Multi factor assessment of spatial accessibility for rural health equity in Diqing China

Abstract

Timely access to essential primary healthcare services is critical for achieving health equity, particularly in geographically constrained mountainous regions where terrain imposes significant barriers to mobility. However, existing national planning standards in China rely on uniform service radii or walking-time thresholds, often failing to reflect the true accessibility conditions in complex highland environments. To address this gap, this study develops a Multi-Factor Integrated Mountain Walkability Model (MIMWM) that incorporates high-resolution Digital Elevation Models, slope-adjusted walking speeds, land-use resistance coefficients, and physiological walking capacity decline at altitude. Embedded within the Two-Step Floating Catchment Area framework, the model is applied to Diqing Tibetan Autonomous Prefecture in Yunnan Province, a high-altitude region characterized by rugged terrain and sparse healthcare infrastructure. Results demonstrate that traditional Euclidean and network-based methods substantially overestimate accessibility, particularly within the 15–60 min walking thresholds. The MIMWM reveals a critical threshold effect at approximately 30 min, beyond which accessibility improvements diminish. Moreover, most residents in the study area fall below the baseline criteria for access set by national healthcare standards, highlighting the inadequacy of uniform service thresholds in mountainous settings. This study underscores the dominant influence of terrain and walking capacity constraints and advocates for location-specific accessibility metrics and near-distance infrastructure investment to improve rural health equity. The model provides a replicable approach for integrating terrain sensitivity into healthcare accessibility planning in other topographically complex regions.

Introduction

Timely access to essential primary healthcare services is a fundamental component of achieving health equity, especially in underdeveloped and geographically constrained regions. In the mountainous areas of western China, residents are confronted with a range of formidable challenges that hinder their ability to reach healthcare facilities within clinically critical timeframes. These barriers are not merely infrastructural but are deeply rooted in the region’s complex physical geography. Steep and uneven slopes, highly fragmented road networks, and diverse land surface conditions substantially increase travel resistance, particularly for pedestrian movement, which remains a common mode of transportation in many rural settlements. Such physical constraints are compounded by systemic healthcare disparities. Western China continues to exhibit significantly lower healthcare facility coverage compared to eastern regions, with many counties lacking sufficient numbers of clinics or township-level health centers. At the same time, the region is home to large and dispersed populations, many of whom reside in remote villages scattered across rugged terrains. This imbalance between sparse medical infrastructure and high potential demand results in pronounced spatial inequities in healthcare accessibility. In this context, conventional accessibility evaluation methods may fail to capture the true extent of spatial disadvantage, underscoring the need for refined, terrain-sensitive models that reflect real-world conditions in mountainous environments.

Traditional spatial accessibility models—most notably the two-step floating catchment area (2SFCA) method—commonly employ circular buffers or simple network radii, which often fail to capture the true travel constraints of complex terrain¹. The traditional 2SFCA method assumes that all locations within the service area have the same accessibility, ignoring the distance attenuation effect caused by factors such as terrain obstacles, which is particularly evident in mountainous areas^2,3. The use of a fixed service area is not applicable in areas with different terrains and population densities⁴. Furthermore, it assumes that all modes of transport have the same travel time or distance, ignoring the differences between multimodal modes of transport⁵. These limitations are particularly problematic in rural Southwest China, where medical resource allocation directly impacts the well-being of vulnerable populations⁶.

Over the past two decades, the 2SFCA method has become a mainstream tool for evaluating healthcare accessibility and guiding health resource planning⁷. Numerous enhancements have addressed limitations related to distance-decay, variable catchment sizes, and multimodal travel modes^8,9. Beyond impedance-focused refinements, non-spatial adjustments to supply and demand have also been proposed, such as the Supply–Demand Adjusted 2SFCA (SDA-2SFCA), which reweights provider capacity and local need to better align effective access with service pressure¹⁰. However, adaptations tailored for rugged mountainous environments are still sparse. Although 2SFCA has been widely used in urban environments, scholars have pointed out that ignoring terrain and surface resistance systematically overestimates accessibility estimates in rugged terrain, prompting the development of terrain-sensitive methods^46,47. Most studies remain at the level of adjusting buffer radii or incorporating simple road-network-based cost distances, without integrating the full spectrum of terrain and land-use constraints. Additionally, online map data is subject to network limitations and typically assumes a default, slope-independent walking speed, which provides limited representation of the non-networked footpaths common in mountainous villages and lacks transparent, repeatable resistance parameters. In contrast, MIMWM constructs a continuous anisotropic cost surface that combines slope-dependent walking ability, land use resistance, and vertical/horizontal factors, enabling the generation of isochrones across both mapped and unmapped terrain with auditable and reproducible parameters.

