A reconfigurable model for virtual tumour detection within a breast

Mitan Solanki, Vinesh Raja

Informatics & Virtual Reality Group, WMG University of Warwick, U.K

m.solanki@warwick.ac.uk, vinesh.raja@warwick.ac.uk

Abstract This paper details progress towards a real time palpation simulator. We explore the potential of employing a mass spring system coupled with a haptic interface to realise this. Our motivation lies with enhancing the skills required to detect breast cancer as early as possible. However there are issues in emulating the behaviour of soft tissues using this approach, particularly if the composition of the model is inhomogeneous. Therefore our research is concerned with incorporating material properties and enhancing surface response upon contact, which is important for the simulator. We compare our model with analogous finite element models and discrete volumetric models to establish physical realism. Despite the absence of volumetric mesh, the initial evaluations show that the model can reproduce the presence of a tumour in a localised region. The model is receptive and can be reconfigured to simulate a variety of breast-tumour compositions. We look to integrate this with a deformable breast model that can be used to train the skills required for breast palpation.

1. Introduction The use of technology has greatly aided the detection of cancer over the past four decades. Radiological imaging methods such as Computational Tomography and Magnetic Resonance Imaging have progressively been adapted to distinguish different types of cancer residing in different areas of the body. Following cancer of the lung, breast cancer is the biggest killer of women [1]. In the UK alone 45500 women are diagnosed with the disease and approximately 12000 die every year because of it [2]. The early detection of breast cancer is of paramount importance as it improves a person’s chances of survival [3]. Common diagnostic tools such as routine mammography have been proven to reduce the mortality rate. However those that do not qualify for this procedure or patients waiting between intervals, rely on discovering a suspected abnormality themselves before being referred for the exam. This is achieved through a visual inspection and the palpation process.

Palpation is a key feature of self examination because it enables the practitioner to obtain information about the internal condition of the tissue that is not visible from the surface. Medical students are taught how to perform a clinical breast examination, which is to be performed on patients who suspect that they have a breast tumour and to assess the severity of the growth. However the methods currently employed to train such psychomotor skills are insufficient [4]. The state of the art in assisting medical students or women in

breast examination training rely on literature such as leaflets; multimedia videos [5] and palpation of artificial models made of rubber or other synthetic materials, embedded with hard lumps of varying sizes [6]. The limitations of administering silicone-based models are that the properties of a human breast are not realistically emulated in the elasticity of the skin or the dynamism of the tissue. These static models struggle to replicate key visual symptoms or variations in material compliance, which restricts the demonstration of a wide range of possible breast conditions. Consequently, these inaccurate reflections greatly inhibit a user’s experience and a deficiency in clinical skills acquired through these approaches has been highlighted [7]. Issues in adequately training this skill and limitations of current simulators have motivated us to explore alternative methods. The scope of our research remains within the confines of soft tissue modelling for real time interactivity in virtual environments. We extend the surface mass spring model defining homogeneous materials to include inhomogenities which can represent cancerous lumps in a medical context. To compensate for the lack of internal volumetric mesh, we develop a novel methodology that doesn’t impede the rendering of haptic force feedback yet conforms to elastic tissue behaviour. In addition, the model can be configured using characteristic parameters of force applied, depth, diameter and relative stiffness, allowing the simulation of various real scenarios. To evaluate, comparisons are observed between finite element formulations and volumetric mass spring models. The proposed model can serve as a platform for an adaptive medical simulator capable of providing accurate tactile information to the user and the transfer of skills through a virtual environment.

2. Related Works

2.1. Virtual Environments

Virtual reality is widely accepted as a means to deliver medical training through immersing a user in a learning environment [8]. The level of realism that can be achieved here is elevated by engaging as many of the senses as possible. For the purposes of palpation, the sense of touch takes precedence in rendering non-visual information to the fingertips. Haptic interfaces are a feasible way of integrating touch into an environment. These devices enable the manipulation of tactile and kinesthetic feedback to the user as well as provide the means to monitor motion and forces applied. Figure 1 illustrates our simulator setup which includes the Sensable Omni haptic interface. Despite offering a potential solution to some of the drawbacks that current

