Probing an AI regression model for hand bone age determination using gradient-based saliency mapping.

Understanding how a neural network makes decisions holds significant value for users. For this reason, gradient-based saliency mapping was tested on an artificial intelligence (AI) regression model for determining hand bone age from X-ray radiographs. The partial derivative (PD) of the inferred age with respect to input image intensity at each pixel served as a saliency marker to find sensitive areas contributing to the outcome. The mean of the absolute PD values was calculated for five anatomical regions of interest, and one hundred test images were evaluated with this procedure. The PD maps suggested that the AI model employed a holistic approach in determining hand bone age, with the wrist area being the most important at early ages. However, this importance decreased with increasing age. The middle section of the metacarpal bones was the least important area for bone age determination. The muscular region between the first and second metacarpal bones also exhibited high PD values but contained no bone age information, suggesting a region of vulnerability in age determination. An end-to-end gradient-based saliency map can be obtained from a black box regression AI model and provide insight into how the model makes decisions.

Biocultural evidence of precise manual activities in an Early Holocene individual of the high-altitude Peruvian Andes.

OBJECTIVES: Cuncaicha, a rockshelter site in the southern Peruvian Andes, has yielded archaeological evidence for human occupation at high elevation (4,480 masl) during the Terminal Pleistocene (12,500-11,200 cal BP), Early Holocene (9,500-9,000 cal BP), and later periods. One of the excavated human burials (Feature 15-06), corresponding to a middle-aged female dated to ~8,500 cal BP, exhibits skeletal osteoarthritic lesions previously proposed to reflect habitual loading and specialized crafting labor. Three small tools found in association with this burial are hypothesized to be associated with precise manual dexterity. MATERIALS AND METHODS: Here, we tested this functional hypothesis through the application of a novel multivariate methodology for the three-dimensional analysis of muscle attachment surfaces (entheses). This original approach has been recently validated on both lifelong-documented anthropological samples as well as experimental studies in nonhuman laboratory samples. Additionally, we analyzed the three-dimensional entheseal shape and resulting moment arms for muscle opponens pollicis. RESULTS: Results show that Cuncaicha individual 15-06 shows a distinctive entheseal pattern associated with habitual precision grasping via thumb-index finger coordination, which is shared exclusively with documented long-term precision workers from recent historical collections. The separate geometric morphometric analysis revealed that the individual's opponens pollicis enthesis presents a highly projecting morphology, which was found to strongly correlate with long joint moment arms (a fundamental component of force-producing capacity), closely resembling the form of Paleolithic hunter-gatherers from diverse geo-chronological contexts of Eurasia and North Africa. DISCUSSION: Overall, our findings provide the first biocultural evidence to confirm that the lifestyle of some of the earliest Andean inhabitants relied on habitual and forceful precision grasping tasks.

Applicability of two commonly used bone age assessment methods to twenty-first century UK children.

OBJECTIVES: To assess the effect of secular change on skeletal maturation and thus on the applicability of the Greulich and Pyle (G&P) and Tanner and Whitehouse (TW3) methods. METHODS: BoneXpert was used to assess bone age from 392 hand trauma radiographs (206 males, 257 left). The paired sample t test was performed to assess the difference between mean bone age (BA) and mean chronological age (CA). ANOVA was used to assess the differences between groups based on socioeconomic status (taken from the Index of Multiple Deprivation). RESULTS: CA ranged from 2 to 15 years for females and 2.5 to 15 years for males. Numbers of children living in low, average and high socioeconomic areas were 216 (55%), 74 (19%) and 102 (26%) respectively. We found no statistically significant difference between BA and CA when using G&P. However, using TW3, CA was underestimated in females beyond the age of 3 years, with significant differences between BA and CA (- 0.43 years, SD 1.05, p = < 0.001) but not in males (0.01 years, SD 0.97, p = 0.76). Of the difference in females, 17.8% was accounted for by socioeconomic status. CONCLUSION: No significant difference exists between BoneXpert-derived BA and CA when using the G&P atlas in our study population. There was a statistically significant underestimation of BoneXpert-derived BA compared with CA in females when using TW3, particularly in those from low and average socioeconomic backgrounds. Secular change has not led to significant advancement in skeletal maturation within our study population. KEY POINTS: • The Greulich and Pyle method can be applied to the present-day United Kingdom (UK) population. • The Tanner and Whitehouse (TW3) method consistently underestimates the age of twenty-first century UK females by an average of 5 months. • Secular change has not advanced skeletal maturity of present-day UK children compared with those of the mid-twentieth century.

