while for elderly, obese or anorectic people accurate results cannot be expected. Particularly noteworthy are the results for individuals with severe obesity ...
Computing methods for fast and precise body surface area estimation of selected body parts Gustaw Rzyman, Grzegorz Redlarski, Aleksander Palkowski, Piotr M. Tojza and Marek Krawczuk Faculty of Electrical and Control Engineering Gdansk University of Technology Gdansk, Poland Abstract—Currently used body surface area (BSA) formulas give satisfactory results only for individuals with typical physique, while for elderly, obese or anorectic people accurate results cannot be expected. Particularly noteworthy are the results for individuals with severe obesity (body-mass index greater than 35 kg/m2 ), for which BSA estimation errors reached 80%. The main goal of our study is the development of precise BSA models for specific body parts. We have achieved satisfactory results for a wide range of patients. Using regression models, such as: support vector regression, multilayer perceptron regressor, stochastic gradient descent, or ridge regression, a fourfold decrease in errors proportion is achieved. Machine learning algorithms led to reduction from 1.2 to 8 times for mean estimation error.
Fig. 1.
Janusz Siebert Department of Family Medicine Medical University of Gdansk Gdansk, Poland
Artec 3D Eva scanner
Keywords—body surface area; estimation; Lund and Browder chart; machine learning; regression
II.
Methods
A. Study design I.
Introduction
Body surface area (BSA) is the calculated or measured surface of a human body. In modern medicine estimation of skin surface is commonly used in many medical procedures. BSA is used in such fields, as: chemotherapy, burn treatment, or cosmetic surgery. Formulas and tables used for BSA estimation are associated with many errors, which may result in, e.g., incorrect dosage calculation. These errors could have a significant impact on the quality of treatment [1]. Currently used BSA estimation methods contain many discrepancies [2]. Furthermore, BSA of selected body parts based on the Lund and Browder chart and the Wallace rule of nines [3] are exposed to approximation errors. Led by previously gained experience in the studies related to BSA estimation and medical experience, we decided to develop a method that limits the described errors. TABLE I.
Errors of Lund and Browder chart and BSA estimation Body part
Average
Maximum
Head Torso Shoulders Thigh Leg Foot Arm Forearm Hand
16.73% 20.16% 8.53% 7.43% 3.53% 7.06% 11.63% 7.01% 27.56%
67.45% 43.59% 20.13% 35.98% 16.91% 27.5% 77.32% 15.9% 58.2%
978-1-5386-6143-7/18/$31.00 ©2018 IEEE
For the purpose of the study 20 high-quality models (Fig. 2) were selected. Models are varied and present a wide range of body structure (diverse BMI). Subsequently, these models were divided into individual body parts and their BSA were calculated. Measurements were made using a high-accuracy 3D scanner with over 99.27% accuracy (Fig. 1) [4]. In order to compare the measured and calculated BSA, the DuBois and DuBois formula and Lund and Browder chart were used as the most common and precise BSA estimation methods [2], [5]. Regression models define correlation between datasets of independent variables (predictors) and dependant variables (target variables). In the discussed case anthropometric parameters are assigned the role of predictors and the value of BSA of selected body parts is considered as the target variable. B. Regression models 1) Stochastic gradient descent: Stochastic gradient descent (SGD) is often used for training in machine learning problems [6]. It is a linear model for classification and regression. It derives from gradient descent optimization method using iteration to find minima or maxima of the function stochasticly approximated. The algorithm for SGD learning is the foundation of SGD regression using different loss functions and penalties to fit linear regression models. The main advantages of SGD are its efficiency and a variety of applications. 2) Kernel ridge regression: Kernel ridge regression (KRR) is based on ridge regression, a method of linear regularization of its way of operation similar to least squares, but it shrinks the
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TABLE II. AN SGD KRR MLP SVR
Average errors using machine learning algorithms
Head
Arm
Forearm
Hand
Torso
Shoulders
Thigh
Leg
Foot
49.23% 11.83% 8.76% 7.41%
46.64% 26.62% 25.11% 5.9%
62.35% 4.08% 6.06% 3.13%
66.71% 4.04% 4.5% 3.42%
52.12% 9.83% 8.04% 8.99%