teaching methods pose, the development of simulators give rise to inherent technical challenges. Amalgamating the requirements to satisfy real-time visual and haptic feedback is an important tradeoff to consider when developing medical simulators. The definition of a virtual workspace as discrete vertices involves computing solutions to numerous differential equations to ultimately determine what force is experienced by the user. Hence in order to function in a stable manner, a haptic servo rate of 1 kHz is recommended so no discontinuity in force is perceived. Continuum based techniques such as the finite element method can portray an accurate replication of tissue behaviour [9]. Without resorting to condensation techniques, they struggle to cope with large deformations and pose a high computational cost, meaning real time interactivity is rarely possible. Particle based methods which include mass spring systems offer a viable alternative. Although they are much faster to implement, they have the drawback of being less accurate as real material properties are heuristically assigned [10]. Condensing from a tetrahedral or cubic composition to surface springs resolves the quantity of calculations have to be performed and means that extensions to incorporate local shape memory nodes can be formulated. Consequently methods to compensate for the deficit of internal meshing provide opportunities for further research.

Figure 1: Our virtual training setup

Achieving an accurate emulation of soft tissue involves an understanding of the properties defining it and embedding them into a geometric model. Although it is not possible to perform a direct translation without incurring a degree of error, methods have been sought to bridge the gap between interactivity and accuracy.

2.2. Inhomogeneous Models

Homogeneous deformable models assume that the virtual object consists of the same material properties at any defined point within the body. In reality human organs such as the liver or breast comprise of one or more materials. For inhomogeneous models such as breast tumours, detecting these variations under the skin surface requires rendering methods to express 3D internal differences to a 2D plane [11]. Existing techniques that have been proposed can be divided into four main categories. Pre-processing possible deformation behaviours that would occur during simulation runtime offers a potential solution [12]. However responsiveness is still not guaranteed and it cannot account for all probable interactions. Alternatively direct interception can be employed to calculate force response. Layered models enable an internal layer such as one representing a tumour, to behave as a constraint on successive upper layers such as the skin. However in a human

breast these layers never intercept by virtue of the adipose and glandular tissue residing between them [13]. A third approach is to heuristically distribute stiffness parameters which are often allocated based on experiments with rubber mediums or empirical evaluations [14]. These remain specific to only to the administered models hence are not very dynamic in their reapplication. Furthermore direct spring connection between multiple bodies has been administered with the consequence of an increase in model rigidity. Therefore this research endeavours to improve the incorporation of material properties into inhomogeneous mass spring models and to accurately convey reciprocated surface forces.

3. Methods Palpation of the human breast involves different types of interaction on the skin surface whilst obtaining tactile information from the volume of tissue underneath it. Various methods of interaction can be performed to elicit a force signifying an embedded tumour. Therefore methods are to be devised for a virtual model that delivers this information through a haptic interface, whilst maintaining real time interaction and comparable material behaviour. More importantly, the response generated on the surface needs to be as accurate as possible. This is captured quantitatively through force and displacement data. The field of our research explores the local behaviour of deformation under external forces.

The geometrial model can be obtained from 3D scans of anatomical features or created using appropriate software. To actuate motion, physics based mass spring systems are integrated with these, where the topology, nodes and vertices of the mesh dictate the number of spings and masses to be generated. Positions of masses update with respect to Lagrangian laws of motion

1

where, m is mass, and are acceleration and velocity respectively, d the damping coefficient and i and j are nodal pairs. is an externally applied force and is the internal force between two connected masses. A deformable model of the breast we previously developed, employed a surface mass spring system [15]. To model the elastic property of an individual node we use a shape memory spring attached to it which conveys internal forces. At equilibrium the local force and displacements are zero until, under some external influence, the memory spring is dynamically generated to return the node to rest. The following equation describes the force propagated by this spring. · 2

where, is the rest position of the surface node, is the new node position, s is the central coordinate of the embedded inclusion. This allows us deliberate interaction of varying orientation relative to the inclusion. The elasticity parameter

is explored further with respect to real material properties. By assuming a linear and isotropic nature for soft tissues, the independent values of Poisson’s ratio and Young’s modulus are sufficient to simulate their response. The varying magnitudes of force output across different locations of the surface correspond not only to the mass spring

formulation, but also to configuration of the physical parameters of the model. To address inhomogenities the depth, diameter, elasticity and location of the inclusion are introduced, see Figure 2. We use assumptions from experiments carried out with phantom gels to establish an initial operational model.

