Research on Optimization of Indoor Layout of Homestay for Elderly Group Based on Gait Parameters and Spatial Risk Factors Under Background of Cultural and Tourism Integration

Abstract

This study, in response to the optimization needs of fall risks for the elderly in the context of cultural and tourism integration in Hebei Province, China, established a quantitative correlation system between ten gait parameters and ten types of spatial risk factors. By collecting gait data (Qualisys infrared motion capture system, sampling rate 200 Hz) and spatial parameters from 30 elderly subjects (with mild, moderate, and severe functional impairments), a multi-level regression model was established. This study revealed that step frequency, step width, and step length were nonlinearly associated with corridor length, door opening width, and step depth (R² = 0.53–0.68). Step speed, ankle dorsiflexion, and foot pressure were key predictive factors (OR = 0.04–8.58, p < 0.001), driving the optimization of core spatial factors such as threshold height, handrail density, and friction coefficient. Step length, cycle, knee angle, and lumbar moment, respectively, affected bed height (45–60 cm), switch height (1.2–1.4 m), stair riser height (≤35 mm), and sink height adjustment range (0.7–0.9 m). The prediction accuracy of the ten optimized values reached 86.7% (95% CI: 82.1–90.3%), with Hosmer–Lemeshow goodness-of-fit x² = 7.32 (p = 0.412) and ROC curve AUC = 0.912. Empirical evidence shows that the graded optimization scheme reduced the fall risk by 42–85%, and the estimated fall incidence rate decreased by 67% after the renovation. The study of the “abnormal gait—spatial threshold—graded optimization” quantitative residential layout optimization provides a systematic solution for the data-quantified model of elderly-friendly residential renovations.

1. Introduction

With the in-depth implementation of the cultural and tourism integration strategy in Hebei Province, the coupling and interaction between cultural resources and the tourism industry has been gradually strengthened. Hebei Province has rich and diverse cultural tourism resources, which have unique historical, aesthetic, and economic values and are favored by elderly tourists. As a major province of health tourism, Hebei Province has an increasing proportion of elderly tourists, and the construction of cultural tourism homestays for the elderly has become an important aspect of improving the quality of tourism services. However, at this stage, the interior layout design of B&Bs generally lacks safety considerations for elderly tourists, especially those with abnormal gaits, which leads to an increased risk of falls for elderly tourists during accommodation, affecting the tourism experience and the healthy development of the industry. Therefore, it is of practical significance to deeply discuss the optimization and age-appropriate transformation of the interior layout of B&Bs in the context of the integration of culture and tourism in Hebei Province to promote the high-quality development of the cultural and tourism industry. According to the “Test Report on Physical Fitness and Fall Risk of the Elderly” released by the China Research Center on Aging (CRCA), the “Technical Guidelines for Fall Intervention in the Elderly” issued by the China Medical Rescue Association (CADERM), and the data from the Chinese Bureau of Statistics [1,2,3], the incidence of falls in indoor spaces for the elderly population with abnormal gait of the lower limbs in China was 32.5% in 2020, increased to 38.7% in 2023, with an average annual growth rate of 4.8%, and is expected to reach 41.2% in 2025. The proportion of fractures following falls increased from 22% in 2020 to 26% in 2023, with hip fractures accounting for the highest proportion (58%). A fall is a sudden, involuntary, unintentional change of position that falls to the ground or a lower plane. According to the International Classification of Diseases (ICD10), falls can be divided into the following two categories: falls from one plane to another; falls on the same plane [4].

The current aging-friendly design has a theoretical gap in the “biomechanical mechanism-environmental intervention”. Converting gait dynamic parameters into quantifiable spatial safety thresholds is the main problem to be solved in this study. By establishing a gait–space correlation model, the cross-scale matching problem between abnormal gait in the elderly and environmental risk factors is addressed. The importance and urgency of falls as a global public health problem is becoming increasingly prominent as the world’s population ages [5]. With the decline of physical function and the increase of chronic diseases, falls are more prevalent in older adults and are one of the important causes of physical pain, disability, disability, and death in older adults, as well as the leading cause of injury-related death in older adults [6,7,8]. Falls can be classified as fatal and non-fatal. The physical consequences of nonfatal falls often include soft-tissue injuries, joint sprains, fractures, and head injuries [9]. The elderly population with abnormal gait is based on the real problem of inconvenient mobility, and most of the range of activities and time are in the indoor space of the home. Studies have shown that approximately 55 percent of fall-related events occur in the home, especially in spaces with stairs and other risk factors [10], especially in restrooms or stairwells, where injuries are most severe and are much more likely to occur in restrooms than in other indoor locations, such as living rooms [11,12].

1.1. Current Status of Research and Measures Related to Fall Risk

According to the summary of many scholars’ research, about 80% of the elderly have at least one risk of falling at home, and about 40% of them have more than five risk factors at home. Only 3.8% of homes in the United States are suitable for older adults with moderate mobility impairment [13]. The Joint Center for Housing Research at Harvard University [14] investigated five characteristics of aging housing in each region, including whether there are steps at the entrance; whether there are stairs in the living space; whether the position of the switch is in line with the elderly population with abnormal gait; and whether the corridors and doors adapt to the passage of older people with abnormal gait. Doorknobs and faucet handles are the most age-friendly in the western United States and the least in the Northeast, according to which only 57% of existing homes have more than one of these age-appropriate features. The English Housing Survey 2014–2015 showed that one in five older people lived in a house that did not meet the DecentHomes Standard in 2014, with those aged 85 or over more likely to live in such a house (29%) [15]. According to a study in Taiwan [16], 60.4% of the elderly have environmental risks in their homes, and the environmental risks are most common in the bathroom, followed by the bedroom, and the risk of indoor risk factors in urban areas is significantly higher than that in rural areas.

For older adults with gait anomalies, insufficient foot clearance may be an important cause of falls [9,17]. When encountering bad road conditions, people tend to avoid imbalance by raising the height of the soles of the swinging legs [18], but this will also consume more energy [19], making people feel tired and uncomfortable. Verdonck M [20] emphasizes that the pre-discharge home visit considers the patient’s home environment and assesses how the patient performs some activities of daily living in his or her familiar environment. A key role of the occupational therapist in the rehabilitation team is to perform pre-discharge home visits and advise on appropriate home modifications to enable patients to live independently after discharge. Nikolaus [21] used a family intervention team to prevent falls in older people with a history of repeated falls. Stevens [22] showed in the American Journal of Preventive Medicine that the risk of falls in the environment can be reduced by occupational therapists providing home-appropriate modifications and clinical management of the risk of falls. For some scholars, they have found and focused on the renovation of indoor spaces, such as poor ventilation and lighting conditions, improper functional zoning, lack of safety handrails, and slippery floors, and the most common renovation needs include the installation of emergency call devices, improved lighting conditions, and the addition of safety handrails [23,24,25]. Other scholars have conducted in-depth research on the age-appropriate transformation of the space in old residential suites in China from the aspects of space design and technical realization in combination with specific communities, apartments, spaces, and other projects [26,27,28]. Research in the field of elderly care services is more inclined to practical application, focusing on the organization and management, resource allocation, and process optimization of home renovation services, as well as focusing more on design details, including the grasp of the size of indoor space, the control of physical space layout, and the selection of facilities and equipment [29]. According to the review of the previous research on the analysis of the risk factors of indoor layouts and the many solutions and methods for the indoor factors of the elderly with lower limb abnormalities, it can be found that from the perspective of the hospital or rehabilitation center, the experiment will be carried out by means of assessment and the use of intervention teams, so that the patient can reduce the risk of falls in a fixed space environment in the future. On the other hand, the researchers used the statistical weighting method to determine the importance of indoor risk factors on the impact of falls through the statistical documents of relevant institutions, such as the modification of the size of each indoor standard to facilitate the passage of different types of patients, the change in friction on the floor in the living room and bathroom, and the safety handrails that often need to be supported. For example, Suzhou divides renovation content into entrance and exit renovation, door renovation, bedroom renovation, bathroom renovation, kitchen renovation, etc. There are also some areas that divide renovation projects according to the purpose of the renovation; for example, Shanghai divides renovation content into safety renovation, barrier-free renovation, and cleanliness renovation. From the specific content, through the statistical content of the relevant policy documents of each city, it is found that the installation of handrails, non-slip floors, the setting of bath stools, the setting of toilet chairs, the elimination of height differences, and toilet renovation are effective, as shown in Figure 1.

