LaTex Template for an EUCOMES 2010 Paper [301425]

Correction method for spine flexion tracking with markers

S. Butnariu1 and C. Antonya1

1[anonimizat], e-mail:[anonimizat]; [anonimizat]

Abstract. The aim of the present paper is to accomplish a virtual model for testing the properties of the outer layers of the human body (skin, [anonimizat]) in order to estimate and calculate the displacements of certain points on the skin surface in relation to the bones (which are considered fixed points). The proposed correction method will be used in the development of a device for tracking the human body postures and the spine movement by using different types of sensors for establishing a preliminary diagnosis of it. There is a major problem identified in this case of tracking the spine with markers: the skin sliding in connection with the bones. In order to obtain a [anonimizat] a [anonimizat].

Key words: [anonimizat], multi-[anonimizat].

1 Introduction, description of problem

The position of the spine can be estimated by tracking the posture of the human body. [anonimizat] a human body posture (Fig. 1). [anonimizat] a [anonimizat] (tracked by the marker) corresponds to its the initial position measured in a fixed reference frame attached to a point on the spine (on the spine vertebra).

Specifically, [anonimizat], for a [anonimizat] a [anonimizat]. [anonimizat].

The question is: the values of outer tissue deformation can be used to estimate the spine flexion and extension? [anonimizat] a correction factor to be taken into account when it will be reconstructed the spine posture based on human body tracking.

Fig. 1 [anonimizat], we cannot consider a rigid approach for involved bodies and surfaces. The skin has a [anonimizat] [2, 9, 15]. This property is the main source of the errors in human motion analysis using reflective markers.

2 Human body modeling

Due to significant developments in computer sciences in the last 20-30 years, [anonimizat] a new level of testing on virtual models in a [anonimizat]. [anonimizat]’ [anonimizat] bringing significant financial savings.

During the last years, analysis models and software for various human activities have been developed, such as reconstruction of accidents, human body biomechanics, applications in ergonomics, medicine, sports and arts. However, the testing of various applications on virtual models involves a laborious work in developing models and validating them.

The applications that use virtual models can be classified into:

deterministic applications (results of an action on the model may be predicted using estimated parameters representing some features of the human body and the environment with which it interacts, according to the laws of physics);

statistical applications (used to assess the proper relationship between loading conditions and results obtained).

Creating the models used for human body testing relies on various principles: the lumped mass models (consists of rigid bodies with masses connected by spring and dampers, 1D or 2D), the multi-body models (MBS, elements connected by various joint types through which the number of degrees of freedom between the elements can be constrained, 2D or 3D) and finite element models (the body is divided into a number of finite volumes, 3D). Note: the lumped model may be considered as a particular case of the multi-body model.

The multi-body model is a very effective method for complex kinematic connections, such are those in the human body. The finite element method can describe the local structural deformations and stress distribution, but it is not very attractive for optimization studies involving many designing parameters. However, an option combining the two methods is considered optimal.

There are several approaches to human body modeling in the literature. Thus, there are different identifiable models of the human body or of certain parts of it.

Human body modeling as a whole is done in order to analyze its kinematics. There are neuromuscular pathologies that lead to motor system dysfunctions. An important challenge for professionals is to identify muscular problems by analyzing the walking kinematics and / or patient’s movement. In this case, the model is carried out using the MBS, being a general method.

The same method is also used to shape parts of the human body, usually comprising some kinematic and couplings (spine, limbs, hands etc.). The tracking can be conducted using with or without markers through various methods and concentrating specially on the position and movement of rigid elements of the human body (bones) [11, 15].

3 Working methodology

Regarding the skin sliding over the spine, we have two main issues to be considered: skin artifacts and 6D relative movement of the spine joints. In the present work we opted for a very small segment analysis, taken from the dorsal surface of the human body, in the region of thoracic vertebrae T1 … T4. At the same time, we tried to simplify the analysis model, eliminating a number of possible movements of the vertebrae, one from the other. Thus, for this study, we considered a single rotation between two adjacent vertebrae (Fig. 2), in sagittal plane (XZ plane, see Fig. 1). We analyzed only clockwise rotation between vertebrae (Fig. 4,b), which causes skin stretching.

Fig. 2 Relative rotation of the vertebrae

Unlike other applications, where skin artifacts can get extremely large values (such as knee) [8, 9], in spine case study we will consider a linear model.

The skin properties will be modeled using a multi-point system with springs and dampers (Fig. 3), which will be set in motion due to the connections to the vertebrae.

Fig. 3 Multi-point system

The skin deformation is modeled with a collection of inter-constrained mass points, using the multi-particle system (MPS) formulation [12]. The multi-particle model is a collection of particles subject to a set of absolute and relative constraints and forces from external sources or springs and dampers. The biomechanical system is replaced by a set of mass points, equivalent from the inertial viewpoint with the original body, and a set of springs and dampers which will reproduce the elastic properties of the skin. The main benefit of MPS formulation is that it works with geometric data that is similar to FEM analysis (particles vs. nodes), which makes it more suitable for use in the study of flexible systems or multi-physics simulations.