Recent attempts in Southwest China, including in Guizhou and Yunnan provinces, have improved the 2SFCA framework by considering road types or approximate travel speeds¹¹. Yet, these models often neglect the cumulative effects of elevation gain, slope-induced fatigue, surface types, and walking network density, leading to potential misestimation of true walkable catchments¹². The traditional 2SFCA’s simple handling of the distance attenuation function also easily leads to errors¹³. Fine-grained integration of these factors remains a critical research gap.

Meanwhile, advances in walkability research—spanning urban studies, transport geography, and public health—demonstrate that high-resolution digital elevation models (DEMs), open-access pedestrian networks (such as OpenStreetMap), and remote-sensing-derived land-cover data can be fused to estimate spatial variations in walking speed¹⁴. Various studies have also improved methods to enhance the model’s responsiveness to distance attenuation effects¹⁵. Nevertheless, the incorporation of such multi-factor walkability surfaces into health service accessibility models, especially in rural mountain regions, is limited.

To address the limitations, this study proposes a Multi-Factor Integrated Mountain Walkability Model (MIMWM), designed to more accurately capture the complexity of pedestrian accessibility in mountainous terrain. The model incorporates four key components. A walkability surface derived from high-resolution Digital Elevation Model (DEM) data, accounting for non-obstructed areas and feasible walking zones; An elevation gain adjustment module that reflects the physiological burden of cumulative uphill movement on human walking capacity; A land-cover-based surface resistance coefficient layer, constructed from recent land-use data to differentiate walking impedance across surfaces such as bare land, forest, cropland, and built-up areas; A slope-informed walking speed correction, integrating empirical relationships between terrain gradient and pedestrian travel velocity. In mountainous residential areas, residents often utilize informal paths such as field ridges, field edges, dry riverbeds, staircase shortcuts, and seasonal trails for mobility. Since these paths are often informal, private, or weather-dependent, obtaining complete and up-to-date path information is challenging, making it difficult for web-based isochrone methods to accurately reflect the actual feasible path set. To address this issue, the MIMWM models’ movement on a continuous anisotropic cost surface (considering slope, land cover, and vertical/horizontal factors) and ‘burns’ reliable paths into low-resistance units, prioritizing them when available. This method retains the advantages of road/sidewalk data while avoiding assumptions about network completeness. Compared to traditional road network-based isochrone methods, MIMWM generates isochrones on continuous terrain constraint surfaces, allowing movement in non-road areas (such as slopes, fields, and trails) and adjusting costs based on terrain and land cover types. This method can generate mixed isochrones to reflect the realistic accessibility of mountainous residential areas and combine with the two-step floating catchment area (2SFCA) framework to generate terrain-sensitive accessibility scores.

The empirical analysis was conducted in Diqing Tibetan Autonomous Prefecture, located in northwestern Yunnan Province, China—an area characterized by highly rugged topography, with elevations ranging from approximately 1500 to over 5500 m, steep slopes often exceeding 15°, and a fragmented terrain structure. These extreme geographical constraints impose significant barriers to pedestrian mobility and make Diqing a representative case for testing terrain-sensitive healthcare accessibility models. Under such conditions, conventional Euclidean or network-based travel estimation methods tend to underestimate the true cost of access.

This study aims to answer four research questions:

1. How effectively can the proposed Multi-Factor Integrated Mountain Walkability Model (MIMWM) delineate realistic pedestrian catchment areas for primary healthcare services in mountainous terrain?

2. How do accessibility scores generated by the MIMWM-based 2SFCA compare to those produced by traditional Euclidean buffer and network-based approaches in terms of spatial coverage and equity sensitivity?

3. How do different walking-time thresholds influence the measurement of spatial accessibility and health equity, and are existing national planning benchmarks suitable for application in high-altitude regions?

4. How do individual factors—including slope-induced walking impedance, altitude-related physiological constraints, and land-use resistance—independently influence pedestrian mobility and healthcare access?

Methodologically, this study bridges walkability modeling and healthcare geography by embedding a multi-factor, physics-informed pedestrian cost surface into the classical Two-Step Floating Catchment Area (2SFCA) framework. Empirically, it produces the first fine-scale, terrain-adjusted accessibility maps for Diqing, providing a robust evidence base for assessing spatial inequality in health service delivery. Policy-wise, the findings support refining uniform service thresholds, advocating for location-specific accessibility standards, and guiding the strategic planning of “last-mile” healthcare infrastructure in topographically constrained regions.

The remainder of the paper is organized as follows: Section “Materials and methods” describes data sources and methods; Section “Results” presents the results; Section “Discussion” discusses implications for healthcare planning in mountainous regions; Section “Conclusions” concludes and highlights avenues for future research.