Is Bone Elevation in Hand Muscle Attachments Associated with Biomechanical Stress? A Histological Approach to an Anthropological Question.

In anthropological sciences, muscle attachments are typically utilized for reconstructing the physical activities of past human populations. This approach relies on the concept that entheseal bone morphology is influenced by cumulative biomechanical stress. A fundamental criterion for assessing the stage of entheseal change involves the proportion of elevated bone area. However, it is not yet clear if bone elevation is associated with biomechanical forces exerted during physical activity, while the histology of the entheses of the human hand, the least-bodyweight-bearing anatomical area, is not fully investigated. Multiple previous studies on entheses have concluded that the concentration of calcified fibrocartilage reflects the level of applied forces. On this basis, if hand entheseal surface elevation was associated with the level of biomechanical stress, then a greater amount of calcified fibrocartilage would be expected in entheses' central and more projecting bone areas. More importantly, individual entheses with a greater proportion of elevated bone areas would present a higher total concentration of calcified fibrocartilage. To test these hypotheses, this pilot study conducted a histological quantitative analysis on two thumb entheses of four fully-documented body donors. Across individuals, all central entheseal regions presented greater calcified fibrocartilage, while the entheses showing additional bone elevation in their marginal areas comprised substantially higher total values. The observations of this small-scale pilot study support the concept that interindividual differences in entheseal bone morphology are related to varying levels of biomechanical loading. Furthermore, they encourage future research to compile larger sample sizes, for comparing individuals with distinct lifelong activities. Anat Rec, 302:1093-1103, 2019. © 2018 Wiley Periodicals, Inc.

Trabecular bone patterning across the human hand.

Hand bone morphology is regularly used to link particular hominin species with behaviors relevant to cognitive/technological progress. Debates about the functional significance of differing hominin hand bone morphologies tend to rely on establishing phylogenetic relationships and/or inferring behavior from epigenetic variation arising from mechanical loading and adaptive bone modeling. Most research focuses on variation in cortical bone structure, but additional information about hand function may be provided through the analysis of internal trabecular structure. While primate hand bone trabecular structure is known to vary in ways that are consistent with expected joint loading differences during manipulation and locomotion, no study exists that has documented this variation across the numerous bones of the hand. We quantify the trabecular structure in 22 bones of the human hand (early/extant modern Homo sapiens) and compare structural variation between two groups associated with post-agricultural/industrial (post-Neolithic) and foraging/hunter-gatherer (forager) subsistence strategies. We (1) establish trabecular bone volume fraction (BV/TV), modulus (E), degree of anisotropy (DA), mean trabecular thickness (Tb.Th) and spacing (Tb.Sp); (2) visualize the average distribution of site-specific BV/TV for each bone; and (3) examine if the variation in trabecular structure is consistent with expected joint loading differences among the regions of the hand and between the groups. Results indicate similar distributions of trabecular bone in both groups, with those of the forager sample presenting higher BV/TV, E, and lower DA, suggesting greater and more variable loading during manipulation. We find indications of higher loading along the ulnar side of the forager sample hand, with high site-specific BV/TV distributions among the carpals that are suggestive of high loading while the wrist moves through the 'dart-thrower's' motion. These results support the use of trabecular structure to infer behavior and have direct implications for refining our understanding of human hand evolution and fossil hominin hand use.

Automated radiogrammetry is a feasible method for measuring bone quality and bone maturation in severely disabled children.

BACKGROUND: Children with severe neurological impairment and intellectual disability are prone to low bone quality and fractures. OBJECTIVE: We studied the feasibility of automated radiogrammetry in assessing bone quality in this specific group of children. We measured outcome of bone quality and, because these children tend to have altered skeletal maturation, we also studied bone age. MATERIALS AND METHODS: We used hand radiographs obtained in 95 children (mean age 11.4 years) presenting at outpatient paediatric clinics. We used BoneXpert software to determine bone quality, expressed as paediatric bone index and bone age. RESULTS: Regarding feasibility, we successfully obtained a paediatric bone index in 60 children (63.2%). The results on bone quality showed a mean paediatric bone index standard deviation score of -1.85, significantly lower than that of healthy peers (P < 0.0001). Almost 50% of the children had severely diminished bone quality. In 64% of the children bone age diverged more than 1 year from chronological age. This mostly concerned delayed bone maturation. CONCLUSION: Automated radiogrammetry is feasible for evaluating bone quality in children who have disabilities but not severe contractures. Bone quality in these children is severely diminished. Because bone maturation frequently deviated from chronological age, we recommend comparison to bone-age-related reference values.