50.83% 10.51% 9.64% 7.36%
51.91% 11.66% 9.09% 4.37%
50.83% 7.7% 7.2% 2.83%
50.2% 8.21% 6.52% 1.07%
estimated coefficients towards zero [7]. Additionally, the KRR is associated with kernel function which intention is to present data as a nonlinear projection of data into high-dimensional feature spaces, which is called the kernel trick. KRR model is similar in operation to support vector regression, the main difference being the use of loss functions (squared error loss in KRR) [8]. 3) Multilayer perceptron: Artificial neural networks (ANN) are currently one of the most widely used tools of computer data analysis. Based on the review of literature [9], it can be seen that they are widely used in technical sciences and biomedical engineering as well. The most popular and efficient type of ANN is the multilayer perceptron (MLP). MLP is a supervised learning algorithm using backpropagation for training. It consists of at least three layers (an input and an output layer with one hidden layer) of nonlinearly-activating nodes. In regression MLP uses square error as a loss function. 4) Support vector regression: Support vector regression (SVR) is derived from the support vector machines method. SVR creates a separating hyperplane or a set of hyperplanes in a high-dimensional space with the largest margin possible. SVR’s assumption is to minimize the generalized error bound (training error and a regularization term) in order to achieve better performance [10]. SVR is using a kernel trick to accomplish non-linear classification. The main advantages of SVR are its effectiveness in high dimensional space and memory efficiency of this method. III.
Results
Preliminary studies confirmed the thesis that commonly used Lund and Browder chart and Wallace rule of nines intensify BSA estimation errors [5]. BSA of selected body parts obtained by applying commonly used methods has average and maximum errors up to 27.56% and 67.45% respectively (Tab. I). The results were compared with real BSA. To reduce the impact of stated errors we used machine learning algorithms with a set of basic anthropometric parameters that are easy and quick to measure. In each case weight and height were used with additional one or two other parameters (e.g., head circumference, height from the ground to the knee, the length of the arm, etc.). These parameters were chosen by physicians to best characterise the structure of a given part of the body. Using more data allows for more accurate results in BSA estimation. This is particularly important in the case of people with unusual body structure (e.g., obese, anorexic or deformed). A comparison of all machine learning methods is presented in Tab. II.
Fig. 2.
Model of human body used for BSA estimation
and 66.35% depending on the body part. Coefficient of determination, defining the quality of the model’s fit, varies between unsatisfactory and poor. SGD is intended for use when the number of samples is very large, which may be a probable explanation of the mismatching of the model. BSA estimation does not show a linear character, which could increase errors when applying linear models. KRR algorithm shows satisfactory results. Errors vary between 4.04% and 26.62% (Tab. II). The errors for individual body parts show increasing inaccuracy of BSA estimation for some of the regions and thus KRR is not an optimal solution for this problem. Only SVR showed higher effectiveness in BSA estimation for each body part in comparison with the previous. However, MLP also gives satisfactory results and in the case of torso BSA estimation is better SVR. There is a need to use different machine learning algorithms for each body part as a result of matching the model to the body part. The next step in the research protocol will be verification of other nonlinear regression models and extension of the database. Research shows that there is a need for implementation of advanced calculation methods in modern medicine. BSA estimated with currently used methods may be too generalised. Properly selected machine learning algorithms and accurately collected measurements will contribute to the effectiveness of treatments based on the calculation of BSA. Acknowledgment
IV.
Conclusions
Our SGD study results are promising but not satisfactory enough. Average BSA estimation errors range between 46.64%
317
We wish to express our deepest gratitude to the National Science Centre, which has funded our research through grant no. 2014/15/B/NZ7/01018.
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