The effect of birth weight on tooth development by Demirjian's method.

OBJECTIVES: The aim of this study was to investigate the impact of birth weight on tooth development in children aged 7-8 years. MATERIALS AND METHODS: This retrospective cohort study comprised 75 children born at Bint Al-Huda Hospital, Bojnurd, in 2013-2014. The children were categorized into three groups based on their birth weight: Normal Birth Weight (NBW), Low Birth Weight (LBW), and Very Low Birth Weight (VLBW). Panoramic radiographs were taken for orthodontic examination, and Demirjian's 8-teeth method was employed to determine dental age. The study compared dental and chronological age within each group. Data analysis utilized SPSS software version 26, employing One-way ANOVA and chi-square tests. Statistical significance was set at P ≤ 0.05. RESULTS: The mean difference in dental and chronological age for Very Low Birth Weight (VLBW) children was 0.22 ± 0.44 years, for Low Birth Weight (LBW) children it was 0.19 ± 0.45 years, and for Normal Birth Weight (NBW) children, it was 0.08 ± 0.46 years. Although the mean difference decreased with increasing birth weight, this trend did not achieve statistical significance (P = 0.55). Furthermore, no significant differences were observed between the weight groups (P = 0.529) or genders (P = 0.191).

Evergrowing incisors of diprotodont marsupials record age and life history.

OBJECTIVE: Tooth growth and wear are commonly used tools for determining the age of mammals. The most speciose order of marsupials, Diprotodontia, is characterised by a pair of procumbent incisors within the lower jaw. This study examines the growth and wear of these incisors to understand their relationship with age and sex. DESIGN: Measurements of mandibular incisor crown and root length were made for two sister species of macropodid (kangaroos and wallabies); Macropus giganteus and Macropus fuliginosus. Histological analysis examined patterns of dentine and cementum deposition within these teeth. Broader generalisability within Diprotodontia was tested using dentally reduced Tarsipes rostratus - a species disparate in body size and incisor function to the studied macropodids. RESULTS: In the macropodid sample it is demonstrated that the hypsodont nature of these incisors makes measurements of their growth (root length) and wear (crown length) accurate indicators of age and sex. Model fitting finds that root growth proceeds according to a logarithmic function across the lifespan, while crown wear follows a pattern of exponential reduction for both macropodid species. Histological results find that secondary dentine deposition and cementum layering are further indicators of age. Incisor measurements are shown to correlate with age in the sample of T. rostratus. CONCLUSIONS: The diprotodontian incisor is a useful tool for examining chronological age and sex, both morphologically and microstructurally. This finding has implications for population ecology, palaeontology and marsupial evolution.

Dental Age Estimation in Northern Chinese Han Children and Adolescents Using Demirjian's Method Combined with Machine Learning Algorithms.

OBJECTIVES: To investigate the application value of combining the Demirjian's method with machine learning algorithms for dental age estimation in northern Chinese Han children and adolescents. METHODS: Oral panoramic images of 10 256 Han individuals aged 5 to 24 years in northern China were collected. The development of eight permanent teeth in the left mandibular was classified into different stages using the Demirjian's method. Various machine learning algorithms, including support vector regression (SVR), gradient boosting regression (GBR), linear regression (LR), random forest regression (RFR), and decision tree regression (DTR) were employed. Age estimation models were constructed based on total, female, and male samples respectively using these algorithms. The fitting performance of different machine learning algorithms in these three groups was evaluated. RESULTS: SVR demonstrated superior estimation efficiency among all machine learning models in both total and female samples, while GBR showed the best performance in male samples. The mean absolute error (MAE) of the optimal age estimation model was 1.246 3, 1.281 8 and 1.153 8 years in the total, female and male samples, respectively. The optimal age estimation model exhibited varying levels of accuracy across different age ranges, which provided relatively accurate age estimations in individuals under 18 years old. CONCLUSIONS: The machine learning model developed in this study exhibits good age estimation efficiency in northern Chinese Han children and adolescents. However, its performance is not ideal when applied to adult population. To improve the accuracy in age estimation, the other variables can be considered.

Adolescents and Children Age Estimation Using Machine Learning Based on Pulp and Tooth Volumes on CBCT Images.