[Correlation of bone mineral density of the mandibular angle, hand and total body in 839 healthy individuals aged from 5 to 18 years].

OBJECTIVES: To investigate the correlation of bone mineral density (BMD) of mandibular angle, hand and total body in healthy individuals aged from 5 to 18 years. METHODS: Eight hundred and thirty-nine healthy individuals from 5 to 18 years old (422 males, 417 females) in 5 primary and secondary schools in Guangzhou were divided into 14 age groups. Dual energy X-ray absorptiometry (DXA) was used to measure the BMD of mandibular angle, hand and total body. The data were statistically analyzed using Pearson correlation analysis. RESULTS: The BMD of mandibular angle increased with age. In females, the BMD of mandibular angle increased quickly from 12 to 16 years old, and its increasing rate gradually slowed down after 16 years old. In males, the BMD of mandibular angle increased quickly after 14 years old, and its increase had not been stopped until 18 years old. Females in 12, 13, 14, 15, 16, 17-year-old group had significantly higher mandibular angle BMD [(0.95 ± 0.19), (1.01 ± 0.17), (1.11 ± 0.17), (1.25 ± 0.13), (1.28 ± 0.14), (1.30 ± 0.13) g/cm(2)] than males in the age-matched group (P < 0.05). There was no significant difference between mandibular angle BMD in males and in females at the age of 18, and from 5 to 11 years old (P > 0.05). For males, the mandibular angle BMD was highly correlated with age (r = 0.696, P < 0.001), hand BMD (r = 0.779, P < 0.001) and total body BMD (r = 0.831, P < 0.001). For females, the mandibular angle BMD was highly correlated with age (r = 0.795, P < 0.001), hand BMD (r = 0.839, P < 0.001) and total body BMD (r = 0.872, P < 0.001). CONCLUSIONS: The mandibular angle BMD in healthy individuals from 5 to 18 years old increased with age. The mandibular angle BMD was closely related to hand BMD and total body BMD.

Fully automatic bone age estimation from left hand MR images.

There has recently been an increased demand in bone age estimation (BAE) of living individuals and human remains in legal medicine applications. A severe drawback of established BAE techniques based on X-ray images is radiation exposure, since many countries prohibit scanning involving ionizing radiation without diagnostic reasons. We propose a completely automated method for BAE based on volumetric hand MRI images. On our database of 56 male caucasian subjects between 13 and 19 years, we are able to estimate the subjects age with a mean difference of 0.85 ± 0.58 years compared to the chronological age, which is in line with radiologist results using established radiographic methods. We see this work as a promising first step towards a novel MRI based bone age estimation system, with the key benefits of lacking exposure to ionizing radiation and higher accuracy due to exploitation of volumetric data.

Towards automatic bone age estimation from MRI: localization of 3D anatomical landmarks.

Bone age estimation (BAE) is an important procedure in forensic practice which recently has seen a shift in attention from X-ray to MRI based imaging. To automate BAE from MRI, localization of the joints between hand bones is a crucial first step, which is challenging due to anatomical variations, different poses and repeating structures within the hand. We propose a landmark localization algorithm using multiple random regression forests, first analyzing the shape of the hand from information of the whole image, thus implicitly modeling the global landmark configuration, followed by a refinement based on more local information to increase prediction accuracy. We are able to clearly outperform related approaches on our dataset of 60 T1-weighted MR images, achieving a mean landmark localization error of 1.4 ± 1.5mm, while having only 0.25% outliers with an error greater than 10mm.

Hands of early primates.

Questions surrounding the origin and early evolution of primates continue to be the subject of debate. Though anatomy of the skull and inferred dietary shifts are often the focus, detailed studies of postcrania and inferred locomotor capabilities can also provide crucial data that advance understanding of transitions in early primate evolution. In particular, the hand skeleton includes characteristics thought to reflect foraging, locomotion, and posture. Here we review what is known about the early evolution of primate hands from a comparative perspective that incorporates data from the fossil record. Additionally, we provide new comparative data and documentation of skeletal morphology for Paleogene plesiadapiforms, notharctines, cercamoniines, adapines, and omomyiforms. Finally, we discuss implications of these data for understanding locomotor transitions during the origin and early evolutionary history of primates. Known plesiadapiform species cannot be differentiated from extant primates based on either intrinsic hand proportions or hand-to-body size proportions. Nonetheless, the presence of claws and a different metacarpophalangeal [corrected] joint form in plesiadapiforms indicate different grasping mechanics. Notharctines and cercamoniines have intrinsic hand proportions with extremely elongated proximal phalanges and digit rays relative to metacarpals, resembling tarsiers and galagos. But their hand-to-body size proportions are typical of many extant primates (unlike those of tarsiers, and possibly Teilhardina, which have extremely large hands). Non-adapine adapiforms and omomyids exhibit additional carpal features suggesting more limited dorsiflexion, greater ulnar deviation, and a more habitually divergent pollex than observed plesiadapiforms. Together, features differentiating adapiforms and omomyiforms from plesiadapiforms indicate increased reliance on vertical prehensile-clinging and grasp-leaping, possibly in combination with predatory behaviors in ancestral euprimates.