However, at present, there are not many indoor layout optimization studies on the elderly with abnormal gait of the lower limbs, and the improvement factors are obtained through expert interviews, questionnaires, literature analysis, census analysis, etc., and the foothold research for the acquisition of gait data is often for engineering robots and positioning research. There is a lack of research on the optimization of risk factors for indoor dwellings by statistically quantifying directly through patient gait acquisition, but this is a more practical way to optimize the indoor layout of patients with lower limb gait problems.

1.2. The Current State of Fall Risk Assessment Tools

In order to achieve the study of fall factors and establish a statistically significant model related to falls, researchers have developed many risk assessment tools for different purposes in the many statistical analyses and evaluations of abnormal gait in the elderly.

The Berg Balance Scale was published by Berg et al. in 1989 [30] and was developed by 10 professionals to investigate 32 people over 60 years old at three different stages. The content includes 14 items: from sitting to standing, standing independently, sitting independently, from standing to sitting, bed–chair transfer, standing with eyes closed, standing with feet together, standing with upper limbs stretched forward, standing from the ground picking up objects, turning around and looking back, turning around, stepping on steps alternately with both feet, standing with both feet back and forth, and standing on one leg. Each entry is 0–4 points and is divided into three groups of 0–20 points, 21~40 points, and 41~56 points according to the score, and the represented balance ability corresponds to the three states of wheelchair riding, assisted walking, and independent walking. Fewer points are scored for worse balance, and a total score of <40 indicates a risk of falling [30]. The Timed get-Up-and-Go Test (TUGT) requires patients to get up from their chairs, walk a short distance, turn around, return, and sit down again. Forty elderly patients with some balance ability were tested and videotaped, observers from different medical backgrounds watched the score, and the balance function was scored on a five-point scale. The less time it takes, the better the balance ability. The same patients underwent laboratory tests for gait and balance, and the subjective scores of observers for clinical trials correlated well with laboratory test tests. TUGT focuses on the assessment of the subject’s ability to balance dynamically, with a time of <20 s to complete movements and an independent ability to move; a time of >30 s indicates that the subject needs help to complete most of the activity and is at risk of falling [31]. In 2020, Liu Shuwen [32] collected data from 20 elderly people and established a logistic regression model through logistic regression, including five items—gender, active position perception of knee joint, bipedal eye opening envelope area, full length of bipedal eye opening pressure center of gravity, and horizontal swing of bipedal eye opening pressure center—with an area under the ROC curve of 0.70, a sensitivity of 71.4%, and a specificity of 61.5%, indicating that the prediction performance was more adaptable.

In summary, many researchers have conducted different forms of research on the statistical prediction model of fall risk assessment according to their respective characteristics, in terms of applicable population, risk assessment index selection, and tool construction methods, but there is still room for improvement in the construction of risk assessment statistical models for abnormal gait populations and indoor residential risk factors, so as to provide a scientific statistical basis for screening high-risk groups of falls and formulating individualized interventions to prevent or slow down the occurrence of falls.

1.3. Objectives

Currently, a relatively mature method system for biomedical signal processing technology has been established in the field of gait analysis and fall risk prediction for the elderly. Through three-dimensional motion capture (such as the Qualisys infrared system), inertial measurement units (IMUs), and plantar pressure distribution sensors, researchers can accurately quantify dynamic parameters such as step frequency, step width, step speed, and joint range of motion. They also use methods like Butterworth filtering and wavelet transform to suppress electromyographic interference and device noise, thereby improving the signal-to-noise ratio. In the field of rehabilitation medicine, such data have been widely used to construct gait abnormality assessment models (such as the Tinetti scale and Berg Balance Scale), and algorithms like logistic regression and random forest are employed to predict fall risk (with the ROC curve AUC reaching 0.70–0.85). However, there is still a significant gap in the application of this technology to architectural environment design. Existing research mainly focuses on clinical diagnosis or the development of rehabilitation assistive devices (such as exoskeleton robot design), and it rarely establishes quantitative correlations between gait dynamic parameters and spatial physical properties (such as the ground friction coefficient and step depth). For instance, an insufficient ankle dorsiflexion angle as a high-risk factor for falls (OR = 8.58) has been confirmed, but its adaptation relationship with handrail density and threshold height lacks systematic modeling. Most aging-friendly renovations rely on static anthropometric dimensions (such as uniformly lowering bed heights to 45 cm), without considering the time-varying characteristics of gait (such as the need to dynamically adjust the switch height when the gait cycle is prolonged) and functional impairment grading (differences between mild, moderate, and severe). Although Peel N and others have identified risk factors such as the absence of bathroom handrails, they have not associated them with gait biomechanical mechanisms (such as the need for trunk instability when lumbar moment exceeds 150 N·m). Rehabilitation medicine emphasizes individualized training programs, while architectural design often adopts universal standards, leading to a break in the mapping chain between biological signals and spatial parameters. For example, the finding that a reduced step frequency (60 steps/min in the severe group) requires a shorter corridor buffer distance has not been incorporated into existing residential design standards.

Based on the research and solution measures of fall risk factors and the current situation of fall risk assessment tools, this paper finds that the relevant research from these two aspects is relatively complete, but the research on the layout design of indoor housing in the elderly population based on gait data to solve gait abnormalities is missing content in the current research, and it is often used as gait data research in the fields of human rehabilitation equipment, medical clinical analysis, and intelligent equipment that requires data learning [33]. However, the design and layout optimization of indoor housing is often completed through the experience of design researchers, and the focus of interior residential design is more for the stylized design of elderly groups with abnormal gait of the lower limbs after quantitative statistical analysis of the interior design after gait data analysis. At the same time, as the research results of interior design based on lower limb rehabilitation, it provides a basis for the systematic and in-depth study of the spatial movement of patients with lower limb problems in the later stage (such as the application of intelligent walkers in space).

This study aims to bridge the technological gap between biomedical signal processing, rehabilitation analysis, and environmental design by establishing a quantitative correlation system of “gait parameters—spatial risk factors”, providing a new paradigm for data-driven precise aging-friendly renovations, Figure 2 shows the flow chart of the visual framework from gait acquisition to spatial optimization in this study.

2. Materials and Methods

In order to comprehensively obtain the classification and gait data of the elderly population with abnormal gait to the greatest extent, this study collected gait data including spatiotemporal parameters as well as the kinematics and dynamics (cadence, step width, step length, stride length, gait cycle, knee range of motion, ankle dorsiflexion angle, lumbar flexion moment, plantar pressure) of patients with mild to severe gait abnormalities by using 3D motion capture (sensor) and then classified the data population by scale. In this way, it provides data for the establishment of regression models to establish the association between gait data and indoor risk factors.

2.1. Acquisition of Abnormal Gait in the Elderly Population

This study selected patients over 60 years old who visited the rehabilitation department of the Traditional Chinese Medicine Hospital in Qinhuangdao City and had abnormal gait of the lower limbs between 2022 and 2024. After the senior doctors in the rehabilitation department understood the purpose of this study, 30 suitable patients and 10 individuals who met the age requirements and had no abnormal gait of the lower limbs were selected and screened to participate in the data collection of this experiment. The inclusion criteria for the healthy group were no history of neuromusculoskeletal diseases, no fall incidents in the past year, and a total Tinetti score of ≥26 points. The diagnosis of abnormal lower limb gait was in accordance with the “Guidelines for Interventional Techniques for Elderly Falls” for those aged ≥ 60 years, along with clear consciousness, self-care ability for daily activities, and being able to cooperate with the examination.

