Cosmetic Breast Surgery Simulation Remis Balaniuk, Ivan Costa, Jairo Melo 1 o ı Universidade Cat´ lica de Bras´lia (UCB) Remis.Balaniuk@yahoo.com, email@example.com, firstname.lastname@example.org Abstract. Cosmetic breast surgery is a surgical procedure to alter or revise the size or shape of the breasts. It is one of the most frequently performed surgical procedures in plastic surgery today. New surgical techniques and devices are continuously created making possible for surgeons to shape a breast in many different ways. For each case the patient have often many options to consider for undergoing the procedure. The ability to visualize the potential outcomes of the surgery and make decisions on their surgical options is very important for patients and for the surgeons. In this paper we discuss the beneﬁts of 3D sim- ulation to Cosmetic Breast Surgery and introduce our ongoing research project on this subject. e Resumo. Cirurgias cosm´ ticas no seio consistem em procedimentos cirurgicos ´ destinados a alterar o tamanho ou a forma dos seios. Essas cirurgias est ao entre ˜ a e as mais frequentes na cirurgia pl´ stica hoje em dia. Novas t´ cnicas cirurgicas e ı a e dispositivos tem surgido com frequˆ ncia, tornando poss´vel ao cirurgi˜ o dar nova forma ao seios de muitas maneiras diferentes. Para cada caso a paciente e ¸˜ ¸˜ tem com frequˆ ncia muitas opcoes a considerar com relacao ao procedimento ı a ser utilizado. A habilidade de visualizar os poss´veis resultados de uma cirur- o ¸˜ ` ¸˜ ı gia e tomar decis˜ es com relacao as opcoes dispon´veis e muito importante ´ a para a paciente e para o cirurgi˜ o. Nesse artigo discutiremos os benef´cios ı ¸˜ e da simulacao tridimensional de cirurgias cosm´ ticas no seio e apresentaremos nosso projeto de pesquisa nesse assunto. 1. Introduction Breast augmentation and reconstruction after tumor removal or for cosmetic reasons are two of the most frequently performed surgical procedures in plastic surgery today. New surgical techniques and devices have made it possible for surgeons to create and shape a breast in many different ways and there are often many options to consider for the patient undergoing the procedure. Anyone contemplating breast implant surgery should thor- oughly research the procedure, learn the advantages and disadvantages, risks and beneﬁts, and familiarize themselves with all of the available options. Plastic surgeons use visualization tools for patient education and surgical plan- ning. Most of the visualization tools currently in use are two-dimensional. They consist of drawings, ﬁlm photography, or digital images and simple computer-based morphing capabilities. Two-dimensional visualization tools can handle certain surgical procedures, such as rhinoplasty, quite well. Simulation of other procedures, however, such as breast augmentation or reconstruction is a much more difﬁcult problem, and requires 3D analy- sis . This fundamental restriction of current 2D visualization and simulation techniques greatly limits the capability of plastic surgeons to measure true three-dimensional shapes of a patient’s body surface and to educate patients on surgical options and the likely out- comes for surgery. Because of the difﬁculty in measuring volume, assessing symmetry, and evaluating changes in volume, projection, and surface area, the desired appearance and shape is currently determined only subjectively by surgeons and patients, rather than objectively . There have been several methods proposed to measure factors that affect breast shape. In addition, there have been several articles exploring the size of the breast as it relates to bra size  , post-operative appearance, and determining patient expectations . The breast, however, is a complexly shaped tissue structure lacking deﬁnitive anatom- ical landmarks that are not subject to change with breast surgery. This has made previous attempts to determine an ideal, reproducible method for breast shape determination difﬁ- cult . Predicting breast shape still remains an enigma because there are numerous vari- ables contributing to the determination of breast shape: Volume from adjacent fatty tissue , curvature of the chest wall contributing addition volume, breast position (supine vs. upright), deﬁnitive landmarks used to deﬁne the breast. In addition, there are still greater variables after operating on the breast: Surgeon technique and experience, plane of tis- sue dissection, tissue compliance or elasticity, deformation of surrounding tissues, tissue volume added (implant) or removed, and breast shape. The ability to accurately make measurements of a patient’s body surfaces in 3D will offer great beneﬁts to pre-operative surgical planning, post-operative evaluation of surgical results, and surgical simulation models. With accurate 3D visualization, simula- tion and planning capability, surgeons will be able to provide their patients with preop- erative images and possible surgical outcomes in a more visual and accurate way, using quantitative data. A surgeon and/or patient will be able to turn a 3D image from side to side and inspect the 3D object from all angles, offering a much greater wealth of infor- mation than 2D images. An accurate surgical simulation model can be established that is supported by quantitative measurement and data analysis. Figure 1. The REM breast model. Breast surgery may be used after breast cancer removal. Reconstructive breast surgery may take place immediately following removal of the tumor or several months af- ter mastectomy and the completion of radiation and chemotherapy. Reconstructive breast surgery is also often performed to address breast asymmetry. Congenital breast asymme- try manifests as a clinically evident difference between the two breasts based on size and often shape of the affected breast, usually as a result of failure of normal breast develop- ment. Breast surgery is also used for cosmetic purposes. Cosmetic surgery has grown in popularity over the last years. A large number of cosmetic procedures are breast aug- mentations (augmentation mammoplasty) . While patient satisfaction of this surgery is extremely high, the surgery is not without potential risks, unsatisfactory results, and unhappy patients . Many of the factors affecting the results of the ﬁnal shape of the implants are not well understood by the plastic surgery community, nor by breast implant manufacturers. These factors include how the implant distributes its volume in the tis- sues, how the implant changes over time , and the effect of the shape of the implant (round vs. anatomical) on the ﬁnal breast shape . Figure 2 shows a typical breast augmentation procedure. Figure 2. Breast augmentation using an implant. Current methods of working with patients to determine implant sizing are largely subjective based on surgeon experience and patient desire. Placing mock implants in the patients bra is a crude way of ”predicting” ﬁnal size of the breast, however, it is widely employed as a decision making tool. A result of this crude method is that patients do not get a clear understanding of what they will actually look and feel like after the procedure. The same implants or ﬂaps can cause different results in different sized or shaped breasts. For example, a breast with slight ptosis will assume a different shape than one with no ptosis, even thought the same volume and shape of implant is used. Excessive ﬁll of an implant or use of an implant too large for the breast causes the breast to assume a different shape than can be expected with small implants. For example, volumes below the ideal implant typically distribute symmetrically within the tissues and still allow a natural, teardrop shape to the breast. Excessive ﬁll volumes distribute asymmetrically, causing signiﬁcantly upper pole fullness and a more rounded shape because of the forces acting on the implant by the surrounding tissue. This is an important issue to demonstrate to the patient, since patients often request implants too large. Clearly, there exists a need for a tool to simulate surgical options and outcomes for patients in terms of volume and to better educate patients, such that they can make better decisions when electing breast augmentation surgery. A more accurate, objective tool to predict surgical outcome and guide the patient and surgeon in the decision making and planning process is feasible with 3D imaging and surgical simulation. Quantitative mea- surements, such as existing breast volume, chest wall diameter (to determine maximum base diameter of implant), and distances such as nipple-inframammary fold can be deter- mined using 3D imaging and simulation. This may help predict an ”ideal implant” for the patient based on the patient’s body characteristics and habitus, resulting in a more natural appearance of the breast. A simulation model will also allow a patient to view themselves with several different sized implants, all based on quantitative data, bridging the commu- nication gap between surgeons and patients, enabling patients to better understand their surgical options and likely outcomes. 2. Project presentation Our research project’s primary purpose is to develop technology, to be utilized for 3D cos- metic and reconstructive surgery simulation and planning applications. We are develop- ping an interactive software application for 3D simulation of breast surgery for individual patient education and for surgical planning, based on the patient’s own body image. The product enables plastic surgeons to simulate (not predict) the outcomes and options for breast augmentation and reconstructive procedures. The distinction between simulation and prediction is important. Simulation is not a guarantee, it is a demonstration of likely outcomes based on the best knowledge of the surgeon and the capability of the tools. Prediction implies absolute accuracy, which is not possible given the inﬁnite variation in individual anatomies. Because of the high complexity and the variety of the problems and circumstances surrounding a real breast surgery case, we decided to initially focus on a speciﬁc and more predictable domain: the cosmetic surgeries for breast augmentation using implants. Our project is divided in 3 major modules: • 1. Model acquisition: basic procedures for the 3D scanning of the pacient’s breast and a model acquisition method that takes various 3D images and scans and com- bine them to create an underlying soft-tissue model approximating the physical properties of the patient’s breast. • 2. Model simulation: 3D soft tissue modeling engine which simulates the behavior of the patient’s breast model with and without implants. • 3. Validation: assess the success of the modeling methodology for accuracy and stability. 2.1. Model acquistion Measuring the physical properties of a breast in a non-invasive way is a key challenge. Only by tuning the simulated breast model to closely follow the behavior of the real or- gan, our software will become an effective tool for cosmetic and reconstructive surgery simulation. Various attempts have been made in the past in order to create tools and methodologies allowing in-vivo measurement of internal organs physical properties, es- pecially with the advent of Virtual Reality based surgical simulators . Non-invasive imaging-based techniques, such as elastography, are based on scanning organs before and after applying a load to the outside of the body. Minimally invasive techniques, on the other side, are based on directly measuring physical properties of internal organs by ap- plying known forces in speciﬁc points and measuring the consequent displacement. All of these techniques, however, have found scarce application in real-life applications. This is due to various factors, namely high costs, low-level of precision and need of long pro- cedures all involving direct contact with the organ being scanned. The approach we propose for this project is simpler and does not imply the above problems. The process involves using 3D surface images of the patient’s chest in com- bination with a generic 3D model of the internal structure of