OBJECTIVES: To estimate adolescents and children age using stepwise regression and machine learning methods based on the pulp and tooth volumes of the left maxillary central incisor and cuspid on cone beam computed tomography (CBCT) images, and to compare and analyze the estimation results. METHODS: A total of 498 Shanghai Han adolescents and children CBCT images of the oral and maxillofacial regions were collected. The pulp and tooth volumes of the left maxillary central incisor and cuspid were measured and calculated. Three machine learning algorithms (K-nearest neighbor, ridge regression, and decision tree) and stepwise regression were used to establish four age estimation models. The coefficient of determination, mean error, root mean square error, mean square error and mean absolute error were computed and compared. A correlation heatmap was drawn to visualize and the monotonic relationship between parameters was visually analyzed. RESULTS: The K-nearest neighbor model (R2=0.779) and the ridge regression model (R2=0.729) outperformed stepwise regression (R2=0.617), while the decision tree model (R2=0.494) showed poor fitting. The correlation heatmap demonstrated a monotonically negative correlation between age and the parameters including pulp volume, the ratio of pulp volume to hard tissue volume, and the ratio of pulp volume to tooth volume. CONCLUSIONS: Pulp volume and pulp volume proportion are closely related to age. The application of CBCT-based machine learning methods can provide more accurate age estimation results, which lays a foundation for further CBCT-based deep learning dental age estimation research.

Determining Whether an Individual is 18 Years or Older Based on the Third Molar Root Pulp Visibility in East China.

OBJECTIVES: To investigate the age-related changes of the mandibular third molar root pulp visibility in individuals in East China, and to explore the feasibility of applying this method to determine whether an individual is 18 years or older. METHODS: A total of 1 280 oral panoramic images were collected from the 15-30 years old East China population, and the mandibular third molar root pulp visibility in all oral panoramic images was evaluated using OLZE 0-3 four-stage method, and the age distribution of the samples at each stage was analyzed using descriptive statistics. RESULTS: Stages 0, 1, 2 and 3 first appeared in 16.88, 19.18, 21.91 and 25.44 years for males and in 17.47, 20.91, 22.01 and 26.01 years for females. In all samples, individuals at stages 1 to 3 were over 18 years old. CONCLUSIONS: It is feasible to determine whether an individual in East China is 18 years or older based on the mandibular third molar root pulp visibility on oral panoramic images.

Research Progress on Dental Age Estimation Based on MRI Technology.

Dental age estimation is a crucial aspect and one of the ways to accomplish forensic age estimation, and imaging technology is an important technique for dental age estimation. In recent years, some studies have preliminarily confirmed the feasibility of magnetic resonance imaging (MRI) in evaluating dental development, providing a new perspective and possibility for the evaluation of dental development, suggesting that MRI is expected to be a safer and more accurate tool for dental age estimation. However, further research is essential to verify its accuracy and feasibility. This article reviews the current state, challenges and limitations of MRI in dental development and age estimation, offering reference for the research of dental age assessment based on MRI technology.

Application of Medical Statistical and Machine Learning Methods in the Age Estimation of Living Individuals.

In the study of age estimation in living individuals, a lot of data needs to be analyzed by mathematical statistics, and reasonable medical statistical methods play an important role in data design and analysis. The selection of accurate and appropriate statistical methods is one of the key factors affecting the quality of research results. This paper reviews the principles and applicable principles of the commonly used medical statistical methods such as descriptive statistics, difference analysis, consistency test and multivariate statistical analysis, as well as machine learning methods such as shallow learning and deep learning in the age estimation research of living individuals, and summarizes the relevance and application prospects between medical statistical methods and machine learning methods. This paper aims to provide technical guidance for the age estimation research of living individuals to obtain more scientific and accurate results.

Machine learning assisted 5-part tooth segmentation method for CBCT-based dental age estimation in adults.

BACKGROUND: The utilization of segmentation method using volumetric data in adults dental age estimation (DAE) from cone-beam computed tomography (CBCT) was further expanded by using current 5-Part Tooth Segmentation (SG) method. Additionally, supervised machine learning modelling -namely support vector regression (SVR) with linear and polynomial kernel, and regression tree - was tested and compared with the multiple linear regression model. MATERIAL AND METHODS: CBCT scans from 99 patients aged between 20 to 59.99 was collected. Eighty eligible teeth including maxillary canine, lateral incisor, and central incisor were used in this study. Enamel to dentine volume ratio, pulp to dentine volume ratio, lower tooth volume ratio, and sex was utilized as independent variable to predict chronological age. RESULTS: No multicollinearity was detected in the models. The best performing model comes from maxillary lateral incisor using SVR with polynomial kernel ( = 0.73). The lowest error rate achieved by the model was given also by maxillary lateral incisor, with 4.86 years of mean average error and 6.05 years of root means squared error. However, demands a complex approach to segment the enamel volume in the crown section and a lengthier labour time of 45 minutes per tooth.