The constraint equations (imposed motion and geometrical constraints) and dynamic equations constitute a set differential algebraic equation (DAE) in the coordinates of the mass points (q) and the Lagrange multipliers (λ):

(1)

where M is the mass matrix, J is the constraints Jacobian matrix, Qex the generalized external applied forces vector and ψ is the term obtained from the second time derivation of the constraint equations.

b.

Fig. 4 The model of outer tissue linked on spine (a) and detail of multi-point model (b)

In this study we aimed to establish a methodology for correction of the measured displacement obtained from the tracking system. For this, we consider a portion of the spine which consists of the first four thoracic vertebrae (Fig. 4,a). Outer tissues (skin) was modeled using multi-point system, using two layers of mass points.

Assumptions are:

dimensional values of the vertebrae and outer tissues are considered for an child;

the spring factor k is calculated for the multi-pattern dimensions shown in Fig. 4,b and based on Young's modulus E determined in [6, 13] and using eq. (2):

(2)

where S is the normal section surface and l0 the initial length.

the inner layer of the outer tissue is rigidly connected to the vertebrae

we consider one marker rigidly attached on the skin;

we consider only elastic behaviour of the tissues.

In the following are presented some technical characteristics of the elements that compose the analyzed model. The bone tissue is one of the most rigid structure of the human body due to the mixture of inorganic (calcium and phosphate) and organic (collagen) components. The bone is an anisotropic material, its behavior will change depending on the direction of load application. In general, the bone can lead to large loads in the longitudinal direction, and a smaller loading value when it is applied to the surface of the bone. The bone is also viscoelastic, which means that it responds differently depending when it receives loads in different speeds: the bone responds more rigidly if the load acts quickly and the bone is not so rigid or strong when it receives the load slowly. The flexibility properties of the bone are provided by the concentration of collagen in the bone. The bone is at the same time a fragile material, its fragility degree depending on the mineral constituents given by the ability of compression [4].

The skin is the largest organ in a human being, representing 15-20% of the human body weight. The mechanical characteristics of the skin are extremely complex and have not been satisfactorily simulated using conventional mathematical models. The ability to predict the human skin behavior and assessing changes in the mechanical properties of tissue are important information for modeling in various fields, which are currently based on experimental animal models.

Some studies have aimed to create an anisotropic predictive model built on hyperelastic properties of human skin and comparing it with the results obtained in the laboratory using Finite Element Method (FEM) [5].

Other research [13] reveals that three distinct types of mechanical behavior of the skin can be defined: immediate expansion when tension is applied, the subsequent expansion continues while the force is maintained and gradually thinning under local compression. Considering all the above in order, the first behavior is called elastic extension, the second which is irreversible and gradual is called viscous extension or viscous slip and the third phenomenon – viscous flow.

Looking at Fig. 5, where the skin behavior as a result of tensions is plotted, the first observation is that the skin can be easily stretched with a few percentages from the initial length, but then it requires much higher force values to stretch it further.

b.

Fig. 3 Strain / stress behavior (adapted by [3, 12])

The graph in Fig. 5,a can be transformed into a single formula, due to very different curvature between the first and last part, these two areas described separately by different equations.

Without using mathematics, there are two parameters which can be deduced from the graph: the average slope of the last area, which is quasi-linear (representing the Young's maximum elasticity modulus for this specimen) and the intersection of extending this zone to horizontal axis.

The average values for the human skin are in the range of 2…10 x 103 N/cm2 [6, 10, 13]. The elasticity modulus increases proportionally with the patient’s age and is lower in women than in men. Through the extension of the last area of the graph and the intersection with horizontal axis it can be determined the residual elongation of the tissue tested, which can vary between 3 and 14% [13].

Other researchers experimented stretch determinations in-vitro on human skin, collected from female patients who underwent reconstructive plastic surgery. The data collected for stress/ strain curve were used to fit the theoretical hyperelastic models (General Polynomial, low Polynomial and Ogden). Among these models, only the low Polynomial model proved to be stable, therefore it has been in an explicit finite element model [7].

Viscous slip is other mechanical properties of skin. To determine the viscous slip, the same equipment is used as in the case of elasticity measurement, the only difference being the time of application of the load. Research in the field shows that for a few seconds load, there is a rapid relaxation of the material in contrast with the demands of lesser value but long lasting, which causes elongation persisting for a few hours (Fig. 5). Viscous extensibility (u) – extension rate / unit of force applied, very slow process –e.g. a request for 10 N/cm2 causes a slip of 0,05 %.