Gait analysis is a core method in rehabilitation medicine, biomechanics, and neuroscience research. Its accuracy and reliability directly affect the validity of clinical and research conclusions. The Qualisys motion capture system, as a representative of optical motion capture technology, captures the trajectories of reflective markers with multiple cameras in synchronization, achieving sub-millimeter-precision measurement of joint kinematic parameters. The Qualisys system is equipped with 8–12 infrared cameras, with a coverage area of up to 6 × 2.5 × 2 m³, and it supports multimodal synchronization with force platforms, surface electromyography (EMG) devices, and inertial measurement units (IMUs), enabling synchronous acquisition of kinematics, dynamics, and electromyographic signals. This article, based on recent research, systematically reviews its reliability and application value in obtaining gait parameters.

Eight Qualisys high-performance infrared cameras were used for gait analysis, along with two force plates and other supporting equipment (information conversion controller, computer workstation, infrared fluorescence labeling sphere), space equipment, and preparation, as shown in Figure 3, Figure 4, Figure 5, Figure 6, Figure 7, Figure 8 and Figure 9.

Before the commencement of the three-dimensional motion capture experiment, all external light sources caused by external signals, except for the laboratory lighting, should be eliminated. During data collection, the indoor temperature should be kept comfortable. Prior to the experiment, calibration should be conducted in the experimental space using measurement devices, and the range to be measured during the experiment should be predetermined. The experiment can commence when the test value is below 0.8, as shown in Figure 5. Prior to each data collection, it is necessary to perform system axis calibration to ensure that the calibrated coordinate system meets the testing requirements, as illustrated in Figure 8.

Sensor calibration is the core guarantee for the reliability of data in the optical motion capture system. The Qualisys system captures the trajectory of marker points with multiple cameras in synchronization, achieving sub-millimeter accuracy measurement of joint kinematic parameters. Firstly, lens distortion is eliminated, including radial distortion (such as barrel distortion) and tangential distortion (due to lens installation tilt). By shooting a chessboard calibration plate with known spacing, the focal lengths (fx, fy), principal point offsets (cx, cy), and distortion coefficients (k1, k2, p1, p2) are calculated to complete the internal parameter calibration. Next, the position and orientation (rotation matrix R and translation vector t) of the camera in the world coordinate system are determined. A global coordinate system needs to be established through a dynamic reference frame (DRF) or a calibration rod (L-Frame) to complete the external parameter calibration.

The subjects’ bilateral lower limbs and lower back were fully exposed for the preparation of the lower limbs, ensuring that the areas where attachments were to be affixed were thoroughly cleaned. Basic information such as the patient’s name, gender, age, height, and weight was entered into Qualisys software. The CAST lower limb model was selected as the gait model, and 30 marker points were chosen according to the CAST lower limb gait model, with infrared fluorescent marker spheres affixed to the subjects’ lower limbs, as shown in Figure 10.

At the same time, we invited 30 patients and 2 control subjects without lower limb gait abnormalities of matching age to begin data collection. During the data collection process, since the ultimate research goal is to optimize risk factors in indoor residential settings, we will only collect the following relevant data, observing the spatiotemporal parameters, kinematics, and dynamics of the four groups of subjects during their walking process: (1) step frequency—the average number of steps taken per minute during walking (steps/min); (2) step width—the horizontal distance (m) between the center points of both heels during walking; (3) step length—the average distance (m) from one foot’s contact with the ground to the opposite foot’s contact during walking; (4) step speed—the average speed (m/s) during the walking process; (5) stride—the distance from the contact of one foot to the subsequent contact of the same foot, also known as step length (m); (6) gait cycle—the time process (s) from when one lower limb’s foot makes contact with the ground to when it makes contact again; (7) knee joint range of motion (knee flexion angle)—the range of motion (°) of knee flexion and extension during the gait cycle; (8) ankle dorsiflexion angle—the angle of the action where the toes are raised towards the tibia; (9) lumbar flexion moment—the bending load produced in the lumbar spine due to external forces when the body is bent forward or under load; (10) plantar pressure—the pressure exerted by both feet on the ground, which can be used to determine the center of pressure distribution during walking. Appendix A contains the relevant data results obtained from a three-dimensional motion capture laboratory for 30 elderly individuals with lower limb gait abnormalities and 2 control group subjects without lower limb abnormalities, processed for availability. The 30 patient datasets in the Appendix are categorized based on assessments of gait abnormalities by experienced rehabilitation physicians, classified, respectively, as mild, moderate, and severe abnormalities.

The gait signals of the elderly are prone to interference from electromyography, joint tremors, and equipment collection errors and thus require digital filtering techniques to suppress noise. In this study, a Butterworth low-pass filter was used for signal smoothing. The Butterworth filter has the smoothest amplitude–frequency response within the passband and can retain the low-frequency features (such as walking speed and step length trend) in the gait cycle to the greatest extent, while attenuating high-frequency noise (such as electromyographic interference and sensor jitter). Compared to adaptive algorithms like Kalman filtering, the parameters of the Butterworth filter are clearly defined (cut-off frequency, order), and it is applicable to periodic biomechanical signals such as gait.

The order of the filter is set to 4 (with a decay rate of 24 dB per octave), and the balance calculation efficiency is determined based on the stopband attenuation requirements; the cutoff frequency is 10 Hz, which is set according to the characteristics of the gait signal (the energy of the gait signal of the elderly is concentrated in the range of 0.5–5 Hz, and high-frequency noise is greater than 10 Hz), and the filtering equation is shown in Formula (1).

$$H(s)={\displaystyle \frac{1}{\sqrt{1+{\left(\frac{s}{s_c}\right)}^8}}}(s_c=2\pi \times 10\mathrm{Hz})$$

(1)

To evaluate the filtering effect, a synchronous test was conducted to assess the retention ability of the three filtering methods for the peak point (heel-strike) of the foot pressure trajectory, as shown in

Table 1. Comparison of the three filtering methods for the peak points of the foot pressure trajectory.

Filtering Method	Signal-to-Noise Ratio Improvement (dB)	Gait Event Detection Error (ms)	Applicable Scene
Butterworth Filter (in this study)	18.7	12.3 ± 4.1	Steady gait under strong noise
Moving average filtering	9.2	35.6 ± 8.7	Slow and smooth movement
SG filtering (Savitzky–Golay)	14.5	18.9 ± 5.3	Retention of high-frequency transient signals

.

After filtering, the coefficient of variation of key gait parameters significantly decreased (the fluctuation of walking speed changed from 18.7% to 9.3%, and the fluctuation of step length changed from 15.2% to 7.8%), and the phase characteristics of the ankle joint angle trajectory became clearer, meeting the stability requirements for subsequent logistic regression modeling.

Next, the Tinetti Balance and Gait Scale (POMA) was used for quantitative assessment and fall risk analysis. The assessment strictly followed the standardized process of the Tinetti scale (balance test: 9 items/16 points + gait test: 8 items/12 points; total score: 28 points), and it was combined with dynamic gait parameters (walking speed, step length, step frequency, etc.) and static biomechanical indicators (joint angles, plantar pressure) for comprehensive mapping. According to the mapping rules of the Tinetti score, in terms of gait initiation, walking speed ≤ 0.3 m/s → 0 points (hesitant initiation); 0.31–0.6 m/s is 1 point; > 0.6 m/s → 2 points. For foot lift height, ankle dorsiflexion angle > 7° or peak foot pressure > 350 kPa is foot dragging (0 points). In terms of spinal stability, lumbar torque > 150 N·m is trunk swaying, requiring support (0–1 points). For gait symmetry, step length difference > 30% → 0 points (unequal step lengths for both feet).

Table 2. Balance test (full score: 16).

Test Item	Standard for Evaluation	Average Score of Group L	Group M Average Score	Group S Average Score
Seated balance	Lean back/slide down = 0; stability = 1	1.0	0.9	0.3
Stand	Unable to stand = 0; requires arm assistance = 1; can stand independently = 2	1.8	1.2	0.5
Number of standing-up attempts	Unable to stand up = 0; requires multiple attempts = 1; successfully completed once = 2	2.0	1.5	0.7
Instant standing balance (first 5 s)	Shaking = 0; requires support = 1; stable without support = 2	1.9	1.3	0.6
Standing balance	Shaking = 0; wide step distance/requires support = 1; narrow step distance without support = 2	1.7	1.0	0.4
Light push test	Fall tendency = 0; shaking to grasp = 1; stability = 2	1.6	1.1	0.3
Stand with eyes closed	Unstable = 0; stable = 1	0.9	0.6	0.1
Turn around 360 degrees	Step interruption = 0; shaking = 1; continuous stability = 2	1.7	1.0	0.4
Be seated	Sitting down = 0; unsteady movement = 1; safe and stable = 2	1.6	1.1	0.5
Total balance score		14.2	9.8	3.8

and

Table 3. Gait test (full score: 12).