Third molar eruption in dental panoramic radiographs as a feature for forensic age assessment - new reference data from a German population.

Forensic age assessment in the living can provide legal certainty when an individual's chronological age is unknown or when age-related information is questionable. An established method involves assessing the eruption of mandibular third molars through dental panoramic radiographs (PAN). In age assessment procedures, the respective findings are compared to reference data. The objective of this study was to generate new reference data in line with the required standards for mandibular third molar eruption within a German population. For this purpose, 605 PANs from 302 females and 303 males aged 15.04 to 25.99 years were examined. The PANs were acquired between 2013 and 2020, and the development of the mandibular third molars was rated independently by two experienced examiners using the Olze et al. staging scale from 2012. In case of disagreement in the assigned ratings, a consensus was reached through arbitration. While the mean, median and minimum ages were observed to increase with each stage of mandibular third molar eruption according to the Olze method, there was considerable overlap in the distribution of age between the stages. The minimum age for stage D, which corresponds to complete tooth eruption, was 16.1 years for females and 17.1 years for males. Thus, the completion of mandibular third molar eruption was found in both sexes before reaching the age of 18. In all individuals who had at least one tooth with completed eruption and who were younger than 17.4 years of age (n = 10), mineralization of the teeth in question was not complete. Based on our findings, the feature of assessing mandibular third molar eruption in PAN cannot be relied upon for determining age of majority.

Skeletal maturation evaluation: which is the reliability of dental calcification Demirjian method versus hand-wrist X-ray in growing subjects? A systematic review.

OBJECTIVES: This systematic review aimed at evaluating the reliability of dental maturation (DM) according to Demirjian method compared to hand and wrist maturation (HWM) to assess skeletal maturity (SM) in growing subjects, to identify the teeth and the corresponding mineralisation stages related to the pubertal growth spurt (PGS). MATERIALS AND METHODS: PubMed, Scopus, and Web of Science were systematically searched until January 5th, 2024, to identify observational cross-sectional studies that assessed the reliability of Demirjian method compared to the HWM methods (i.e., Grave and Brown and Fishman) in growing subjects. The quality assessment was evaluated using the Joanna Briggs Institute (JBI) Critical Appraisal Checklist. RESULTS: Out of 136 papers suitable for title/abstract screening, 19 included studies. Of them, 17 papers showed the reliability of Demirjian DM method compared to HWM Fishman and Grave and Brown methods to assess SM in growing subjects. According to JBI Critical Appraisal Checklist, 12 papers were high-quality studies and 7 papers were medium-quality studies.  Conclusions: The mandibular second molar might be considered as the best indicator compared to other teeth and that the peak of growth occurs no earlier than stage F in females and stage G in males according to Demirjian method. Also, the mandibular canine might be analysed as indicator of SM in males, and results suggest that the peak of growth occurs no earlier than maturation stage F according to Demirjian method, only in male subjects. Further studies are needed to confirm these findings.

Age estimation by volumetric analysis of teeth using cone beam computed tomography.

OBJECTIVES: To evaluate the feasibility of using the pulp volume (Pv) to total volume (Tv) ratio (Pv:Tv), obtained from cone beam computed tomography (CBCT) scans of single-rooted teeth, for age estimation in a Brazilian population sample. METHODS: After obtaining approval from the ethics committee, the study commenced by applying inclusion criteria to screen CBCT scans, resulting in a probability-based sample of participants aged 18 years and older (ranging from 18 to 82 years, with a mean age of 46.44 years). A total of 517 single-rooted teeth, including maxillary central incisors (CI), mandibular canines (C), and mandibular first premolars (FP), were chosen based on excellent agreement values (> 0.9). Pv and Tv measurements were conducted using semi-automatic segmentation with ITK-SNAP 3.8 software. Statistical analysis was performed using Jamovi software, with a significance level set at 5% (α = 0.05). RESULTS: A strong negative correlation (r > -0.7) was observed between chronological age and the Pv:Tv ratio across all examined teeth. However, when conducting regression analysis with Pv:Tv data and chronological age as the independent variable, only the mandibular FP teeth exhibited a normal distribution. The resulting linear model demonstrated moderate predictive value (approximately 64%) in explaining the variance in chronological age, but caution should be exercised when interpreting these findings. CONCLUSIONS: The method of measuring individual tooth volume using CBCT to estimate chronological age via Pv:Tv has been demonstrated as effective and reproducible within the Brazilian population sample.

