high fracture risk at BMFI <14.32, but a low risk of falls.At BMFI ≥16.24, the older may have non-osteoporotic and low fracture risk but a high risk of falls.

Discussion
The study is a diagnostic test analyzing qualitative and quantitative measures of BMFI models to identify patients with DS.The relevant factors of BMFI and the accuracy of BMFI in predicting DS were also analyzed.It is believed that early and accurate identification of older adults with severely reduced musculoskeletal function and appropriate and effective intervention can slow the rate of decline (Keith et al., 2017).Thus, the definition of BMFI is invaluable in identifying the elderly individuals with DS who are susceptible to falls and fractures due to the deterioration of muscle and bone function (Khaleghi et al., 2023).
In our study of older adults, subjects with DS had a higher fracture   W. Sun et al. risk than normal subjects.DS is related to a high risk of fracture, Giovanni et al. (Giovanni et al., 2015) reviewed medical records of 121 postmenopausal women over 50 years of age, and cases who had already developed fragile fractures had a higher risk of dysmobility syndrome.Bjoern Buehring et al. (Buehring et al., 2018) found a higher risk of osteoporotic fractures in men with DS.Hong et al. (2018) analyzed 1369 community-dwelling older adults and found that DS was related to an increased incidence of fragility fractures and that DS was superior to the FRAX score in discriminating fractures.The decreased SPPB scores and grip strength in subjects with DS suggest decreased levels of limb function in DS patients.A study Santos et al. (2019) has shown that jumping ability and exercise status are associated with the incidence of DS, physical activity of subjects with DS is less than their peers.Body mass index (BMI) measures the level of human health, degree of obesity, and trend of obesity.BMI increases progressively with age.Because physical activity decreases, total body energy expenditure is also gradually decreasing, and muscle loss and fat gain lead to sarcopenic obesity (Poggiogalle et al., 2021) .Because both muscle mass and fat mass are part of calculating BMI, BMI cannot distinguish different P-value <0.05 was considered statistically significant; ASMI (appendicular skeletal muscle mass index); SPPB (short physical performance battery); f (self-oscillation frequency); BMFI (body mass frequency index); B (regression coefficient beta); OR (odds ratio); CI (confidence interval).P-value <0.05 was considered statistically significant; AUC (area under the curve); BMI (body mass index); BMD (bone mineral density); ASMI (appendicular skeletal muscle mass index); SPPB (short physical performance battery); MF (major osteoporotic fracture); HF (hip fracture); BMFI (body mass frequency index).P-value <0.05 was considered statistically significant; AUC (area under the curve); BMFI (body mass frequency index); DS (dysmobility syndrome).
W. Sun et al. tissues and cannot accurately evaluate people with high body fat and low muscle mass.Skeletal muscle loss and obesity (assessed by BMI, waist circumference, and body fat percentage) are both associated with worse physical performance (Mikkola et al., 2018) .The self-oscillation frequency f reflects the trajectory of body centroid movement.Combined with BMI, this study defined BMFI as the integration of body mass and movement to reflect the status of musculoskeletal function.
The results showed that self-oscillation frequency f was low and BMFI was higher in older than in young subjects.BMFI comprehensively evaluated the relevant muscle and bone state in the whole body.The self-oscillation frequency f is closely related to the human body density.The self-oscillation frequency f was higher in young people, indicating that the muscle and bone system function was better than in older people.Older people have low reaction speed and low self-oscillation frequency f.When encountering ground obstacles or emergencies, the gait balance is affected, and muscle strength also decreases with age, making older people highly susceptible to falls (Grimmer et al., 2019) .BMFI was lower in young people than in older people.Among older subjects, those with high BMFI had a lower risk of DS.However, low BMFI was present in young adults, while the prevalence of DS was low and musculoskeletal mobility was higher than in older adults.Therefore, we believe a more profound connection exists between BMI and f, and BMFI may have a different scope of application between different ages.
The FRAX Tool is an assessment software based on a large sample of evidence-based medical data and has reasonable specificity for assessing osteoporotic fracture risk (Sheffield Uo, n.d.).FROP-Com is a fall risk assessment tool that can identify risk and contributing risk factors, with good reliability and modest fall prediction ability (Mascarenhas et al., 2019) .BMFI had some predictive effect on DS, and AUC area and specificity were higher than BMI, FRAX fracture risk tool.Frop-com falls risk tool for DS, providing relevant information for clinical practice.Low BMFI was associated with DS even after adjusting for confounding factors (sex, age).Even if DS represented a high fracture risk and a high fall risk population, there were differences in the diagnostic results of DS and the results of fracture and fall risk assessment tools.Therefore, the range of BMFI in different musculoskeletal statuses was obtained according to the cut-off point of BMFI in the prediction results.Older adults may have DS when BMFI is low.Older adults may have osteoporosis and high fracture risk with lower BMI or higher f, but at the same time, they also mean a lower risk of falls.When BMFI is too high, older people may be diagnosed with non-DS, non-osteoporosis, and low fracture risk, but elevated BMFI may predispose subjects to falls.Therefore, BMFI may also require a comprehensive multifactorial assessment of musculoskeletal status in clinical applications.
The predictive ability of BMFI for DS has some correlation with the specific influential factors of BMFI and DS diagnosis.Decreased bone mineral density is a major risk factor for fragility fractures (National Institute for Health and Care Excellence, 2012).BMFI has specific diagnostic values for osteoporosis.BMFI positively correlates with bone mineral density, and high BMFI is a protective factor for bone mass.In previous studies, BMI was a protective factor for bone mass, and BMFI was consistently associated with bone mass in the absence of significant changes in f.Whereas subjects with high fracture risk had lower BMFI than healthy older, BMFI was associated with high fracture risk in community-dwelling older people.There was no difference in BMFI in subjects with a high risk of falls compared to normal older, and further analysis showed that BMFI remained not significantly associated with the risk of falls in this study.However, in an analysis where BMFI predicted the risk of falls, subjects had a low risk of falls when BMFI <14.32.BMFI has some association with the risk of falls, and further evidence is needed.
BMFI was positively correlated with grip strength and gait speed in this study, and BMFI was lower in subjects with low grip strength and slow gait speed than in normal subjects, suggesting that BMFI is closely related to muscle strength.Grip strength not only reflects an individual's overall muscle strength, physical function, and nutritional level (Ostolin et al., 2021), but also is related to osteoporosis risk, length of hospital stay, and mortality (Richard and Bohannon., 2015).Katharina Denk et al. (Katharina et al., 2018) revealed a close relationship between reduced grip strength and the incidence of hip fracture in a metaanalysis and concluded that further investigation of the relationship between grip strength and fracture risk might be used to identify people at high risk of fracture in the future.Sufficient lower limb muscle strength is required for functional activities in older adults, which correlates with gait speed and SPPB scores.SPPB scores included sit-tostand, balance, and gait speed.BMFI was not significantly correlated with the total score, suggesting BMFI may not be significantly associated with sit-to-stand and balance.This study had an association between BMFI and body fat percentage, and BMFI was higher in the high body fat percentage group than in the normal body fat percentage group, indicating that BMFI increases with body fat percentage.BMFI was positively correlated with ASMI, and BMFI in the low ASMI group was lower than that in the normal ASMI group, representing that BMFI gradually decreased with the decrease of ASMI.The study showed a correlation between BMFI and muscle mass.
Besides the weakening of musculoskeletal system, there are many  factors that affect the quality of life of the elderly.A study found that the components that most influence the quality of life are closely linked to health, interpersonal relationships, functional autonomy and maintaining an active life.These key factors are maintaining a good level of functional abilities, the absence of physical illnesses and psychological problems, maintaining adequate levels of physical activity and regularly using health and social services, and showing satisfaction with the quality of these services (Agustí et al., 2023).This study still with few limitations.Firstly, the sample size limit the generalizability of the findings.Secondly, the subjects recruited were limited to elderly individuals residing in the community proximal to the researcher's hospital, excluding those from other regions and provinces.This geographical bias may have influenced the representativeness of the study population.Future research endeavors should aim to broaden the recruitment scope and increase the sample size to provide a more comprehensive and robust dataset for subsequent analysis.