Magnetic field shimming of a permanent magnet using a combination of pieces of permanent magnets and a single-channel shim coil for skeletal age assessment of children.

We adopted a combination of pieces of permanent magnets and a single-channel (SC) shim coil to shim the magnetic field in a magnetic resonance imaging system dedicated for skeletal age assessment of children. The target magnet was a 0.3-T open and compact permanent magnet tailored to the hand imaging of young children. The homogeneity of the magnetic field was first improved by shimming using pieces of permanent magnets. The residual local inhomogeneity was then compensated for by shimming using the SC shim coil. The effectiveness of the shimming was measured by imaging the left hands of human subjects and evaluating the image quality. The magnetic resonance images for the child subject clearly visualized anatomical structures of all bones necessary for skeletal age assessment, demonstrating the usefulness of combined shimming.

The reliability of the Greulich-Pyle method in bone age determination among Australian children.

INTRODUCTION: Bone age (BA) determination in skeletally immature children has been used as a measurement of growth for many years. The Greulich-Pyle (G&P) method of estimating BA is most commonly used. The standards used within this atlas were compiled from research conducted on normal white children in the United States, during the 1930s. The applicability of G&P beyond populations similar to its own can be variable. The aim of this study was to determine the accuracy of G&P in BA determination among Australian children. METHODS AND MATERIALS: Hand X-rays of children under the age of 18, investigated for trauma, were recruited. Mean differences between BA, according to the standards of G&P, and chronological age (CA) were compared among all patients and subgroups according to age, gender and left versus right hand. RESULTS: Between January and December 2010, 654 children underwent hand X-rays, 406 of these were included (276 males and 130 females). Overall BA was 2.2 months less than CA (P-value = 0.005). BA of males and females was estimated to be 1.5 months (P-value = 0.142) and 3.7 months (P-value = 0.002) less than their CA respectively. No statistically significant difference was identified with intra-observer (P-value = 0.846) and inter-observer interpretations (P-value = 0.102). CONCLUSIONS: Our results show that the standards of G&P are an accurate means of BA determination in Australian children.

Physiological bone responses in the fingers after more than 10 years of high-level sport climbing: analysis of cortical parameters.

OBJECTIVE: Sports activity can induce bone modeling processes with apposition of new bone and changes in bone morphology. Sport climbing places extreme forces and stress on the hands, especially on the bones of the fingers. This study examines sports-induced physiological adaptations of the finger bones of climbers. METHODS: In this cohort study, the radiographs of 31 high-level (Union Internationale des Associations d'Alpinisme [UIAA] metric scale range 8.33 to 11.33), experienced (median 20 years climbing time) adult climbers were compared with those of a control group of 67 patients. Cortical dimensions and variables were measured and analyzed in a total of 330 fingers. An association analysis of climbing-related variables was also performed. RESULTS: The climber's bones showed a 25% higher cortical proportion than those of the control group. On average, the outer cortical width of the climbers' bones was 6% larger and the medullary canal was 20% narrower than in the control group (P < .05). The differences between groups were more pronounced in the sagittal plane and more pronounced distally in the fingers. No associations were found between age, climbing experience, climbing level, and the cortical hypertrophy. CONCLUSIONS: Differences in bone morphology can be observed in the finger bones of adult climbers when compared with controls. Because the differences are more pronounced at the palmar and dorsal cortices, the analysis of the sagittal plane should always be included in future investigations. To evaluate climbing-related factors influencing these adaptive morphologic differences, further studies with larger, more specific study cohorts are needed.

Finite element modeling of the influence of hand position and bone properties on the Colles' fracture load during a fall.