This process is irreversible. The viscous flow – it is a very little studied process. It is determined by measuring the modification of skin thickness after some type of demands pressure (compression) [13].

On the other hand, there are approaches of some researchers [1] measuring this property in vivo, on human patients. The equipment used is based on mechanical and optical measurements.

In practice, the three properties of the skin (elastic extension, viscous slip and viscous flow) cannot be separated, but in research activity we could take into account every phenomenon in part in order to obtain suggestive results [13].

To calculate the displacements of points on the outer tissue we used the MSC ADAMS® software.

In Fig. 6,a the initial position of the multi-point system is presented. On the outer surface of the skin, we consider a marker M3 (see Fig. 1, reflexive marker attached to the skin). The points P1, P2, P3 and P4 correspond to thoracic vertebrae T1, T2, T3 and T4. During the simulation, it is considered that these points remain in contact with the vertebrae and movements of these points are known, due to spine flexion with angle (Z-axis rotation angle in XZ plane).

The simulation was performed assuming that the segment P1P5 remains fixed; points P’1 and P’5 from Fig. 6,b (final position of the multi-point system) are the same with P1 and P5 from Fig. 6,a. It is assumed that during flexion of the spine, the relative position of the point M3 to P1 … P4 has changed.

Fig. 6 Initial (a) and final (b) position of the multi-point system

In order to determine the position of point M’3 during the simulation, it was measured the length of P’4M’3 segment and the angle between segment P’4M’3 and X axis.

The multi-point model will have dimensions close to the actual dimensions of the subject. Thus, the distances between the defined above points are: P1P2 = 21 mm, P2P3 = 24 mm and P3P4 = 26 mm. These dimensions were measured on reconstructed 3D model of human spine used in this research. The thickness of the tissue was 2 x 5 mm (P1P5 = 10 mm), similar to those of the human body.

The results obtained lead to the following considerations: during the flexion of the spine we can observe that it is a deformation of the tissue, which leads to a new position of the marker M3 in the reference frame of the considered vertebra.

Fig. 7 Relative displacement of marker, x and z direction

Variation of tissue deformation has a linear trend, which is explained by a constant factor k used. For these analyzes, the value of damping factor c has no influence over the results.

Another way of illustration of the results is presented below. In Fig. 8,a a series consists of several vertebrae and the outer surface of the tissue (skin) is shown. Considering the first vertebra fixed, when the spine is flexed with angle (Fig. 8,b), it can be seen that the outer tissues are subjected to tensile stresses, leading to a change in their thickness from h0 to h. Also, in addition to changing the thickness of tissue, a lag (sliding) can be observed of the outer tissue against the rigid part (vertebrae).

Fig. 8 The scheme illustration of skin deformation

Any point on the surface of the outer tissue will have a sliding (red line) point compared to the theoretical geometrical position (the blue line), corresponding to 1…n angles of flexion.

Knowing the coordinates of a point on the surface of the skin and knowing that this is a position relative to a vertebra, in conjunction with the value of correction of relative displacement of the point, we can say that it is possible to estimate the positions of the vertebrae in relation to external markers. The relative displacement of the markers can be obtained from the marker’s coordinates acquired from the motion capture system, followed by the assessment of the spine’s flexion from the results shown in Fig. 7. This can be very important in the primary diagnosis of spine disease using reflexive markers and a motion capture system.

4 Conclusions

It was considered a segment of tissue outside the human body in order to establish a possible inconsistency between the markers glued on the skin surface and the fixed markers. Not taking into account the size on the Z-axis. For analysis, it was built a 2D model of human skin, in the XZ plane, corresponding positions of thoracic vertebrae T1 … T4.

Points P1 … P4 are considered fixed on extremities of the vertebrae T1 … T4. On the outside of the model we consider a point M3, corresponding of vertebra T3. We considered that the segment P1P5 is fixed, and we watched the movement of point M3 depending on the movement of points P2….P4 and elastic characteristics of the built model (see Fig. 6).

The results show that the relative displacement of the point M3 point follows an approximately linear trend due to constant factor k and because the damping factor c was not considered (see Fig. 7).

By analyzing the results, we can highlight some clear conclusions. First, we believe that the markers on the skin surface don’t keep their positions on benchmarks represented by hard tissues (bones), but there will be a slip due to the elastic properties of the skin (Fig. 8,b).

If there is a boundary condition that involves fixing segments analyzed at one extremity of the model, then the displacements values to the fixed benchmarks will be summed, and will get very high values on the extremity of the analyzed segment.

The results are approximately anticipated, considering the assumptions used. For the future, it is necessary to make the analysis taking into consideration the hyperelastic properties of the skin.

Acknowledgments   This paper was realized within the Partnership Programme in priority domains – PN-II, which runs with the financial support of MEN-UEFISCDI, Project no. 227 / 2014, System for Diagnosis and Therapy of Spine Diseases (SPINE).

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