Test Item	Standard for Evaluation	Average Score of Group L	Group M Average Score	Group S Average Score
Starting	Hesitation/multiple attempts = 0; normal startup = 1	1.0	0.7	0.2
Foot lifting height (left and right)	Mopping floor/too high = 0; distance from the ground ≤ 5 cm = 1 (scored independently for each foot)	1.8	1.2	0.5
Step length (left and right)	Not exceeding the contralateral limb = 0; exceeding = 1 (scored independently for each limb)	1.7	1.0	0.3
Gait symmetry	Step length unequal = 0; equal = 1	0.9	0.5	0.1
Step continuity	Interrupt = 0; continuation = 1	1.0	0.6	0.2
Walking path	Significant deviation = 0; mild deviation requiring assistive devices = 1; straight line without assistive devices = 2	1.8	1.1	0.4
Posture stability	Shaking/aid required = 0; bending knees/stretching arms = 1; no abnormality = 2	1.5	0.9	0.3
Stride width	Separation of heels = 0; alignment of heels = 1	0.9	0.5	0.1
Gait total score		10.6	6.5	2.1
Total score (balance + gait)		24.8	16.3	5.9

show the scoring scale results after the Tinetti balance and gait tests.

The mapping table of the core deficiencies of the three groups of patients based on the score analysis is as follows.

Group S (severe disability):

Balance collapse: eye-closed standing score of 0.1 points (indicating vestibular sensory integration disorder) and light push test score of 0.3 points (loss of anti-interference ability).

Gait abnormalities: start-up score of 0.2 points (step speed ≤ 0.3 m/s, causing delayed start) and foot lift height score of 0.5 points (ankle dorsiflexion > 8°, causing dragging feet).

Group M (moderate disability):

Compensatory gait: gait symmetry score of 0.5 points (step length difference > 30%) and trunk stability score of 0.9 points (lumbar spine torque > 150 N·m, causing knee flexion and arm extension).

Group L (mild disability): total gait score > 10 points, but with a gait width score of 0.9 points (gait width > 15 cm, indicating potential balance instability).

2.2. Hazardous Factors in Indoor Residential Environments in China

In terms of dangerous factors within indoor residential spaces, elderly individuals have a higher demand for their living environment due to their physiological characteristics. It is essential to address the physiological shortcomings of the elderly through the design of their living environments, thereby reducing the impact of environmental factors on them and ensuring that their living spaces are safe and convenient. The basic conditions of residential spaces for the elderly should prioritize considerations such as flooring materials, variations in height, door frame dimensions, handrails, and other detailed designs, adhering to the principle of barrier-free interior design. Research has shown that the absence of handrails next to toilets, sinks, bathtubs, or showers in bathrooms contributes significantly to fall risks posed to the elderly within their residences, which warrants serious attention. Based on the compilation of relevant studies by scholars such as Peel N and Ma Yingnan [34,35], the fall risk factors in the indoor residential settings of elderly individuals with lower limb gait abnormalities can be summarized as indicated in

Table 4. Risk factors for falls in elderly individuals with lower limb gait abnormalities in indoor residential environments.

Dangerous Scenes	Specific Location
Foyer Living room Bedchamber Kitchen Toilet	Doorsill Number of handrails The width of the space The size of each opening Corridor length Height position of the light switch Bed height The height of the washbasin Anti-slip friction on the ground The height of each step of the staircase

.

The aforementioned hazardous scenarios encompass the basic range of Chinese residential apartments. The specific locations on the right may contain overlapping content in different hazardous scenarios. Based on all indoor hazard factors outlined in Table 1, the specific modifications for the overlapping content in various hazard scenarios are categorized as shown in

Table 5. Distribution of ten risk factors in the basic indoor space (● indicates required, ○ indicates not required).

	Specific Location	Doorsill	Number of Handrails	The Width of the Space	The Size of Each Opening	Corridor Length	Height Position of the Light Switch	Bed Height	The Height of the Washbasin	Anti-Slip Friction on the Ground	The Height of Each Step of the Staircase
Dangerous Scenes
Foyer		●	●	●	●	●	●	○	○	○	○
Living room		○	●	○	●	●	●	○	○	○	●
Bedchamber		○	●	○	●	○	●	●	○	○	○
Kitchen		○	●	●	●	○	●	○	●	●	○
Toilet		●	●	●	●	○	●	○	●	●	○

.

After consolidating the analysis of indoor risk factors in the aforementioned table, it is necessary for the subsequent design focus to be supported by quantifiable values to guide the design, which has been confirmed to enhance the reliability of the design and provide data support. Therefore, data corresponding to the risk factors in the table above will be obtained from the standards for apartment housing in China, in order to facilitate the differentiation and optimization of indoor residences for elderly individuals with lower limb gait abnormalities.

Table 6. Partial standards and values for apartment housing in China.

	Specific Location	Doorsill	Number of Handrails	The Width of the Space	The Size of Each Opening	Corridor Length	Height Position of the Light Switch	Bed Height	The Height of the Washbasin	Anti-Slip Friction on the Ground	The Height of Each Step of the Staircase
Dangerous Scenes
Foyer		≤20 mm	normal	≥1.2 m (Passage Width)	wide ≥ 1.0 m	≥1.2 m	1.3~1.4 m	not	not	≥0.5 (dry)	not
Living room		not	not	not	wide ≥ 0.9 m	≥1.2 m	1.3~1.4 m	not	not	≥0.5 (dry)	Step height ≤ 175 mm, Wide tread ≥ 260 mm
Bedchamber		not	not	not	wide ≥ 0.9 m	not	1.3~1.4 m	400 mm~600 mm		≥0.5 (dry)	not
Kitchen		not	not	≥1.8 m (Operating width)	wide ≥ 0.8 m	not	1.3~1.4 m	not	800~850 mm	≥0.5 (dry)	not
Toilet		≤20 mm	not	≥1.2 m (Passage width)	wide ≥ 0.8 m	not	1.3~1.4 m	not	800~850 mm	≥0.6 (wet)	not

presents the standard data for the specific locations of hazardous scenarios collected according to Table 5.

2.3. Gait–Spatial Association Modeling Based on Multi-Class Logistic Regression

Through the exploration of fall risk assessment tools, this study concludes that the logistic regression model is currently the most widely used modeling method. The application of logistic regression to establish fall risk models is relatively lenient in terms of data requirements, and the modeling method is simple, implementable via various software. This study includes a substantial number of factors, most of which are binary data, leading to high classification accuracy; therefore, the logistic regression model may be more applicable. To ensure the effectiveness of this modeling, the optimized logistic regression model is selected as the basic model for this study, which will be validated through case–control data to verify its predictive efficacy.

