Applied Bionics and Biomechanics

Volume 2017 (2017), Article ID 2014961, 7 pages

https://doi.org/10.1155/2017/2014961

## Using a Bayesian Network to Predict L5/S1 Spinal Compression Force from Posture, Hand Load, Anthropometry, and Disc Injury Status

Departments of Orthopaedic Surgery, Biomedical Engineering, and Industrial & Operations Engineering, University of Michigan, Ann Arbor, MI 48109, USA

Correspondence should be addressed to Richard E. Hughes

Received 3 July 2017; Accepted 14 September 2017; Published 1 October 2017

Academic Editor: Craig P. McGowan

Copyright © 2017 Richard E. Hughes. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Stochastic biomechanical modeling has become a useful tool most commonly implemented using Monte Carlo simulation, advanced mean value theorem, or Markov chain modeling. Bayesian networks are a novel method for probabilistic modeling in artificial intelligence, risk modeling, and machine learning. The purpose of this study was to evaluate the suitability of Bayesian networks for biomechanical modeling using a static biomechanical model of spinal forces during lifting. A 20-node Bayesian network model was used to implement a well-established static two-dimensional biomechanical model for predicting L5/S1 compression and shear forces. The model was also implemented as a Monte Carlo simulation in MATLAB. Mean L5/S1 spinal compression force estimates differed by 0.8%, and shear force estimates were the same. The model was extended to incorporate evidence about disc injury, which can modify the prior probability estimates to provide posterior probability estimates of spinal compression force. An example showed that changing disc injury status from false to true increased the estimate of mean L5/S1 compression force by 14.7%. This work shows that Bayesian networks can be used to implement a whole-body biomechanical model used in occupational biomechanics and incorporate disc injury.

#### 1. Introduction

Stochastic modeling has become a useful analytical method in biomechanics over the last twenty years. Applications have included lumbar region muscle forces [1], musculoskeletal injury risk prediction [2–4], upper extremity joint mechanics [5–8] muscle modeling [9], population morphological modeling [10], probabilistic sensitivity analyses [11], tissue repair [12], and orthopaedic implant design [13, 14]. Past stochastic biomechanical models use Monte Carlo simulation, advanced mean value theorem, or Markov chain models. Unfortunately, these methods are all “forward” simulation methods that produce probability estimates of outcomes based on model inputs represented as random variables.

Bayesian networks are well established in artificial intelligence [15, 16], risk analysis [17], and reliability engineering [18–21] and have the potential to enhance biomechanical modeling. A Bayesian network is a graphical probabilistic model containing nodes and directed edges that can be used to compute probabilities when evidence has been entered at a variety of nodes in the graph, some of which are descendants of the primary variable of interest [22]. Consider the problem of predicting lumbar spine compression force during lifting, which is a common task in occupational biomechanics. Existing biomechanical models require task-related inputs like mass in the hands, anthropometry, and joint angles to predict compression force [23, 24]. Physiologically driven models also require electromyographic measurements [25–28]. The results of these models are predictions of spinal compression and shear forces. In theory, a Bayesian network could be used to also incorporate intervertebral disc injury status, which existing models cannot.

Therefore, the purpose of this project was to evaluate the feasibility of implementing a well-established static two-dimensional biomechanical model of lifting as a Bayesian network and extend it to include disc prolapse as a model input.

#### 2. Methods

The design of this study consisted of five steps: (1) implement a well-established deterministic static two-dimensional biomechanical model for predicting L5/S1 shear and compression force as a Bayesian network, (2) extend the Bayesian network to include uncertainty in model inputs, (3) verify the implementation, (4) augment model to include disc injury status, and (5) evaluate effect of including disc injury status on L5/S1 compression force estimates.

A well-established deterministic model for predicting L5/S1 compression force during lifting was selected as the basis for this model [29] (pp. 130-131). This model computes intersegmental reaction forces and moments at the elbow, shoulder, and L5/S1 disc. Body segment lengths and masses are scaled from status and total body mass, respectively. The location of the center of mass for each segment is scaled to segment length. All necessary body segment anthropometric parameters are described in Chaffin et al. [29] (pp. 41–47). The model allows for a downward directed hand force representing the holding of an object in the hands. The model is bilaterally symmetric. A 50th-percentile female (161.8 cm stature and 65.6 kg body mass) was used for all simulations. The erector spinae moment arm was 5.3 cm according to Chaffin et al.’s recommendation for models not incorporating intra-abdominal pressure (p. 134).

The deterministic and stochastic versions of the lifting model were also coded in MATLAB R2014a (The Mathworks, Natick, MA) for purposes of validation. Monte Carlo simulation was used for the stochastic simulation, and each simulation contained 10^{7} iterations. Hand calculations were also performed for selected deterministic cases for code verification.

The next step was to implement the same model as a Bayesian network [30] using AgenaRisk software (Agena, Cambridge, UK). A Bayesian network is a graphical probabilistic modeling framework developed initially in artificial intelligence [15, 16]. A Bayesian network is a directed acyclic graph in which the directed edges represent conditional independence assumptions and node probability tables are associated with each node. Each node represents a random variable. The probability table associated with a node consists of a full statement of conditional probabilities for all nodes that are parents of the node. It is also possible to code deterministic relationships between nodes. Probability distributions can be defined for nodes, as well as observed values of the random variables. Junction tree methods are used to propagate probability distributions through the network [31].

In the Bayesian network implementation of the lifting model, nodes for input data were defined: *mass in hands*, *elbow angle*, *shoulder angle*, *torso angle*, *knee angle*, and *ankle angle* (Figure 1). Note that in this paper, variables are indicated in italics. Intermediate nodes were also defined for purposes of computation. Nodes were introduced for the reaction forces and moments at the elbow (*elbow reaction force and elbow reaction moment*), shoulder (*shoulder reaction force* and *shoulder reaction moment*), and L5/S1 level (*L5/S1 reaction force* and *L5/S1 reaction moment*). A node was created for the *erector spinae moment arm*, and another for *erector spine force*. The effect if intra-abdominal pressure was excluded because of the nonlinearity of the relationship between hip moment and pressure (p. 132). A node for *L5/S1 disc angle* was included, as were three nodes (*β*, *T*, and *K*) to implement a regression model for predicting deviation of disc angle from 40 degrees [32], which is how Chaffin et al. compute disc angle (p. 132). Two output nodes were defined: (1) *L5/S1 compression force* and (2) *L5/S1 shear force*. Edges were introduced to link the nodes in a way that represented mechanics. In AgenaRisk, each arc was given the deterministic relationships linking nodes. This defined the deterministic version of the lifting model.