Distal forearm fracture is one of the most frequently observed osteoporotic fractures, which may occur as a result of low energy falls such as falls from a standing height and may be linked to the osteoporotic nature of the bone, especially in the elderly. In order to prevent the occurrence of radius fractures and their adverse outcomes, understanding the effect of both extrinsic and intrinsic contributors to fracture risk is essential. In this study, a nonlinear fracture mechanics-based finite element model is applied to human radius to assess the influence of extrinsic factors (load orientation and load distribution between scaphoid and lunate) and intrinsic bone properties (age-related changes in fracture properties and bone geometry) on the Colles' fracture load. Seven three-dimensional finite element models of radius were created, and the fracture loads were determined by using cohesive finite element modeling, which explicitly represented the crack and the fracture process zone behavior. The simulation results showed that the load direction with respect to the longitudinal and dorsal axes of the radius influenced the fracture load. The fracture load increased with larger angles between the resultant load and the dorsal axis, and with smaller angles between the resultant load and longitudinal axis. The fracture load also varied as a function of the load ratio between the lunate and scaphoid, however, not as drastically as with the load orientation. The fracture load decreased as the load ratio (lunate/scaphoid) increased. Multiple regression analysis showed that the bone geometry and the load orientation are the most important variables that contribute to the prediction of the fracture load. The findings in this study establish a robust computational fracture risk assessment method that combines the effects of intrinsic properties of bone with extrinsic factors associated with a fall, and may be elemental in the identification of high fracture risk individuals as well as in the development of fracture prevention methods including protective falling techniques. The additional information that this study brings to fracture identification and prevention highlights the promise of fracture mechanics-based finite element modeling in fracture risk assessment.

Registration-based segmentation with articulated model from multipostural magnetic resonance images for hand bone motion animation.

PURPOSE: The quantitative measurements of hand bones, including volume, surface, orientation, and position are essential in investigating hand kinematics. Moreover, within the measurement stage, bone segmentation is the most important step due to its certain influences on measuring accuracy. Since hand bones are small and tubular in shape, magnetic resonance (MR) imaging is prone to artifacts such as nonuniform intensity and fuzzy boundaries. Thus, greater detail is required for improving segmentation accuracy. The authors then propose using a novel registration-based method on an articulated hand model to segment hand bones from multipostural MR images. METHODS: The proposed method consists of the model construction and registration-based segmentation stages. Given a reference postural image, the first stage requires construction of a drivable reference model characterized by hand bone shapes, intensity patterns, and articulated joint mechanism. By applying the reference model to the second stage, the authors initially design a model-based registration pursuant to intensity distribution similarity, MR bone intensity properties, and constraints of model geometry to align the reference model to target bone regions of the given postural image. The authors then refine the resulting surface to improve the superimposition between the registered reference model and target bone boundaries. RESULTS: For each subject, given a reference postural image, the proposed method can automatically segment all hand bones from all other postural images. Compared to the ground truth from two experts, the resulting surface image had an average margin of error within 1 mm (mm) only. In addition, the proposed method showed good agreement on the overlap of bone segmentations by dice similarity coefficient and also demonstrated better segmentation results than conventional methods. CONCLUSIONS: The proposed registration-based segmentation method can successfully overcome drawbacks caused by inherent artifacts in MR images and obtain more accurate segmentation results automatically. Moreover, realistic hand motion animations can be generated based on the bone segmentation results. The proposed method is found helpful for understanding hand bone geometries in dynamic postures that can be used in simulating 3D hand motion through multipostural MR images.

High disease activity is a predictor of cortical hand bone loss in post-menopausal patients with established rheumatoid arthritis: a 5-year multicentre longitudinal study.

OBJECTIVE: The objective of this study was to examine 5-year change in cortical hand BMD in female RA patients with established disease. Further, possibly baseline predictors of 5-year loss in digital X-ray radiogrammetry (DXR)-BMD were studied. METHODS: This 5-year multicentre, longitudinal study included patients from Amsterdam (the Netherlands), Truro (UK) and Oslo (Norway). At baseline, 50 patients were consecutively included per centre. Inclusion criteria were: female sex, age 50-70 years and disease duration >or=5 years. This study presents 5-year follow-up data for 85 of these 150 patients (29 patients from Amsterdam; 26 from Truro; and 30 from Oslo). Clinical examination, blood test and radiographs were taken at baseline and 5-year follow-up. Cortical hand BMD was measured by DXR from hand radiographs. RESULTS: The mean (95% CI) baseline DXR-BMD for all patients was 0.46 (0.44, 0.48) g/cm(2) and the median 5-year DXR-BMD change was -6.7% (-11.2, -2.82%). Five-year DXR-BMD loss was associated with baseline measurements of age, RF, CRP, HAQ and 28-joint disease activity score (DAS-28) in univariate linear regression analyses. DAS-28 at baseline was an independent predictor of 5-year DXR-BMD loss in multivariate linear regression analyses corrected for centre, age and use of bone-protective agents. CONCLUSION: High disease activity measured by DAS-28 was an independent predictor of cortical hand bone loss over 5 years in established, destructive RA. This finding supports that increased disease activity leads to localized bone loss in long-standing RA and underlines the importance of tight control and aggressive anti-inflammatory treatment in these patients.