Materials and methods

Study area

This study focuses on Diqing Tibetan Autonomous Prefecture, a representative high-altitude mountainous region located at the junction of Yunnan, Tibet, and Sichuan provinces in northwestern Yunnan, China (Fig. 1). According to the Seventh National Population Census (2021), Diqing Tibetan Autonomous Prefecture has a permanent population of approximately 395,000, with an urbanization rate of 33.92%. The region is predominantly rural and ethnically diverse, with Tibetan communities constituting the majority of the population¹⁶. The prefecture spans approximately 23,870 km² and is characterized by steep terrain, deep river valleys, and widely scattered settlements. The average elevation exceeds 2000 m, and the terrain undulation index is greater than 2, indicating considerable vertical relief and complex topography. According to China’s topographic and geomorphological classification system, elevation and surface undulation are essential indicators for delineating mountainous regions^17,18. Based on this classification, areas with elevation above 2000 m (Fig. 2a) and undulation index greater than 2 (Fig. 2b) are defined as high-altitude mountainous zones. Diqing meets both criteria, making it an ideal case for assessing healthcare accessibility in remote mountainous settings.

Fig. 1.

Research object location. * Maps were generated by the authors using ArcGIS Pro 3.2 (Esri, Redlands, CA, USA; https://pro.arcgis.com).

Fig. 2.

Analysis of Yunnan Province’s topography: (a) Yunnan Province altitude, (b) Yunnan Province Terrain. * Maps were generated by the authors using ArcGIS Pro 3.2 (Esri, Redlands, CA, USA; https://pro.arcgis.com).

Data

The data sources include residential points, roads, rivers, and land use data from the National Basic Geographic Information Center (2021)¹⁹. DEM data is obtained from ASTER GDEM (90 m, 2022) and SRTM (30 m and 90 m, 2022) through the Geospatial Data Cloud²⁰. Population data is sourced from the seventh national census of China (2021)²¹. The location information of medical facilities is sourced from the Baidu API²², while information on the number of medical beds, medical technicians is obtained from the Yunnan Provincial Health Statistical Yearbook (2021)²³.

2SFCA measuring accessibility

The Two-Step Floating Catchment Area (2SFCA) method, first developed by Radke and Mu²⁴ and refined by Luo and Wang^25,26, is a gravity-based model widely used to measure healthcare accessibility. It includes two steps^27,28.

Step 1: Create a catchment area of a certain radius around each service facility. Calculate the service supply of each facility within its catchment area using the formula:

1

where is the service supply of facility i. is the population of demand point j. is the distance or travel time between facility i and demand point j. D (i, ) is the set of all demand points within the catchment area radius of facility i. Step 2: From the perspective of the demand points, create a catchment area of the same radius around each demand point. Calculate the overall accessibility of each demand point to all service facilities within its catchment area using the formula:

2

where is the overall accessibility of demand point j. is the service supply of facility i (calculated in Step 1). is the distance or travel time between facility i and demand point j. F (j, ) is the set of all service facilities within the catchment area radius of demand point j.

This method overcomes limitations of simple proximity or ratio-based measures but assumes uniform access within catchments. To address this, the Enhanced 2SFCA (E2SFCA) introduces distance decay weights⁷. Furthermore, in mountainous regions, traditional buffer or network-based methods may misrepresent actual access. This study proposes a new distance accumulation approach to enhance catchment delineation under rugged terrain.

Euclidean buffer

The Euclidean buffer is a basic spatial analysis technique in Geographic Information Systems (GIS), used to delineate service areas by generating circular zones around points or parallel buffers along lines and polygons based on straight-line (Euclidean) distance (Fig. 3). For healthcare facilities, this approach approximates service coverage within a predefined radius, but it assumes uniform travel conditions and neglects terrain, infrastructure, and individual movement constraints. Consequently, it may overestimate service accessibility, especially in complex environments such as mountainous or urbanized regions.

Fig. 3.

Euclidean buffer and network-based analysis for service.

Network-based analysis

Unlike the Euclidean method, network-based analysis integrates the structure and constraints of transportation infrastructure into spatial accessibility assessment (Fig. 3). When coupled with the 2SFCA method, it models real-world travel by computing shortest travel times or distances between demand and supply points using algorithms such as Dijkstra or A*. The approach typically employs an Origin-Destination (OD) cost matrix to evaluate accessibility based on actual travel paths. Advanced versions incorporate multiple travel modes (e.g., walking, driving, transit) to better reflect urban mobility behaviors²⁹, thereby improving the accuracy and policy relevance of healthcare accessibility models.

Multi-factor distance accumulation analysis

Distance accumulation calculates the minimum accumulated cost from each raster cell to source points by integrating straight-line, cost, and true surface distances, with vertical and horizontal cost adjustments³⁰. Considering increased energy expenditure and physiological strain during walking at altitudes above 2000 m³¹, this study incorporates multiple factors—mountainous terrain, elevation-induced penalties, terrain undulation, directional anisotropy, and impassable barriers—into a composite friction surface (Fig. 4). Using this friction surface, accurate walking accessibility zones for medical facilities in high-altitude mountainous areas are derived, improving service radius estimation compared to traditional Euclidean and network-based methods.

Fig. 4.

Multi-factor distance accumulation analysis.