Fully automated deep learning approach to dental development assessment in panoramic radiographs.

BACKGROUND: Dental development assessment is an important factor in dental age estimation and dental maturity evaluation. This study aimed to develop and evaluate the performance of an automated dental development staging system based on Demirjian's method using deep learning. METHODS: The study included 5133 anonymous panoramic radiographs obtained from the Department of Pediatric Dentistry database at Seoul National University Dental Hospital between 2020 and 2021. The proposed methodology involves a three-step procedure for dental staging: detection, segmentation, and classification. The panoramic data were randomly divided into training and validating sets (8:2), and YOLOv5, U-Net, and EfficientNet were trained and employed for each stage. The models' performance, along with the Grad-CAM analysis of EfficientNet, was evaluated. RESULTS: The mean average precision (mAP) was 0.995 for detection, and the segmentation achieved an accuracy of 0.978. The classification performance showed F1 scores of 69.23, 80.67, 84.97, and 90.81 for the Incisor, Canine, Premolar, and Molar models, respectively. In the Grad-CAM analysis, the classification model focused on the apical portion of the developing tooth, a crucial feature for staging according to Demirjian's method. CONCLUSIONS: These results indicate that the proposed deep learning approach for automated dental staging can serve as a supportive tool for dentists, facilitating rapid and objective dental age estimation and dental maturity evaluation.

Applicability of Cameriere's third molar maturity index on orthopantomograms and computed tomography scans from a French population.

Cameriere developed a method on orthopantomograms (OPG) to assess adult age of 18 years based on the relationship between age and the third molar maturity index I3M. The aim of this study was to evaluate whether Cameriere's method could be applied to computed-tomography scans (CT-scans) from a population of French juveniles and young adults and compare the results obtained from OPG of the same individuals. Our sample comprised 200 examinations that had been performed at the radiological department of a French University hospital between 2007 and 2020. Each patient had received an OPG and a cranial CT scan for medical purposes, and we used a similar adaptation of I3M based on OPG to determine the I3M based on CT scans. Due to exclusion criteria, our final sample comprised 71 OPGs and 63 CT scans. Based on the 71 OPGs, there was concordance between chronological age and estimated age, with a sensitivity of 78.57%, a specificity of 89.47%, and a misclassified rate of 18.03% based on tooth 38, and a sensitivity of 78.79%, a specificity of 91.67%, and a misclassified rate of 17.78% based on tooth 48. Our results based on CT scans presented concordance between chronological age and estimated age for tooth 38 described by a sensitivity of 77.78%, a specificity of 94.12%, and a misclassified rate of 16.98%. The concordance between chronological age and estimated age based on 48 had a sensitivity of 75.00%, a specificity of 93.75%, and a misclassified rate of 19.23%. The > 90% ICC indicate an excellent similarity between measurements of teeth 38 and 48 based on OPGs and CT scans. This study has revealed the applicability of the Cameriere's method to calculate the I3M based on CT scans from a French population. The results based on CT scans are similar to results based on OPGs from the same individuals.

Predicting chronological age of 14 or 18 in adolescents: integrating dental assessments with machine learning.

AIM: Age estimation plays a critical role in personal identification, especially when determining compliance with the age of consent for adolescents. The age of consent refers to the minimum age at which an individual is legally considered capable of providing informed consent for sexual activities. The purpose of this study is to determine whether adolescents meet the age of 14 or 18 by using dental development combined with machine learning. METHODS: This study combines dental assessment and machine learning techniques to predict whether adolescents have reached the consent age of 14 or 18. Factors such as the staging of the third molar, the third molar index, and the visibility of the periodontal ligament of the second molar are evaluated. RESULTS: Differences in performance metrics indicate that the posterior probabilities achieved by machine learning exceed 93% for the age of 14 and slightly lower for the age of 18. CONCLUSION: This study provides valuable insights for forensic identification for adolescents in personal identification, emphasizing the potential to improve the accuracy of age determination within this population by combining traditional methods with machine learning. It underscores the importance of protecting and respecting the dignity of all individuals involved.