Conclusions
In summary, we established a BMFI index that showed significant differences in musculoskeletal status between DS and non-DS older people.Compared to other measures, including the FRAX tool, fall risk assessment tool, and SPPB performance score, BMFI is more suitable for predicting DS with high specificity.We recommend BMFI examination for older adults as a screening tool to warn of the risk of DS.The cut-off value of BMFI can be used as a reference value for identifying and intervening DS.In addition, BMFI has a specific correlation with bone mineral density, muscle mass, body fat percentage, and grip strength but has no significant correlation with gait speed and fall risk.We investigate BMFI to gain a deeper understanding of the musculoskeletal system among the elderly, enabling us to proactively manage the risk of falls and fractures.The future research would dedicated to exploring the predictive and management potential of BMFI in olderly individuals with musculoskeletal system diseases.

Fig. 2 .
Fig. 2. Comparison of self-oscillation frequency f, BMFI in young and older groups.

Table 1
Baseline data analysis of the subjects [x ± s or M (Q1, Q3)].

Table 2
Comparative analysis of BMFI and f (x ± s).The difference was statistically significant compared to the young group (p < 0.05).BMI (body mass index); f (self-oscillation frequency); BMFI (body mass frequency index). *

Table 3
Comparative analysis of f and BMFI in different groups (x ± s).

Table 4
Logistic regression analysis of BMFI influential factors.

Table 6
Logistic regression analysis of BMFI in different DS groups of communitydwelling older adults.

Table 7
BMFI Diagnostic analysis of DS, bone quality, and risk of fall fracture.

Table 8
BMFI in community-dwelling older people musculoskeletal status range.DS, osteoporosis, high fracture risk, low risk of falls 14.32 ≤ BMFI <14.87 DS, non-osteoporosis, high fracture risk, low risk of falls 14.87 ≤ BMFI <16.04 DS, non-osteoporosis, high fracture risk, high risk of falls 16.04 ≤ BMFI <16.24 Non-DS, non-osteoporosis, high fracture risk, high risk of falls BMFI ≥16.24 Non-DS, non-osteoporosis, low fracture risk, high risk of falls