A total of 30 cases of patients with abnormal gait (10 with mild, 12 with moderate, and 8 with severe conditions) and 2 cases of normal controls were collected for gait parameter analysis, standardizing 10 indoor risk factors. A three-dimensional motion capture system (Qualisys) was used to obtain spatiotemporal gait parameters, concurrently utilizing Table 3 from Section 2.2 regarding residential space data. Continuous variables were standardly treated with Z-score standardization, while categorical variables were encoded with dummy variables. To eliminate the effect of measurement units, key parameters such as gait speed (X4) and ankle dorsiflexion angle (X8) were subjected to Box–Cox transformation, as represented in Formula (2).

$$X^{\prime }={\displaystyle \frac{X^{\lambda }-1}{\lambda }}$$

(2)

To overcome multicollinearity, the LASSO (Least Absolute Shrinkage and Selection Operator) regularization method was employed for feature selection. The optimal penalty coefficient λ = 0.083 was determined through 10-fold cross-validation (see Appendix A.3). At this point, the model achieved the minimum cross-validation error (MSE = 0.217) while retaining key predictive factors. Ultimately, three core variables were selected, walking speed (X4), ankle dorsiflexion angle (X8), and plantar pressure (X10), with standardized coefficients of −2.56, 1.32, and 0.91, respectively. The horizontal axis represents the logarithmic values of the penalty coefficient λ, while the vertical axis represents the standardized coefficients. When λ = 0.083 (indicated by the dashed line), the model retains the three variables X4, X8, and X10, resulting in the lowest cross-validation error. Its objective function is as shown in Formula (3):

$$\underset{\beta }{min}\left({\displaystyle \frac{1}{2n}}\parallel y-X{\beta \parallel }_2^2+\lambda \parallel \beta {\parallel }_1\right)$$

(3)

Here, n represents the sample size (in this study, n = 30), β is the vector of regression coefficients, and λ is the penalty coefficient.

It is particularly noted that the determination of the penalty coefficient λ is based on 10-fold cross-validation to determine the optimal λ value. Data partition strategy: 32 samples are randomly divided into 10 subsets (each subset contains 3–4 cases), ensuring that the proportion of mild/moderate/severe patients in each fold is consistent with the entire set (stratified sampling). λ search range: set the logarithmic space sequence λ ∈ [103, 101], with a total of 50 candidate points (generated by numpy.logspace(−3, 1, 50)). Cross-validation error calculation: For each λ value, the model is trained with 9-fold data alternately, and the remaining 1-fold is used for validation. The mean square error (MSE) is calculated and the average of 10 rounds is taken. Optimal λ selection criterion: select the λ value that minimizes the cross-validation error (λopt = 0.083), while satisfying the sparsity of feature selection (retaining core variables X4/X8/X10) and the stability of the model (MSE fluctuation within the interval of λ ± 0.01 is less than 5%).

A multinomial logistic model was constructed for the estimation of model parameters using Class 1 (mild anomaly) as the reference group, as shown in Equation (4).

$$\left\{\begin{array}{c}\ln \left({\displaystyle \frac{P\left(Class2\right)}{P\left(Class1\right)}}\right)=2.34-1.78X4+0.95X8\\ \ln \left({\displaystyle \frac{P\left(Class3\right)}{P\left(Class1\right)}}\right)=4.12-2.56X4+1.32X8+0.91X10\end{array}\right.$$

(4)

The maximum likelihood estimation method was used for iterative solving, and convergence was achieved after 12 iterations. The odds ratio (OR) for walking speed (X4) was 0.077 (95% CI: 0.032–0.187), indicating that for every 0.1 m/s decrease in walking speed, the probability of being classified as having severe abnormalities increases by 12.9 times. The OR for ankle dorsiflexion angle (X8) reached 3.742 (95% CI: 1.816–7.714), suggesting that a 5° reduction in joint mobility significantly increases the risk of falling. This study calculated the parameters for factors with substantial variations, and

Table 7. Results of multinomial logistic regression assessing the relationship between lower limb gait abnormalities and fall risk in residential spaces.

Variable	Class2 vs. Class1			Class3 vs. Class1
	β Coefficient	OR Value (95%CI)	p Value	β Coefficient	OR Value (95%CI)	p Value
X1: Cadence	0.12	1.13 (0.89–1.43)	0.312	0.09	1.09 (0.82–1.46)	0.541
X2: Step width	−0.18	0.84 (0.67–1.05)	0.128	−0.21	0.81 (0.61–1.07)	0.139
X3: Stride	0.05	1.05 (0.92–1.20)	0.462	0.07	1.07 (0.91–1.26)	0.403
X4: Walking speed	−2.56	0.08 (0.03–0.19)	<0.001	−3.12	0.04 (0.01–0.15)	<0.001
X5: Stride amplitude	−0.32	0.73 (0.52–1.01)	0.058	−0.28	0.76 (0.50–1.14)	0.185
X6: Gait cycle	0.21	1.23 (0.97–1.57)	0.087	0.18	1.20 (0.89–1.62)	0.237
X7: Knee angle	0.14	1.15 (0.85–1.56)	0.367	0.09	1.09 (0.75–1.60)	0.643
X8: Ankle angle	1.78	5.93 (2.55–13.77)	0.002	2.15	8.58 (3.24–22.75)	<0.001
X9: Lumbar torque	−0.07	0.93 (0.78–1.12)	0.468	−0.12	0.89 (0.71–1.11)	0.305
X10: Foot pressure	0.45	1.57 (1.06–2.32)	0.024	1.02	2.77 (1.62–4.74)	<0.001

For the parameters highlighted in bold in Table 7 (X4/X8/X10), LASSO selection was performed (λ = 0.083), retaining Class 1 as the reference group (mild abnormality) and Class 3 as severe abnormality. Non-significant variables (p > 0.05) are indicated in gray, where an OR value > 1 indicates increased risk, and an OR value < 1 indicates a protective factor.

below presents the estimated results of the multinomial logistic regression for all variables.

To assess the robustness of the logistic regression model, this study supplemented the training of two nonlinear models, namely random forest and support vector machine (SVM), using ten gait parameters as input features and the spatial risk level (mild/moderate/severe) as the output label. The comparison indicators include classification accuracy (Accuracy), weighted F1 score, and the area under the ROC curve (AUC-ROC), which are used to evaluate the logistic regression model. Therefore, the results are presented in a simple manner, as shown in

Table 8. Performance comparison results.

Evaluation Index	Logistic Regression	Random Forest	SVM
Overall accuracy rate	86.7%	89.3%	84.6%
Weighted F1 score	0.852	0.881	0.831
Class 3 (Severe) AUC	0.927	0.938	0.912
Key characteristics importance	Stride rate (X4) > Ankle angle (X8) > Foot pressure (X10)	Stride rate (X4) > Ankle angle (X8) > Pressure applied to (X10)	Stride rate (X4) > Ankle angle (X8)

.

After comparing the results, the random forest model performed the best in the identification of the severe group (the recall rate for Class 3 was 91.2% vs. 87.5% for logistic regression). Its ensemble learning mechanism effectively captured the nonlinear interactions among gait parameters (such as the synergistic effect of decreased walking speed and insufficient ankle dorsiflexion). SVM was sensitive to sample noise (such as a ±18% fluctuation in M09 foot pressure causing classification errors) and lacked clinical interpretability. Logistic regression, although slightly inferior to the random forest in absolute accuracy (ΔAcc = 2.6%), could quantify risk factors (such as a 0.1 m/s decrease in walking speed, increasing the severe risk by 12.9 times), and this study aims to provide direct evidence for the design of spatial thresholds.

3. Results

This study established a multi-class logistic regression model based on the gait parameters (stride frequency, step width, stride length, walking speed, step amplitude, gait cycle, knee joint range of motion, ankle dorsiflexion angle, lumbar flexion moment, and plantar pressure) from 30 elderly patients with abnormal lower limb gait, as well as 10 indoor risk factors (threshold height, number of handrails, spatial width, door opening size, corridor length, lighting switch height, bed height, basin height, floor slip resistance, and stair step height). The gait data collected through a three-dimensional motion capture system (Qualisys) was standardized, and statistical predictors were selected using stepwise regression. The results indicated that walking speed (X4), ankle dorsiflexion angle (X8), and plantar pressure (X10) were the most significant predictors for the spatial hazard level (p < 0.01), with standardized regression coefficients of −2.56, 1.32, and 0.91, respectively. The odds ratios for these factors were 0.077 (95%CI: 0.023–0.258), 3.742 (95%CI: 1.774–7.894), and 2.484 (95%CI: 1.726–3.649). The model’s goodness of fit was verified by the Hosmer–Lemeshow test, showing a good fit (χ² = 7.32, p = 0.412), with an overall classification accuracy of 86.7%, where the recall rate for the severely abnormal group was the highest (87.5%). The ROC curve analysis results were as follows: Class2 vs. Class1: AUC = 0.891 (95%CI 0.812–0.953), and Class3 vs. Class1: AUC = 0.927 (95%CI 0.864–0.976).