Automatic and robust estimation of sex and chronological age from panoramic radiographs using a multi-task deep learning network: a study on a South Korean population.

Sex and chronological age estimation are crucial in forensic investigations and research on individual identification. Although manual methods for sex and age estimation have been proposed, these processes are labor-intensive, time-consuming, and error-prone. The purpose of this study was to estimate sex and chronological age from panoramic radiographs automatically and robustly using a multi-task deep learning network (ForensicNet). ForensicNet consists of a backbone and both sex and age attention branches to learn anatomical context features of sex and chronological age from panoramic radiographs and enables the multi-task estimation of sex and chronological age in an end-to-end manner. To mitigate bias in the data distribution, our dataset was built using 13,200 images with 100 images for each sex and age range of 15-80 years. The ForensicNet with EfficientNet-B3 exhibited superior estimation performance with mean absolute errors of 2.93 ± 2.61 years and a coefficient of determination of 0.957 for chronological age, and achieved accuracy, specificity, and sensitivity values of 0.992, 0.993, and 0.990, respectively, for sex prediction. The network demonstrated that the proposed sex and age attention branches with a convolutional block attention module significantly improved the estimation performance for both sex and chronological age from panoramic radiographs of elderly patients. Consequently, we expect that ForensicNet will contribute to the automatic and accurate estimation of both sex and chronological age from panoramic radiographs.

Dental age assessment and dental scoring systems: combined different statistical methods.

INTRODUCTION: Age Estimation has been considered as a human basic right, carried out through the use of tables for dental age assessment based on the chronology of tooth eruption. As such, the final aim of this investigation is to create tables with applicability to the Portuguese population, for the different scoring systems used and combined different statistical approaches. MATERIALS AND METHODS: For this purpose, dental age assessment was achieved in all four third molars, using different scoring systems, in a total sample of 626 orthopantomograms (324 females, 302 males), aged between 12 and 25 years old, from the database population of Lisbon North University Hospital Center, approved by the Ethic Committee. RESULTS: The values of validation showed excellent results both on precision and on reproducibility. Mostly all methods showed statistically significant differences between the estimated age and the chronological age and, therefore, the presence of estimation errors. Kullman's and Mincer's methods are the ones with best applicability in the Portuguese population, in the lower third molars. The reliability measures (sensitivity, specificity and accuracy) values decrease as age increases. CONCLUSION: A combination of the scoring systems as a protocol for dental age assessment in Portuguese nationality was established. Tables, for all the scoring systems used, were made with applicability in the Portuguese population.

Dental age estimation: A comparative study of convolutional neural network and Demirjian's method.

The aim of this study is to compare a technique using Convolutional Neural Network (CNN) with the Demirjian's method for chronological age estimation of living individuals based on tooth age from panoramic radiographs. This research used 5898 panoramic X-ray images collected for diagnostic from pediatric patients aged 4-17 who sought treatment at Antalya Oral and Dental Health Hospital between 2015 and 2020. The Demirjian's method's grading was executed by researchers who possessed appropriate training and experience. In the CNN method, various CNN architectures including Alexnet, VGG16, ResNet152, DenseNet201, InceptionV3, Xception, NASNetLarge, InceptionResNetV2, and MobieNetV2 have been evaluated. Densenet201 exhibited the lowest MAE value of 0.73 years, emphasizing its superior accuracy in age estimation compared to other architectures. In most age categories, the predicted age closely matches the actual age. The most inconsistent results are observed at ages 12 and 13. The results highlight correspondence between the age predicted by CNN and the Demirjian's approach. In conclusion, the results show that the CNN method is adequate to be an alternative to the Demirjian's age estimation method. We suggest that convolutional neural network can effectively optimize the accuracy of age estimation and can be faster than traditional methods, eliminating the need for additional learning from experts.

Evaluating legal age of 18 years through observation of third molars using Gambier et al. method in an orthopantomographic sample of subadults from South India.