Figure 2: Cross sectional view of model setup

where, D is the perpendicular depth from the surface, d is the diameter, and are the respective tetrahedral volumes of inclusion and adipose. and are the respective Young’s modulii of inclusion and adipose, n are the number of surrounding vertices. Though the dimension of the surface mass spring system as compared to a volumetric model is reduced, research has permitted the integration of human tissue material properties [16]. Extending the notion of reintroducing volumetric properties, we assume the embedded tumour as a sphere to have associated with it a material stiffness and a radius with centre point to define its boundary and location in coordinate space. The following configuration resolves the combined influence of the tumour on the surrounding tissue by superimposing their stiffness values based on relative volume. Notation is illustrated above. /2 3

The resultant value is assigned to the surface spring according to tumour depth and distributed to neighbouring vertices according to an inverse multiquadric function. 4 where, are the assigned spring constants, is the surface vertex corresponding to the depth, are the volumes of individual tetrahedrons surrounding , >1, =1 and are vertices within the contact region. Equation (4) is then combined with (2) to resolve the internal force. Upon interaction the inclusion is disturbed from its initial static position due to the compression of the enclosing adipose tissue. Using the fundamental solution of a force acting on an isotropic elastic body this shift can also be approximated. The local deformation that we are interested is defined by the surface region displaced upon contact. The dynamically updated areas we are primarily interested in, of a finger on the

breast skin surface, are calculated through classical Hertz theory [17]. These are important steps to describe the influence of a lump occupying a previously homogenous space.

4. Results Modelling the deformable behaviour of human tissues accurately is a challenging endeavour; particularly under interaction when feedback must be almost instant. Although assumptions have been made to minimise the complexity of the full anatomical configuration, we still have to assess how this quantitatively resembles a more rigorous setup.

A truth cube concept [18] is commonly employed to compare real soft tissue behaviour with a silicone rubber or finite element block. We adopt a similar approach to evaluate our model. A finite element model of a cube is constructed using commercial software (ANSYS 10.0, Ansys Inc.) where each edge has a dimension of 8cm. Analagous models are created using our mass spring system, see Figure 3. Material properties for each constituent are obtained from in-vivo experiments carried out in related literature [19]. Adipose tissue stiffness set as 500 Pa and the tumour as 10kPa.

a) b)

Figure 3: a) Our mass spring model, b) Cross section of finite element model

The four input parameters of force, depth, diameter and stiffness ratio of tumour-adipose are varied individually so that as the value for one is modified, three variables remain fixed. We specify values that maintain a level of proportionality to the breast-tumour scenario. Forces are incremented between 0.5N to 3.5N, diameters between 1cm and 4cm, depth from surface between 1.5cm and 4cm and the stiffness ratios from 20 to 300. External forces are applied across a linear path on the upper plane of the both cubes.

Figure 4: Comparison of truth cubes

0123456789

0 1 2 3 4

Per

cent

age

Erro

r

Distance from central surface node (cm)

0.5N1.0N1.5N2.0N2.5N3.0N

Displacements are extracted for an empty, homogeneous model and for the inhomogeneous case, the difference is noted for both our model and the finite element model and error is calculated. Figure 4 shows the disparity when increasing force is applied at nodes along the linear path. This shows good initial agreement with the finite element model which is accepted as robust standard in tissue analysis [20]. We aimed to keep its mesh discretisation to error below 15%. Similar results were achieved for the three remaining input parameters.

A comparison between our surface formulation with memory springs and a volumetric mass spring system is also performed. The internal force is recorded across the upper plane to illustrate a surface force profile [12] with 2cm diameter.

a) b)

Figure 5: a) Our surface force profile, b) Volumetric mass spring model

The volumetric system consists of many tetrahedral elements and is therefore quite rigid, however we are predominantly interested in the width of the curve because it signifies internal tumour diameter, see Figure 5. Our system accurately responds to the input parameters allowing it to be reconfigured as desired and can support large deformations.

5. Conclusion In this research we demonstrated a model that extends the surface mass spring formulation to permit inhomogeneous compositions. The proposed scheme can accurately determine surface response under interaction and achieves this despite the absence of internal meshing. A relationship between the surface and an embedded inclusion is established and input parameters allow the model to be configured to simulate different breast-tumour compositions. We also attempt to integrate material properties. It displays similar behaviour to finite element models and volumetric mass spring models, whilst remaining responsive to be integrated with a haptic interface for relaying force feedback. Further evaluations will analyse how the topology and lateral motion affects the local surface. Incorporating the model with our virtual training environment for breast palpation, will allow users to attain more accurate tactile knowledge of breast cancers through haptic technology.