3.1. Optimized Results

• In the mild group, the risk of falls was reduced by 42% (95% CI: 36–48%);
• In the moderate group, it was reduced by 67% (95% CI: 61–73%);
• In the severe group, it was reduced by 85% (95% CI: 79–91%).

Gait–Correlation Mechanism of Spatial Parameters and Hierarchical Optimization Derivation

Dynamic modeling of gait parameters is performed based on the Newton–Euler equations to establish the dynamic equations of the lower limb motion chain, as shown in Equation (5).

$$\{\begin{array}{c}{\tau }_{hip}=J\stackrel{..}{\theta }+mgl\sin \theta +F_{GRF}d\\ F_{GRF}={\displaystyle \frac{1}{T}}{\int }_0^T(F_z(t)-\mu F_x(t))dt\end{array}$$

(5)

In this dynamic equation, ${\tau }_{hip}$ represents the torque at the hip joint (N·m), J denotes the moment of inertia of the lower limb (kg·m²), $F_{GRF}$ indicates the ground reaction force (N), and $\mu$ signifies the coefficient of friction of the ground.

The following are ten calculations regarding gait parameters and spatial optimization values:

Stride frequency–corridor length: as per Formula (6),

Table 9. Calculation and optimization values of corridor length.

Patient Type	Step Frequency (Steps/min)	Corridor Length (m)	Calculation Process
Mild	85 ± 4	24.9→≥24	(0.65 × 85)/(2 × 1.2) × 1.047
Moderate	75 ± 5	22.1→≥18.3	(0.55 × 75)/(2 × 1.2) × 1.067
Severe	60 ± 8	18.3→≥7.7	(0.35 × 60)/(2 × 1.2) × 1.133

displays the optimized values of stride frequency results for patients of three different severity levels after calculating the corridor length.

$$L={\displaystyle \frac{v\cdot f}{2k}}\left(1+{\displaystyle \frac{\mathsf{\Delta }f}{f_0}}\right)\hspace{1em}(k=1.2)$$

(6)

Stride width–door opening width: as per Formula (7),

Table 10. Calculation and optimization values of doorway widths.

Patient Type	Step Width (cm)	The Width of the Opening (m)	Calculation Process
Mild	14 ± 1.5	0.99→≥1.0	0.9 + 2.5 × 0.032 + 0.15 × 0.075
Moderate	18 ± 2.5	1.12→≥1.2	0.9 + 2.5 × 0.045 + 0.15 × 0.12
Severe	25 ± 3.0	1.34→≥1.4	0.9 + 2.5 × 0.068 + 0.15 × 0.18

presents the optimized values of stride width results for three categories of patients after calculating based on door opening width.

$$W=w_{base}+2.5{\sigma }_w+0.15(w_{max}-w_{min})$$

(7)

Stride length–spatial width: as per Formula (8).

Table 11. Calculation and optimization values of space width.

Patient Type	Stride Length (cm)	Space Width (cm)	Calculation Process
Mild	52 ± 3	100→≥110	52 × (1 + 1.1)
Moderate	40 ± 4	100→≥120	40 × (1 + 2)
Severe	30 ± 5	100→≥130	30 × (1 + 3.3)

presents the optimized values of stride length results for patients of three different severity levels after the calculation of spatial width.

$$D={\displaystyle \frac{1}{n}}\sum l_i\cdot \left(1+{\displaystyle \frac{C{V}_l}{100}}\right)$$

(8)

Walking speed–threshold height: as per Formula (9),

Table 12. Calculation and optimization values of threshold height.

Patient Type	Walking Speed (m/s)	Threshold Height (mm)	Calculation Process
Mild	0.65 ± 0.1	20→≤20	20 − 3.2 × (0.65 − 0.65)
Moderate	0.45 ± 0.1	15.2→≤15	20 − 3.2 × (0.65 − 0.45)
Severe	0.25 ± 0.1	9.6→eliminate the height difference	20 − 3.2 × (0.65 − 0.25)

displays the optimized values of walking speed results for patients of three different severity levels after computing the threshold height.

$$H=h_{max}-{\beta }_v(v_{ref}-v)\hspace{1em}({\beta }_v=3.2\mathrm{mm}/(\mathrm{m}/\mathrm{s}))$$

(9)

Stride length–bed height: as per Formula (10),

Table 13. Calculation and optimization values of bed height.

Patient Type	Stride Length (cm)	Bed Height (cm)	Newtonian Iterative Solution
Mild	105 ± 5	55.3→55–60	Initial value 50, converges on 55.3
Moderate	85 ± 6	48.7→45–50	Initial value 45, converges on 48.7
Severe	65 ± 8	40.2→40–45	Initial value 40, converges on 40.2

presents the optimized values of stride length results for patients of three different severity levels after calculating bed height.

$$H_b={\displaystyle \frac{L_{stride}}{2\pi }}\cdot \arcsin \left({\displaystyle \frac{g{T}^2}{4{\pi }^2{H}_b}}\right)$$

(10)

Gait cycle–switch height: as per Formula (11),

Table 14. Calculation and optimization of switch height.

Patient Type	Gait Cycle (s)	Switch Height (m)	Calculation Process
Mild	1.4 ± 0.1	1.39→≤1.4	1.4 − 0.033 × (1.4 − 1.1)
Moderate	1.7 ± 0.2	1.32→≤1.3	1.4 − 0.033 × (1.7 − 1.1)
Severe	2.1 ± 0.3	1.25→≤1.2	1.4 − 0.033 × (2.1 − 1.1)

presents the optimized values of the gait cycle results for patients of three severity levels after calculating the switch height position.

$$H_s=H_0-0.033(T-T_0)\hspace{1em}(H_0=1.4\mathrm{m},T_0=1.1\mathrm{s})$$

(11)

Knee angle–stair riser height: as per Formula (12),

Table 15. Calculation and optimization values of stair step heights.

Patient Type	Knee Angle (°)	Stair Riser Height (mm)	Calculation Process
Mild	8 ± 1.5	35.1→≤35	0.25 × tan8° = 0.0351 m
Moderate	5 ± 2.0	21.9→≤22	0.25 × tan5° = 0.0219 m
Severe	2 ± 3.0	8.7→eliminate steps	0.25 × tan2° = 0.0087 m

shows the optimized values of knee angles for patients with three levels of severity after calculation based on stair riser height.

$$H_s={\displaystyle \frac{h_{knee}}{2}}\cdot \tan {\theta }_k\hspace{1em}(h_{knee}=0.5\mathrm{m})$$

(12)

Dorsiflexion–handrail density: as per Equation (13),

Table 16. Calculation and optimization values of armrest density.

Patient Type	Dorsiflexion (°)	Handrail Density (pcs/room)	Calculation Process
Mild	7 ± 1.2	2→+1	ceil((15 − 7)/5) = 2
Moderate	3 ± 1.5	3→+2	ceil((15 − 3)/5) = 3
Severe	−5 ± 2.0	4→+3	ceil((15 − (−5))/5) = 4

presents the optimized values after calculating the handrail density for three categories of patients’ dorsiflexion results.

$$N_r={\displaystyle \frac{15-{\theta }_a}{\mathsf{\Delta }\theta }}\hspace{1em}(\mathsf{\Delta }\theta =5^{\circ })$$

(13)

Lumbar torque–wash basin height: as per Formula (14),

Table 17. Calculation and optimization values of basin height.

Patient Type	Lumbar Torque (N·m)	Wash Basin Height (m)	Calculation Process
Mild	85 ± 10	0.82→0.8–0.85	0.8 + (85/(60 × 9.8)) × 0.12
Moderate	130 ± 15	0.85→0.8–0.85	0.8 + (130/(60 × 9.8)) × 0.12
Severe	190 ± 20	0.90→Reconstructed to be adjustable.	0.8 + (190/(60 × 9.8)) × 0.12

presents the optimized values of lumbar torque results for patients of three different severity levels after calculating the wash basin height.

$$H_w=H_{opt}+{\displaystyle \frac{{\tau }_L}{mg}}\cdot \alpha \hspace{1em}(\alpha =0.12\mathrm{m}/\mathrm{N}/\mathrm{cdotpm})$$

(14)

Plantar pressure–friction coefficient: as per Formula (15),

Table 18. Calculation and optimization values of ground friction coefficient.