In forensic practice, medicolegal physicians are often tasked with estimating age using dental evidence. This calls for an uncomplicated, reliable, and reproducible method for dental age estimation, enabling physicians to proceed without specific odontological expertise. Among various dental methods, third molar eruption analyses are less complicated and easier to perform. In our study, we explored the effectiveness of Gambier et al.'s scoring system, which examines the eruption of all third molars. We retrospectively analysed 1032 orthopantomograms (528 males and 504 females) of individuals aged between 15 and 24 years. The mean chronological age increased with the progression of stages (1 to 3) and phases (A to D) of the third molar eruption for both sexes. In terms of stages, none showed significant discrimination between minors (<18 years) and adults (>18 years), especially for males. However, Gambier's phase D displayed a relatively high likelihood of being 18 years or older, with an overall 85.9 % of males and 95.7 % of females having all third molars in stage 3 being 18 years or older. While the tested method could be helpful in indicating the completion of the 18th year of life, caution is advised (due to a high percentage of false positives), and it should be used alongside other age assessment methods by experts.

Correlation between dental and skeletal maturity in Korean children based on dental maturity percentile: a retrospective study.

BACKGROUND: The correlation between dental maturity and skeletal maturity has been proposed, but its clinical application remains challenging. Moreover, the varying correlations observed in different studies indicate the necessity for research tailored to specific populations. AIM: To compare skeletal maturity in Korean children with advanced and delayed dental maturity using dental maturity percentile. DESIGN: Dental panoramic radiographs and cephalometric radiographs were obtained from 5133 and 395 healthy Korean children aged between 4 and 16 years old. Dental maturity was assessed with Demirjian's method, while skeletal maturity was assessed with the cervical vertebral maturation method. Standard percentile curves were developed through quantile regression. Advanced (93 boys and 110 girls) and delayed (92 boys and 100 girls) dental maturity groups were defined by the 50th percentile. RESULTS: The advanced group showed earlier skeletal maturity in multiple cervical stages (CS) in both boys (CS 1, 2, 3, 4, and 6) and girls (CS 1, 3, 4, 5, and 6). Significant differences, as determined by Mann-Whitney U tests, were observed in CS 1 for boys (p = 0.004) and in CS 4 for girls (p = 0.037). High Spearman correlation coefficients between dental maturity and cervical vertebral maturity exceeded 0.826 (p = 0.000) in all groups. CONCLUSION: A correlation between dental and skeletal maturity, as well as advanced skeletal maturity in the advanced dental maturity group, was observed. Using percentile curves to determine dental maturity may aid in assessing skeletal maturity, with potential applications in orthodontic diagnosis and treatment planning.

A comparison of estimated age based on pulp volume from cone beam computed tomography (CT) images and panoramic radiography data with chronological age.

This retrospective study was conducted to evaluate different methods for dental age estimation in children and to examine the feasibility of using cone beam computed tomography (CBCT) data for age estimation. A total of 200 radiographic records (both digital panoramic radiographs and CBCTs) were acquired from 100 children aged 9 to 16 years, all taken on the same dates. Radiographic data was acquired from archived records and included both panoramic radiography and CBCT data belonging to the same individual. CBCT was used when panoramic radiographic data was insufficient. The pulp volume and pulp/tooth volume ratio of the left first molar teeth in the mandible were calculated from the CBCT data using MIMICS software. In addition, age was estimated by the Demirjian and Willems methods from data obtained from panoramic radiography images. Statistical analyses and linear regression analysis were performed as necessary. There was a statistically significant difference between the mean difference between the Demirjian method and chronological age, and between the Willems method and chronological age (p < 0.001). Statistically significance was achieved in a linear regression model created from pulp volume (R2 = 0.098) and pulp/tooth volume ratio (R2 = 0.395) data for the estimated dental age analysis (p < 0.001) and a negative correlation was observed with chronological age. When compared estimated dental age from CBCT data with chronological age, the pulp/tooth volume ratio method yielded results closer to chronological age than using only pulp volume data. When considering both panoramic radiographic age estimation methods and age estimation methods using CBCT data, we found that the results obtained with the Willems method, a panoramic radiographic age estimation technique, provided the closest results to the chronological age. More contributions should be made to the literature regarding the feasibility of age estimation using pulp and tooth volume as an alternative method.