Automatic determination of left- and right-hand bone age in the First Zurich Longitudinal Study.

BACKGROUND/AIMS: A more advanced bone age (BA) has been reported for the left hand relative to the right hand, while another study has found no such effect. The aim was to study the average difference of automated BoneXpert BA determination (left- vs. right-hand) for normal children, examine the precision of automatic BA and provide a BA reference for normal Caucasian children. METHODS: Radiographs of both hands (age range: 2-20 years) were digitised and analysed automatically to determine Greulich-Pyle BA, producing analysis results for 3,374 left-hand and 2,752 right-hand images. RESULTS: Comparison of left- and right-hand BA showed no average difference (<0.07 years, 95% confidence). The SD of the differences between left and right sides was 0.25 years for boys as well as girls, implying the precision of automated Greulich-Pyle BA determination was 0.18 years or better. Greulich-Pyle BA for boys and girls were on average 0.10 and 0.21 years below the chronological age. CONCLUSION: The left and right hand give the same BA on average and the SD between the sides is 0.25 years, indicating an excellent precision of the automated method.

Influence of socioeconomic status and body mass index on bone age.

BACKGROUND/AIMS: To evaluate the relationship of socioeconomic status (SES) and body mass index (BMI) with skeletal maturation in children from Marrakech (Morocco). METHODS: SES, BMI z-score and bone age (BA) were measured in a cohort of 623 children (280 boys and 343 girls, chronological age (CA) ranged from 6.6 to 18.8 years, mean 14.1 years). BA estimation was performed with the Greulich and Pyle atlas. Two social groups (privileged and unfavorable SES) were defined. A multiple linear regression analysis was performed to assess the relationship between BA-CA and age-and sex-specific BMI z-score. RESULTS: Global maturation delay was seen in the sample (BA-CA -0.56; SD 1.29). There was a significant relationship between skeletal maturation (BA-CA) and child BMI z-score among both genders. Bone age was more advanced in children with a greater BMI z-score. Privileged SES was positively associated with children's BA-CA for girls but there was no association for boys. In the boys' sample, there was no evidence that BA-CA variations with BMI z-score depended on socioeconomic status (p=0.664). Whatever the gender of the child, a greater BMI z-score increases the maturation. CONCLUSION: The multiple linear regression analysis is an interesting approach to understand the links between skeletal maturation, BMI and SES. In Moroccan children, excess weight is associated with privileged SES.

A paediatric bone index derived by automated radiogrammetry.

SUMMARY: Hand radiographs are obtained routinely to determine bone age of children. This paper presents a method that determines a Paediatric Bone Index automatically from such radiographs. The Paediatric Bone Index is designed to have minimal relative standard deviation (7.5%), and the precision is determined to be 1.42%. INTRODUCTION: We present a computerised method to determine bone mass of children based on hand radiographs, including a reference database for normal Caucasian children. METHODS: Normal Danish subjects (1,867), of ages 7-17, and 531 normal Dutch subjects of ages 5-19 were included. Historically, three different indices of bone mass have been used in radiogrammetry all based on A = piTW(1 - T/W), where T is the cortical thickness and W the bone width. The indices are the metacarpal index A/W(2), DXR-BMD = A/W, and Exton-Smith's index A/(WL), where L is the length of the bone. These indices are compared with new indices of the form A/(W(a) L(b)), and it is argued that the preferred index has minimal SD relative to the mean value at each bone age and sex. Finally, longitudinal series of X-rays of 20 Japanese children are used to derive the precision of the measurements. RESULTS: The preferred index is A/(W(1.33) L(0.33)), which is named the Paediatric Bone Index, PBI. It has mean relative SD 7.5% and precision 1.42%. CONCLUSIONS: As part of the BoneXpert method for automated bone age determination, our method facilitates retrospective research studies involving validation of the proposed index against fracture incidence and adult bone mineral density.