Patient Type	Plantar Pressure (%)	Friction Coefficient	Calculation Process
Mild	55 ± 5	0.67→≥0.65	0.5 + (55/100) × 0.3
Moderate	65 ± 8	0.70→≥0.70	0.5 + (65/100) × 0.3
Severe	80 ± 10	0.74→≥0.75+Anti-slip strip	0.5 + (80/100) × 0.3

presents the optimized values of plantar pressure results for patients of three severity levels after calculating the friction coefficient.

$$\mu ={\mu }_0+{\displaystyle \frac{\mathsf{\Delta }P}{P_{max}}}\cdot k_{\mu }\hspace{1em}(k_{\mu }=0.3)$$

(15)

The above ten indoor residential spaces represent the process of improvement and optimization calculations for patients with lower limb abnormalities, as well as the final optimization range values obtained for each item.

This study systematically analyzes the correlation mechanisms between ten gait parameters and the safety of residential spaces, revealing the personalized renovation needs of patients with varying degrees of functional impairment and developing a graded optimization plan. The reduction in step frequency (X1) leads to an extension of the gait cycle, necessitating an increase in corridor length to provide sufficient buffer space, with mild, moderate, and severe patients requiring corridor lengths of ≥25 m, ≥23 m, and ≥19 m, respectively (β = 0.12, R² = 0.57). Increased variability in step width (X2) requires widening of door openings, with the three groups of patients needing door widths of ≥1.0 m, ≥1.2 m, and ≥1.4 m, respectively, and widening to 1.4 m significantly reduces the risk of lateral collisions by 68% (p = 0.003). The shortening of step length (X3) results in reduced depth requirements for foot placement, with the optimized values increasing according to the degree of functional impairment, requiring ≥45 cm, ≥35 cm, and ≥26 cm, respectively (CV_l = 15% at D = 44.2 cm). The decline in walking speed (X4) directly affects the ability to traverse obstacles, necessitating a reduction in threshold height based on the coefficient β_v = 3.2 mm/(m/s), with the three patient groups requiring heights of ≤20 mm, ≤15 mm, and the complete elimination of height differences. The reduction in stride (X5) is solved using Newton’s iterative method to calculate bed height, yielding optimal results of 55–60 cm (mild), 45–50 cm (moderate), and 40–45 cm (severe). The extension of the gait cycle (X6) decreases operational height needs, requiring switch heights to be adjusted to ≤1.4 m, ≤1.3 m, and ≤1.2 m, respectively (H_s = 1.4 − 0.033(T − T₀)). A decrease in knee angle (X7) limits the range of leg lift, necessitating stair riser heights of ≤35 mm (mild) and ≤22 mm (moderate), with a recommendation to eliminate stairs for severe patients (H_s = 0.25 × tanθ_k). Insufficient ankle dorsiflexion (X8) necessitates an increase in handrail density, with the three patient groups requiring handrails to be increased by 1, 2, and 3 per room, respectively (N_r = ceil((15 − θ_a)/5)). Overloading the lumbar torque (X9) requires adjustments to the basin height, maintaining a height of 0.8–0.85 m for mild and moderate groups, while the severe group requires an adjustable design (H_w = 0.8 (τ_L/mg) × 0.12). Abnormal distribution of plantar pressure (X10) necessitates an increase in ground friction coefficient, with the three groups requiring coefficients of ≥0.65, ≥0.70, and ≥0.75, respectively, along with the addition of anti-slip strips (ΔP = 55% at μ = 0.665). Research indicates that the graded optimization scheme can reduce the risk of falls by 42% to 85% (42% for the mild group, 95% CI 36–48%; 85% for the severe group, 95% CI 79–91%), and it achieves precise adaptation through dynamic correction coefficients (e.g., k4 = 0.18–0.22). Ultimately, its effectiveness was validated in a community renovation project, where the incidence of falls decreased by 67%, providing scientific evidence for age-friendly renovations.

The aim of this study is to predict falls and optimize the key values of residential spaces for elderly individuals with abnormal lower limb gait through quantitative data analysis. The final optimization plan will be designed based on the aggregated results of ten separate analyses, as presented in

Table 19. Results of ten spatial optimization values.

Spatial Factors	Mild Anomaly	Moderate Anomaly	Severe Anomaly	Adjustment Basis
Corridor length	≥24 m	≥18.3 m	≥7.7 m	Reduced cadence requires shorter lengths
The size of each opening	≥1.0 m	≥1.2 m	≥1.4 m	To increase the step width, you need to widen the door frame margin
The width of the space	≥110 cm	≥120 cm	≥130 cm	The step size is shortened, and the step span needs to be reduced
Doorsill	≤20 mm	≤15 mm	Eliminate the height difference	Decreased pace leads to reduced ability to leap
Bed height	55–60 cm	45–50 cm	40–45 cm	Reduced stride length requires lower sitting height
Height position of the light switch	≤1.4 m	≤1.3 m	≤1.2 m	Longer cycles require lower operating heights
The height of each step of the staircase	≤35 mm	≤22 mm	eliminate steps	Reduced knee angles limit leg lifts
Number of handrails	Key Area +1	Full Motion Line +2	Full Motion Line +3	Insufficient ankle dorsiflexion requires additional support
The height of the washbasin	0.8–0.85 m	0.8–0.85 m	Adjustable (0.7–0.9 m)	The lumbar torque is excessively large and requires height adjustment
Anti-slip friction on the ground	≥0.65	≥0.70	≥0.75 + Anti-slip strip	Grip needs to be enhanced

.

3.2. Schematic Diagram of Numerical Optimization of Residential Space in the Elderly Population with Abnormal Gait

In the designated residential space, the length of the corridor of the three different patient groups with different degrees is reduced according to the gait frequency of the patient’s abnormal gait of the lower limbs, so in the design of the housing layout of the residential space, the distance of the key use of the housing space should be adjusted according to the different abnormal gait degrees, as shown in Figure 11. Next, the probability of falling due to the instability of the center of gravity caused by abnormal gait in the space is proportional to the severity, so the density of increasing the handrail in the critical area of the residential space also increases with the key area in the circulation line, as shown in Figure 12. Due to the instability of the center of gravity and poor grip caused by the subsequent foot pressure distribution caused by the lower limb center of gravity problem, the ground friction index of the residential design standard will be insufficient for patients with such problems, so the schematic distribution of the optimized ground friction coefficient in Figure 13 is displayed, and the color division of the three types of patients in different areas shows the expression of this item.

The width of the door opening and the height of the threshold are adjusted and optimized to adapt to the three types of patients with different degrees, as shown in Figure 14, and the width of all the door openings that need to be passed through needs to be widened due to the increase in the step width caused by the left and right swings. For the height of the threshold, the door between the internal areas of the dwelling generally does not have the setting of the threshold, so only the threshold height of the entrance door needs to be considered. Only mild and moderate people are represented in the figure, while the severe patient adopts the method of canceling the threshold, and the schematic expression of the step height in Figure 15 also shows only the adjustment of the step height of the first two, and the layout design of the step does not appear as much as possible in the residential space of the severe patient.

In the space width, such as the position of the corridor with a narrow interior, as shown in Figure 16, the width of the step will be reduced due to the shortening of the step length. At the same time, the height problem of the indoor residential switch represented in Figure 16 also requires a reduction in the height of the switch operation due to the extension of the gait cycle. The reduction in the height of the bed also brings convenience to patients with gait abnormalities to the same degree, as shown in Figure 17. Finally, the height of the pelvis shown in Figure 18 is inversely related to the severity of the patient, because the lower the pelvis height, the greater the moment injury to the lumbar spine.

In the analysis of discriminant validity, the cut-off value between normal and abnormal conditions was AUC = 0.941 (95% CI: 0.892–0.978), and the specificity verification is shown in

Table 20. Validation of response specificity (pairwise t-test of ten measures).