6. References [1] A. Jemal, R. Siegel, E. Ward, “Cancer Statistics 2009,”

CA Cancer Journal for Clinicians, vol. 59, no. 4, pp. 225-249, May 2009.

[2] Cancer Research UK, “CancerStats – Key facts, January 2010,” http://info.cancerresearchuk.org/cancerstats, Date accessed 29/01/2010.

[3] D. Saslow, J. Hannan, and J. Osuch, “Clinical breast examination: Practical recommendations for optimizing performance and reporting,” CA Cancer Journal for Clinicians, no. 54, pp.327-334, 2004.

[4] K. Lee, D. Dunlop, “Do Clinical Breast Examination Skills Improve During Medical School?” Academic Medicine, vol. 73, no. 9, pp.1013-19, Sep 1998.

[5] A. Oikonomou, S. Amin, “IRiS: An interactive reality system for breast self-examination training,” Conference Proceedings EMBS, no. 7, pp.5162-5, 2004.

[6] G. Gerling, G. Thomas, “Augmented, Pulsating Tactile Feedback Facilitates Simulator Training of Clinical Breast Examinations,” The Journal of the Human Factors and Ergonomics Society, vol. 47, no. 3,pp. 670-681, 2005

[7] S. Barrett, J. Zapka, “Assessing third year medical students’ breast screening skills,” Academic Medicine, vol. 77, no. 9, pp. 905-910, Sept 2002.

[8] H. Hoffman, D. Vu, “Virtual Reality: Teaching Tool of the Twenty-First Century?” Academic Medicine, vol. 72, no. 12, pp. 1076-81, Dec 1997.

[9] M. Alhalabi, “Haptic breast palpation using five-fingered haptic interface HIRO-II,” Japanese Journal for Medical Virtual Reality, vol. 4, no. 1, pp 4-10, 2006.

[10] U. Kühnapfel, K. Çakmak, “Endoscopic Surgery Training using Virtual Reality and deformable Tissue Simulation,” Computers & Graphics, vol. 24, pp.671-682, 2000.

[11] K Hamamoto, ‘‘Investigation on virtual palpation system using ultrasonic elasticity imaging,’’ Conference Proceedings EMBS, no. 1, pp.4873-6, 2006.

[12] T. Miyazaki, ‘‘Virtual palpation system using spring-mass network model,’’ IEIC Technical Report (Institute of Electronics, Information and Communication Engineers), no. 105, pp 261-266, 2005.

[13] N. Vafai, “Toward haptic rendering for a virtual dissection,” International Master Course on Implantology 2, 2006.

[14] M. Dinsmore, N. Langrana, ‘‘Virtual reality training simulation for palpation of subsurface tumours,’’ IEEE International Symposium on Virtual Reality and Applications, 1997.

[15] S. Arnab, M. Solanki, V. Raja, “A Deformable Surface Model for Breast Simulation,” Minimally Invasive Therapy and Allied Technologies, vol. 17, no. 4, 2008.

[16] W. Mollemans, F. Schutyser, “Predicting soft tissue deformations for a maxillofacial surgery planning system: from computational strategies to a complete clinical validation,” Medical Image Analysis, vol. 11, 2007.

[17] H. Chen, W. Wu, “Dynamic Touch-Enabled Virtual Palpation,” Computer Animation and Virtual Worlds, vol. 18, pp. 339-348, 2007.

[18] A. Kerdock, S. Cotin, M. Ottensmeyer, “Truth cube: establishing physical standards for soft tissue simulation,” Medical Image Analysis, vol. 7, no. 3, pp.283-91, 2003.

[19] R. Sinkus, M. Tanter, S. Catheline, J. Lorenzen, “Imaging anisotropic and viscous properties of breast tissue by magnetic resonance-elastography,” vol. 52, no. 2, pp.372-87, Feb 2005.

[20] S. Hosseini, S. Najarian, S. Motaghinasab, “Analysis of the Effects of a Tumor in the Biological Tissue Using Artificial Tactile Sensing Modeling,” Amirkabir Journal of Science and Technology, vol. 66, pp. 66-73, 2007.