Methods

This study applies the Two-Step Floating Catchment Area (2SFCA) method to evaluate healthcare accessibility in high-altitude mountainous regions (Fig. 5). To more accurately reflect pedestrian mobility in such complex terrains, we developed a Multi-Factor Integrated Mountain Walkability Model. This model accounts for key constraints unique to mountainous environments, including topography, surface conditions, human physiological limitations, slope-specific walking characteristics, and route selection preferences. Building upon this model, we systematically compare the effects of individual factors on healthcare accessibility and assess how varying walking-time thresholds influence accessibility outcomes. Furthermore, the study evaluates and contrasts the performance of three different catchment delineation approaches in computing accessibility, highlighting their respective strengths and limitations in the context of mountainous settings.

Fig. 5.

Workflow diagram of the study.

Multi-factor integrated mountain walkability model

To account for the influence of terrain, slope, and altitude on pedestrian movement in mountainous regions, a modified cost function was constructed to estimate the walking impedance between a demand location i and a supply location j. The cumulative accessibility score for each medical facility j is defined as:

3

where the cost is calculated by:

4

Here: denotes the horizontal distance between points i and j; represents the land use resistance coefficient (Table 1); is the base walking speed at sea level, set to 5 km/h ; indicates the slope between points i and j; is the elevation of the destination medical facility j; α is an empirically derived coefficient reflecting the decline in walking capacity with elevation. This formulation extends the classical Tobler’s hiking function³² by incorporating land surface resistance³³ and high-altitude physiological constraints^34,35, making it suitable for accessibility modeling in complex mountainous terrain.

Table 1.

Land use types, average walking speeds, and derived resistance coefficients.

Land use type	Average walking speed (km/h)	Resistance coefficient	Data sources
High-grade road	5.00	1.00	32
General road	3.50	1.43	36
Farmland	3.24	1.54	37
Forest	3.24	1.54	37
Shrubland	3.60	1.39	37
Grassland	4.86	1.03	37
Water body	0.06	99.00	37
Snow and ice	1.62	3.09	37
Barren land	3.00	1.67	37
Impervious surface	4.70	1.06	38
Wetland	2.41	2.07	39

*Resistance coefficients were normalized using the formula , where = 5 km/h.

The land use resistance coefficient was derived based on walking speeds associated with different surface types. Specifically, resistance values were inversely calculated from empirically or literature-supported average walking speeds under various land cover conditions, such as paved roads, bare soil, grassland, forest, and water bodies. A slower walking speed indicates a higher resistance value. These values were normalized to ensure comparability across land use categories. The final resistance coefficients are presented in Table 1.

To quantify the impact of high-altitude environments on pedestrian mobility, this study adopts an exponential decay function to model the reduction in walking capacity with increasing elevation:

5

where represents the relative walking capacity at elevation H, normalized to 1 at sea level; is the elevation (in meters); α is the decay coefficient representing the rate of physiological decline per 1000 m. Based on previous studies on maximal oxygen uptake (VO₂ max) decline at high altitudes, which typically report a 6–10% reduction per 1000 m gain in elevation ^40–42, the coefficient α is set to 0.10 in this study to represent an average 10% reduction in walking capacity per 1000 m of elevation gain.

To integrate the combined influences of terrain, directional preference, and physical barriers into accessibility modeling, the Distance Accumulation tool in ArcGIS Pro (Esri, Redlands, CA, USA) was employed. Specifically, we utilized digital elevation models (DEM) to derive slope and elevation factors, integrated directionality via horizontal factor surfaces and applied barrier raster to represent impassable geographic features such as water bodies or steep cliffs. The modified cost function (Eq. 4) was input as the fundamental impedance surface, and the cumulative least-cost travel-time raster from each medical facility was generated. Subsequently, the accumulated cost values were extracted for use in the subsequent two-step floating catchment area (2SFCA) accessibility analysis.

Defining distance thresholds by transport model

This study focuses on walking as the primary mode of transportation, given that environmental conditions—such as terrain, slope, and surface characteristics—have a substantial influence on pedestrian accessibility, particularly in mountainous regions. According to the Residential Area Planning and Design Standards of China (GB 50180-2018)⁴³, the recommended walking time to access primary healthcare facilities should not exceed 15 min. To examine the sensitivity of accessibility outcomes to walking range assumptions, a series of travel-time thresholds were defined, starting at 15 min and increasing in 15 min increments up to 120 min. The upper bound reflects the generally accepted maximum walking time for healthcare-seeking behavior in rural and mountainous contexts.

Comparing accessibility measures

This study applies the Two-Step Floating Catchment Area (2SFCA) model to evaluate the accessibility of medical facilities in mountainous regions, using two core indicators: the number of hospital beds per capita and the number of medical technicians per capita. Multiple scenarios were designed to examine accessibility under varying assumptions and methods.