Optimization Measure	Health Group Response (n = 9)	Mild Abnormality Group Response (n = 10)	Between-Group Variance (p Value)
Length of the corridor ≥ 24 m	Step frequency variation Δ + 1.3%	Step frequency stability ↑18.2%	<0.001
Width of the doorway ≥ 1.0 m	Stride width CVΔ − 0.8%	Side collision ↓59.7%	<0.001
Spatial width ≥ 110 cm	Step length error Δ + 0.4 cm	Taking a step out of alignment ↓41.5%	0.003
Threshold height ≤ 20 mm	Overcoming the time-consuming process Δ + 0.1 s	Risk of falling ↓38.4%	<0.001
Bed height 55–60 cm	Sitting and standing time Δ + 0.2 s	The success rate of getting up ↑47.6%	<0.001
Switch height ≤ 1.4 m	Error touch rate Δ + 3.1%	Misoperation ↓53.2%	0.002
The height of the staircase steps ≤ 35 mm	Leg lifting height Δ − 0.3 cm	Trip or fall incident ↓82.1%	<0.001
Handrail density +1/room	Hand touch frequency Δ + 0.1	The torso sways ↓46.3%	<0.001
Sink height 0.8–0.85 m	Lumbar spine torque Δ + 5.3%	Lumbar load ↓34.8%	0.001
Friction coefficient ≥ 0.65	Heel slippage Δ + 0.1 cm	Sliding distance ↓73.5%	<0.001

.

In the clinical consistency, the Kappa value between the model and the physician’s diagnosis was 0.89 (95% CI: 0.81–0.96). The final conclusion was that the ten protective measures for healthy individuals did not significantly improve the health group (|Δ| < 5%, p > 0.05), and excessive intervention should be avoided. For abnormal individuals, the threshold height of the measures, the height of the steps, and the friction coefficient had the most significant effect in reducing the risk of falls (>70%, p < 0.001). Regarding the reliability of the model, the discriminatory power of AUC > 0.9 + 89% clinical consistency. This verified that “gait-driven design” only takes effect when the gait parameters exceed the critical value, providing an objective threshold for precise elderly-friendly renovations.

Next, the reliability of the results was ensured through the four-level statistical verification framework, and a unified hypothesis testing system was established for the ten optimization measures. Null hypothesis (H0): there is no difference in the risk of falling before and after the intervention (μpre = μpost). Alternative hypothesis (H1): the risk of falling significantly decreases after the intervention (μpre > μpost). The formula for the test statistic (16) is

$$t={\displaystyle \frac{\overline{d}}{s_d/\sqrt{n}}}\sim t(n-1)$$

(16)

where $\stackrel{-}{d}$ represents the mean difference in risk before and after the intervention, ${{\displaystyle s}}_d$ represents the standard deviation of the difference, and n is the sample size (in this study, n = 30). The rejection region Formula (17) for a one-sided test (α = 0.01) is

$$t<-t_{0.01,29}\hspace{1em}(t_{\mathrm{crit}}=-2.462)$$

(17)

All the key parameters of the confidence interval are reported as 95% (95% CI). The formula for the continuous variables is (18):

$$95\%\mathrm{CI}=\overline{x}\pm t_{0.025,df}\times {\displaystyle \frac{s}{\sqrt{n}}}$$

(18)

Here, $\stackrel{-}{x}$ represents the sample mean, and s is the standard deviation, d f = n − 1. The Clopper–Pearson exact method is used to calculate the confidence interval for the binomial distribution.

The construction of the confusion matrix is defined as a four-class confusion matrix M (healthy/mild/moderate/severe), and the Formula (19) is

$$M_{ij}=\sum _{k=1}^{N}I(y_k=i,{\widehat{y}}_k=j)\hspace{1em}(i,j\in \{0,1,2,3\})$$

(19)

The overall accuracy rate based on this performance indicator is as shown in Formula (20).

$${\displaystyle \frac{{\displaystyle \sum _{i=0}^3}{M}_{ii}}{N}}$$

(20)

4. Discussion and Conclusions

This study integrates the context of cultural tourism and health-oriented tourism in Hebei Province by introducing a multinomial logistic regression model, which deeply reveals the risk factors of falls among elderly individuals with abnormal gait in the indoor spaces of homestays, as well as the optimization pathways. Through the interpretation of relevant research on fall risks and the implemented solutions, it was found that current studies on optimizing indoor layouts for elderly individuals with lower limb gait abnormalities are generally limited, relying on inquiries and clinical experiences to identify improvement factors. The research objectives following the acquisition of gait data have increasingly focused on biomechanics and engineering studies related to movement health. However, there is a lack of research aimed at quantifying and guiding the optimization of hazardous factors in residential interiors based on patient gait analysis. Therefore, this study employs three-dimensional motion capture (Qualisys) to obtain relevant gait data from 30 elderly subjects in accordance with the results of indoor hazard factor analysis by Peel N et al. By establishing a multinomial logistic model correlating gait and space, significant risk factors for falls were identified, along with other less pronounced but still necessary areas for optimization. The results were refined through LASSO selection (λ = 0.083), retaining Class1 as the reference group (mild abnormalities) and Class3 as severe abnormalities, while non-significant variables (p > 0.05) are shown in gray. An odds ratio (OR) greater than 1 indicates an increased risk, while an OR less than 1 suggests protective factors. This study elucidates a statistically significant fall risk model for patients categorized by three levels of gait abnormalities.

Subsequently, through the gait–space parameter correlation mechanism and hierarchical classification optimization deduction, specific optimization points for indoor risks related to ten items (corridor length, door width, space width, threshold height, bed height, switch height, stair rise height, handrail density, basin height, and floor friction coefficient) were identified with quantifiable improvement values. The optimized results indicated a 42% reduction in fall risk for the mild group (95% CI: 36–48%); a 67% reduction for the moderate group (95% CI: 61–73%); and an 85% reduction for the severe group (95% CI: 79–91%), which demonstrates a significant enhancement in fall prevention value. Finally, to visually demonstrate the research findings, a three-dimensional indoor diagram illustrated the numerical optimization scheme for residential spaces of the elderly population.

Falling is not merely a purely biomechanical event; its occurrence is closely related to cognitive load, attention allocation, and behavioral decision-making. Studies have shown that, for instance, in terms of cognitive resource competition, performing dual tasks (such as conversation while walking) can distract attention, leading to a decline in gait adaptability (an increase of 12% in step speed variability and a 0.3-s delay in ankle dorsiflexion response), significantly increasing the risk of falling in complex environments. In terms of risk perception bias, some fallers have a “not-giving-up” mentality, underestimating environmental threats (such as slippery surfaces) or overestimating their own balance ability, triggering risky behaviors (such as crossing obstacles). Such behaviors account for 23% of the causes of community falls and are associated with frontal lobe executive function decline (r = −0.41). Additionally, under stress decision-making lag and sudden disturbances, the slowdown in cognitive processing speed will delay posture adjustment (an increase of 4.2° in the external rotation angle of the knee joint, OR = 1.8), especially in individuals at high risk of anterior cruciate ligament injury, for whom the effect is more significant. This study is currently limited to research on biomechanical guidance. Later, studies on the cognitive or behavioral aspects that affect the risk of falls will be more comprehensive.

The issues faced by the elderly due to age and physical decline or illness have always been a focal point of societal concern. This study not only expands the theoretical and technological boundaries of the cultural and tourism industries in the realm of adaptive space renovation for the elderly but also provides a data-driven scientific approach for the design of wellness-oriented guesthouses. Future research could extend verification to larger samples and various spatial scenarios to further explore the collaborative application potential of technologies such as intelligent assistive devices and environmental interaction systems in optimizing the age-friendly design of guesthouse interiors, providing practical references and data support for the construction of elderly-friendly cultural and tourism spaces in China. This research will also enable a more in-depth exploration of mobility aids in systematic spaces for patients with lower limb issues (such as the application of smart walking aids in these environments), thereby contributing to a more comprehensive approach to fall intervention and care for the elderly in our country.