First, we compared accessibility outcomes across three different catchment delineation approaches: Euclidean Buffer, Network-Based Analysis, and Multi-Factor Distance Accumulation Analysis, such as Fig. 6. Second, using the Multi-Factor Distance Accumulation Analysis method, we evaluated accessibility across multiple walking-time thresholds (ranging from 15 to 120 min in 15 min intervals) to assess how accessibility changes with increased walking capacity in high-altitude mountainous environments. Pairwise t-tests were conducted to identify the threshold beyond which accessibility values become statistically stable (i.e., differences are no longer significant). Finally, under a fixed threshold, we isolated the influence of individual factors within the Multi-Factor Distance Accumulation framework by recalculating accessibility with only one variable included at a time. The examined factors included mountain terrain, walking capacity, and geomorphological conditions, and correlation analyses were used to assess their respective impacts on accessibility patterns (Fig. 7).

Fig. 6.

Service radius for three methods.

Fig. 7.

Service radius of multi-factor distance accumulation analysis for single factors.

Results

As shown in Table 2, disparities between the novel approach (Group A: Multi-Factor Distance Accumulation) and conventional methods (Group B: Euclidean Buffer; Group C: Network-Based Analysis) exhibit significant spatiotemporal variations. In terms of time, the most pronounced differences occur at the 45 min threshold, AVS C: Significant differences for both Number of medical beds (p = 0.023) and Medical Technicians (p = 0.021); AVS B: Extremely significant differences for both metrics (p = 0.000). In terms of accessibility standards, Medical Technicians shows greater sensitivity to methodological differences at 60 min (AVS C: p = 0.047), while accessibility for Number of medical beds is non-significant (p = 0.067). In addition, differences diminish beyond ≥90 min (e.g., 120 min: p > 0.05), as extended time buffers dilute terrain impacts, validating the walking capacity threshold effect described in the Methods.

Table 2.

Accessibility analysis of three methods under different time thresholds.

Time category	Group comparison	Accessibility standards	Correlation coefficient	p value
15 Min	A* versus B*	Number of medical beds	–	0.012
		Medical technicians	–	0.013
	A versus C*	Number of medical beds	–	0.012
		Medical technicians	–	0.014
30 Min	A versus B	Number of medical beds	0.171	0.001
		Medical technicians	0.213	0.001
	A versus C	Number of medical beds	0.324	0.007
		Medical technicians	0.415	0.002
45 Min	A versus B	Number of medical beds	0.478	0.000
		Medical technicians	0.482	0.000
	A versus C	Number of medical beds	0.232	0.023
		Medical technicians	0.238	0.021
60 Min	A versus B	Number of medical beds	0.515	0.012
		Medical technicians	0.499	0.007
	A versus C	Number of medical beds	0.317	0.067
		Medical technicians	0.332	0.047
75 Min	A versus B	Number of medical beds	0.593	0.001
		Medical technicians	0.580	0.001
	A versus C	Number of medical beds	0.501	0.014
		Medical technicians	0.503	0.012
90 Min	A versus B	Number of medical beds	0.586	0.000
		Medical technicians	0.563	0.001
	A versus C	Number of medical beds	0.641	0.002
		Medical technicians	0.626	0.004
105 Min	A versus B	Number of medical beds	0.635	0.006
		Medical technicians	0.622	0.008
	A versus C	Number of medical beds	0.609	0.003
		Medical technicians	0.597	0.006
120 Min	A versus B	Number of medical beds	0.609	0.194
		Medical technicians	0.606	0.165
	A versus C	Number of medical beds	0.694	0.366
		Medical technicians	0.694	0.363

*Group A: multi-factor distance accumulation; Group B: Euclidean buffer; Group C: network-based analysis. Values in bold indicate statistical significance, with p values below 0.05.

According to Chinas national standards for healthcare resource allocation⁴⁴, this study defines the qualified accessibility thresholds as: Number of medical beds accessibility: ≥ 6.46 beds per 1000 population; Medical Technicians accessibility: ≥ 2.9 persons per 1000 population.

As shown in Table 3, the three methods yield markedly different accessibility results across varying time thresholds. Within 15 min, the estimated accessibility to medical technicians reaches 18.13% using the Euclidean method and 14.29% using the network-based method, while the multi-factor distance accumulation model reports 0%, reflecting its sensitivity to terrain constraints. With increasing time thresholds, accessibility improves under all methods, yet the multi-factor model consistently reports lower values. At the 60 min threshold, accessibility to medical technicians is estimated at 32.42% (Euclidean), 29.67% (network-based), and only 8.24% (multi-factor). Even at 120 min, the multi-factor model yields 17.58%, significantly lower than the Euclidean (47.80%) and network-based (35.16%) approaches. Overall, the multi-factor model—by integrating terrain, land-use resistance, and walking capacity—produces more conservative estimates, offering a more realistic reflection of access limitations in mountainous regions. In contrast, traditional methods may overestimate service coverage. All three approaches confirm the generally low accessibility of healthcare facilities in the high-altitude mountainous study area.

Table 3.

Percentage of accessibility criteria met.

Time category	Accessibility standards	Method 1: Euclidean buffer (%)	Method 2: network-based analysis (%)	Method 3: multi-factor distance accumulation (%)
15 Min	Number of medical beds	8.79	7.69	0.00
	Medical technicians	18.13	14.29	0.00
30 Min	Number of medical beds	12.09	11.54	2.75
	Medical technicians	23.08	21.98	2.20
45 Min	Number of medical beds	16.48	14.84	3.85
	Medical technicians	28.57	25.27	6.59
60 Min	Number of medical beds	17.58	16.48	4.95
	Medical technicians	32.42	29.67	8.24
75 Min	Number of medical beds	25.27	18.68	5.49
	Medical technicians	39.01	29.67	9.89
90 Min	Number of medical beds	24.73	20.33	6.04
	Medical technicians	42.31	31.87	12.09
105 Min	Number of medical beds	20.88	22.53	7.69
	Medical technicians	37.36	34.07	13.74
120 Min	Number of medical beds	25.27	26.37	9.34
	Medical technicians	47.80	35.16	17.58

*The number of medical beds and medical technicians is calculated per 1000 residents.

Figure 8 shows a series of visualizations generated by the MIMWM that was built. The system shows how the spatial accessibility of medical beds and medical personnel for residents in the Diqing area changes at different walking time thresholds. To assess the significance of accessibility improvements across time thresholds, a series of paired t-tests were conducted for both accessibility standards—number of medical beds and number of medical technicians. As shown in Table 4, the comparison between 15 and 30 min revealed a statistically significant increase in accessibility to medical beds (t = − 2.053, p = 0.041), while the improvement in access to medical technicians approached significance (p = 0.088). For other consecutive time intervals, no statistically significant differences were observed (p > 0.05), although the mean accessibility values continued to increase (Figure 9). This suggests that the most notable change in accessibility occurred within the first 30 min, after which improvements became more gradual and statistically nonsignificant. These findings highlight a potential threshold effect in mountainous healthcare accessibility, where additional walking time beyond 30 min yields diminishing returns in terms of population coverage.

Fig. 8.

Temporal trends of healthcare accessibility under two evaluation standards using multi-factor distance accumulation. *The figure shows the accessibility spatial distribution map calculated using the MIMWM method at a specific time threshold. The redder the color, the higher the accessibility; the greener the color, the lower the accessibility. Maps were generated by the authors using ArcGIS Pro 3.2 (Esri, Redlands, CA, USA; https://pro.arcgis.com).

Table 4.

Accessibility analysis based on multi-factor distance accumulation under different time thresholds.

Pairing group	Accessibility standards	Mean	Standard deviation	t value	p value
15 Min versus 30 Min	Number of medical beds	− 0.618	4.063	− 2.053	0.041
	Medical technicians	− 0.544	4.278	− 1.717	0.088
30 Min versus 45 Min	Number of medical beds	− 0.868	8.935	− 1.310	0.192
	Medical technicians	− 1.438	12.108	− 1.602	0.111
45 Min versus 60 Min	Number of medical beds	− 1.106	12.559	− 1.188	0.236
	Medical technicians	− 1.379	16.565	− 1.123	0.263
60 Min versus 75 Min	Number of medical beds	− 0.314	3.132	− 1.354	0.177
	Medical technicians	− 0.475	4.722	− 1.358	0.176
75 Min versus 90 Min	Number of medical beds	− 0.235	6.897	− 0.459	0.647
	Medical technicians	− 0.554	9.555	− 0.782	0.435
90 Min versus 105 Min	Number of medical beds	− 0.291	4.951	− 0.793	0.429
	Medical technicians	− 0.209	6.071	− 0.464	0.643
105 Min versus 120 Min	Number of medical beds	− 1.694	14.246	− 1.604	0.110
	Medical technicians	− 2.774	23.048	− 1.624	0.106

Value in bold indicates statistical significance, with p values below 0.05. The number of medical beds and medical technicians is calculated per 1000 residents.

Fig. 9.

Qualified accessibility rates by time threshold using multi-factor distance accumulation. *The number of medical beds and medical technicians is calculated per 1000 residents.

To evaluate the relative influence of individual walking constraints, we compared the accessibility outcomes of the full-factor MIMWM against three single-factor models: Mountain Terrain only, Walking Capacity only, and Geomorphology only, as visually illustrated in Fig. 10. The paired t-test results are summarized in Table 5, using both the number of medical beds and the number of medical technicians as evaluation standards. The comparison with the Mountain Terrain only model revealed significant differences for both evaluation standards, with p = 0.006 for medical beds and p = 0.003 for medical technicians, indicating that the inclusion of other factors (e.g., walking capacity, surface resistance) significantly alters accessibility outcomes. For the Walking Capacity only model, the difference was statistically significant for medical technicians (p = 0.026), while the result for medical beds was marginally non-significant (p = 0.064), suggesting walking capacity plays a more substantial role in access to human resources than physical infrastructure. The comparison with the Geomorphology only model showed a significant difference only for medical technicians (p = 0.008), while the difference in medical bed accessibility was not significant (p = 0.161). This suggests geomorphological variation has a more limited impact on facility-based accessibility compared to human resource availability. Overall, the results demonstrate that no single factor can adequately substitute for the integrated effects captured in the full-factor model. Among the three, mountain terrain exerts the most consistent and significant influence across both accessibility standards.

Fig. 10.

Comparison of accessibility outcomes between full-factor and single-factor models. * The value in the figure represents the accessibility score calculated using MIMWM, which indicates the level of medical resources available at each location. Warmer colors (such as red) indicate higher accessibility, while cooler colors (such as blue) indicate lower accessibility. Maps were generated by the authors using ArcGIS Pro 3.2 (Esri, Redlands, CA, USA; https://pro.arcgis.com).

Table 5.

Paired t-test results comparing full-factor and single-factor accessibility models.

Pairing group	Accessibility standards	Mean	Standard deviation	t value	p value
All factors versus Mountain Terrain only	Number of medical beds	− 0.004	0.018	− 2.806	0.006
	Medical technicians	− 0.006	0.027	− 2.964	0.003
All factors versus Walking Capacity only	Number of medical beds	− 0.002	0.012	− 1.860	0.064
	Medical technicians	− 0.002	0.015	− 2.244	0.026
All factors versus Geomorphology only	Number of medical beds	− 0.001	0.005	− 1.407	0.161
	Medical technicians	− 0.001	0.006	− 2.693	0.008

*p is significant below the 0.05 level. The number of medical beds and medical technicians is calculated per 1000 residents.

Discussion

Our findings carry important methodological and policy implications for evaluating healthcare accessibility in mountainous regions.

First, about delineating realistic service areas (Q1), the Multi-Factor Integrated Mountain Walkability Model (MIMWM) has advantages over traditional Euclidean distance methods and network-based methods in capturing the physical barriers posed by rugged terrain. These advantages are especially evident at shorter walking thresholds (15–30 min), where the MIMWM model revealed substantial service gaps that were overlooked by conventional approaches^45–47.This corroborates prior research indicating that neglecting terrain and surface-resistance factors can lead to substantial overestimation of healthcare accessibility, particularly in mountainous and remote settings.

Second, in comparing different modeling strategies (Q2), MIMWM -based 2SFCA scores were consistently lower and more spatially differentiated than those derived from Euclidean or network-based models. This finding highlights the limitations of uniform buffer zones and underscores the need for spatial models that reflect pedestrian experience in complex terrains. Relying on simplistic proximity measures risks masking critical inequalities in access to care, particularly in under-resourced areas with sparse infrastructure^7,48,49.

Third, concerning the impact of walking-time thresholds (Q3), our results identified a threshold effect at approximately 30 min, beyond which further increases in travel time yield diminishing returns in accessibility improvements. This has direct implications for national planning benchmarks, which often employ fixed thresholds without consideration of geographic context. Our findings suggest that standardized thresholds may misrepresent access in high-altitude settings and contribute to misallocation of health resources^50–52.

Fourth, in assessing individual spatial constraints (Q4), the comparison between the full-factor and single-factor models confirmed the dominant role of terrain in shaping healthcare accessibility, followed by walking capacity and land-use resistance. Specifically, walking capacity had a stronger influence on access to medical technicians, likely due to their dispersed distribution compared to centralized infrastructure. In contrast, geomorphological variation exerted a more limited impact, particularly on access to hospital beds, reinforcing the importance of selecting appropriate accessibility indicators depending on the service type^6,53.

Notably, walking capacity exerted a significant impact on access to medical technicians, likely due to the dispersed locations of human resources compared to centralized healthcare infrastructure. In contrast, geomorphology alone demonstrated a more limited influence, particularly concerning medical beds, highlighting the differential impacts of various physical constraints on different healthcare accessibility standards.

Together, these findings advocate for the integration of multifactorial environmental and physiological constraints into spatial accessibility models, particularly in topographically complex regions. Doing so not only improves the technical validity of accessibility assessments but also enhances their relevance for equity-oriented policymaking^54,55. Policymakers aiming to promote inclusive healthcare coverage in mountainous regions must explicitly account for the physical realities of walking-based mobility, especially where formal transport networks are sparse.

Based on these findings, we offer several policy recommendations. First, national and regional health planners should adopt differentiated service coverage benchmarks for mountainous regions. A flexible 30 min walking-time threshold could be integrated as a context-sensitive standard to guide rural facility allocation. Second, decentralized, near-distance infrastructure investments should be prioritized in high-altitude and topographically fragmented areas to reduce access barriers. Third, terrain-sensitive accessibility models such as the MIMWM should be incorporated into routine health planning, budget allocation, and service evaluation frameworks to ensure that spatial equity is operationalized in practice. Finally, indicators used to measure healthcare accessibility should be tailored to environmental context, distinguishing between infrastructure-based and workforce-based access constraints.

Building on these recommendations, our findings offer several actionable directions for planners:

• iFacility siting and upgrading: Cells and villages that remain below the national benchmarks within the 0–30 min walking isochrone should be prioritized for new village clinics, outreach stations, or capacity upgrades⁵⁶. The 30 min threshold, where gains start to diminish, can be used as a terrain-sensitive service benchmark when screening candidate sites.
• iiPedestrian micro-infrastructure: In deficit clusters identified by the MIMWM maps, small-scale works—trail hardening, stairways/switchbacks on steep segments, footbridges, slope stabilization, and wayfinding—can materially expand effective catchments at low cost⁵⁷.
• iiiLow-volume motorized support: For dispersed hamlets beyond 30 min on foot, demand-responsive shuttles or scheduled market-day minibuses linking hamlets to the nearest clinic can convert otherwise unreachable populations into the service area⁵⁸, especially for maternal/child and chronic care.
• ivLand-use coordination: new housing, public service points, and village regeneration should prefer locations that co-locate with the 15–30 min isochrones, avoiding further dispersion into high-resistance terrain.
• vMobile and outreach services: Periodic mobile clinics and medicine drop-points targeted at the most persistent low-access cells can hedge against seasonal isolation^59,60.

Together, these strategies translate MIMWM outputs into a practical portfolio that improves equity under rugged topography.

Future studies should continue refining the MIMWM by incorporating dynamic components such as time-varying service availability, emergency mobility behavior, seasonal accessibility constraints, and population-specific walking capacities. These enhancements will be critical to designing resilient, evidence-based, and equitable health resource allocation strategies that meet the needs of geographically marginalized populations.

Conclusions

This study demonstrates the critical importance of integrating terrain-sensitive factors into healthcare accessibility models for mountainous regions. The proposed Multi-Factor Integrated Mountain Walkability Model (MIMWM) can more accurately and realistically reflect service coverage compared to traditional Euclidean and network-based approaches. By incorporating slope-induced walking impedance, high-altitude physiological decline, and land-use resistance, the model captures the real-world mobility constraints faced by residents in rugged terrains.

Our findings reveal a 30 min walking-time threshold beyond which accessibility improvements plateau and show that conventional national standards may systematically overestimate service access in high-altitude contexts. The comparison with single-factor models further highlights the dominant influence of terrain and walking capacity on access inequality, underscoring the inadequacy of one-size-fits-all planning benchmarks.

Policy implications include the need to revise healthcare service coverage standards for mountainous regions, prioritize decentralized infrastructure development, and adopt terrain-sensitive models in routine planning and resource allocation. The MIMWM framework provides a replicable and adaptable tool for improving spatial equity in healthcare access across diverse topographies.

While this study focused on walking to foreground terrain effects, the framework is readily extensible. First, a road-network layer with class-specific speeds, gradient penalties, and weather/seasonal adjustments can generate door-to-door driving times for 2SFCA^5,29. Second, scheduled public transport can be integrated using stop access/egress walking, timetable-based travel times (GTFS), transfer/waiting penalties, and service frequency to compute time-dependent transit accessibility^9,52. Third, informal transport (e.g., village vans or motorcycle taxis) can be represented via headway-based waiting time and empirical speeds along minor tracks. These mode-specific impedance surfaces can be combined either as separate accessibility layers for targeted policy (e.g., maternal care transit planning) or as a composite generalized-cost surface (e.g., log sum or minimum-time fusion) to assess realistic multimodal catchments. Embedding these extensions within E2SFCA variants⁷ would help inform national planning where walking, driving, and transit jointly shape access in mountainous regions.

Future research should extend this framework by incorporating dynamic travel patterns, seasonal accessibility fluctuations, and demographic-specific walking constraints. For example, seasonal changes (such as snow, rain, and vegetation changes) may significantly affect walking behavior and accessibility. To model these factors, time series analysis or seasonal adjustment models can be introduced to capture the impact of environmental conditions on walking behavior. Additionally, combining geographic information system data and climate data can more accurately simulate walking conditions and accessibility changes across different seasons. Such enhancements will support the development of resilient and equitable health systems that better serve geographically marginalized populations.

Author contributions

Conceptualization, X.D.; methodology, X.D.; software, X.D.; validation, X.D.; formal analysis, X.D.; investigation, X.D.; data curation, X.D.; writing—original draft prepara-tion, X.D.; writing—review and editing, S.Z.; visualization, X.D.; supervision, M.D.; project administration, S.Z. All authors have read and agreed to the published version of the manuscript.

Data availability

All data that support the findings of this study are included in this article.