the breast (fat tissue, lobes, muscles of the chest wall, skin, connective ﬁbrous tissue). The generic model is adapted using numerical methods in order to ﬁt the patient’s breast shape in a number body pos- tures under the action of gravity. Figure 3. The torso 3D scan. 2.2. Model Simulation The development of sufﬁciently fast modeling of biomaterials is a topic of intense interest to a worldwide research community, and methods to simulate deformable materials have been the focus of our past research activity. Over the last thirty years a number of methods have been proposed to simulate deformable objects ranging from non-physical methods, where individual or groups of control points or shape parameters are manually adjusted to shape editing and design, to methods based on continuum mechanics, which account for material properties and internal and external forces on object deformation. Simpler methods, as the mass-spring, are mainly non-physical and inaccurate. Accurate physically based methods, as the Finite Elements, are typically simulated off-line, and the changes on these methods to achieve real time performance normally compromise or their accuracy or their interactivity. Three critical aspects explored on our project are the simulation of non- homogeneous deformable materials, the simulation of an implant as an independent ob- ject constrained inside the breast volume and the implementation of a simpliﬁed surgery interface to inform the details of the surgical procedure. Simulating deformable objects that are made of different layers of tissues (skin, muscles, fat tissue, etc), each having different physical properties, drastically increases the complexity of the modeling problem. Approximations and simpliﬁcations are always needed in order to restraint the complexity of the model to the limits of the methods and technologies being used. The differences in response to load, stretch, compression and cutting between different layers of the model need to be taken into account by the model, while keeping the model’s complexity compatible with the real time performance required by the application. The simulation of an implant inside the chest volume is also a tricky problem. Independent dynamics for the chest and the implant, as well as forces created by the per- sistent contact between the surrounding tissues and the implant, create a strongly coupled system whose simulation can easily become largely unstable. The application requires a simpliﬁed surgery interface that allows the surgeon to specify the surgical procedure that will be performed on the patient. Basically, he speciﬁes the ﬁnal volume of the implant used, the shape of the implant used (round vs. anatomical or teardrop-shaped) and the technique of implantation used (sub-mammary or sub-pectoral). The ﬁnal position of the implant and the plane of tissue dissection are also informed. The patient speciﬁc model is then modiﬁed to reﬂect the changes graphically and physically and is simulated in order to reproduce the effects of the surgical procedure. It is important to stress that the simulation outcome of our tool is not a surgery plan. The typical usage for the simulator will follow some main steps: ﬁrst, a patient speciﬁc model will be acquired, simulated and validated; second, a speciﬁc procedure is chosen by the surgeon and informed to the system using the simpliﬁed interface; third, the model is adapted considering the changes caused by the procedure; fourth, the new model is simulated to reproduce the likely outcomes, enabling the patient to see in 3D those outcomes in any body posture and also considering dynamic effects as the body movements and the gravity. 2.3. Validation Post-operative scans are a fundamental element in the process of reﬁnement of our tech- nology. Such scans are, in fact, the ultimate means to assess the validity of our method- ology. Volume intersection between simulated implanted model and real post-operative volumes obtained in different conﬁgurations are used as an index of performance of the method. Post-operative 3D surface images will be taken every two months for a total period of one year postoperatively. This will allow us to take into account that the breast changes shape signiﬁcantly for up to a year postoperatively and to model this in our future prototypes. 2.4. Status of the project We decided to initially focus our efforts on the model simulation module. A prototype of the modeling engine was developed using virtual reality tools and soft-tissue modeling methods. We previously proposed two soft-tissue simulation methods: the Long Elements Method (LEM)  and the Radial Elements Method (REM) . The LEM and the REM were conceived for the real time, physically based, dynamic simulation of deformable objects. The methods can simulate deformations and dynamics of highly deformable objects. The real time performance of these methods and their intrinsic properties of volume conservation, modeling based on material properties and simple meshing make it attractive for soft tissue modeling and surgery simulation. We introduced two new concepts to the simulation of deformable objects: the meshing based on long elements and the combination of static and dynamic approaches to simulate the same object. The long element is a long elastic spring, linking a point inside the object directly to a point at the object surface. The LEM and the REM differ by their meshing strategy. The LEM mesh consist of 3 sets of long elements, each set consisting of elements disposed parallely following one cartesian axis (see Fig. 4(a)). The REM mesh consist of one point located inside the object and a set of radial long elements disposed around this point following a spherical meshing (see Fig. 4(b)). Figure 4. The LEM mesh (a) The REM mesh (b) The REM, due to its radial meshing technique, is particularly well suited for simu- lating a breast. The breast is simulated as a 3D convex volume ﬁlled with uncompressible ﬂuid. The REM deformation engine simulates a radial element as a mass-less spring, de- ﬁned by its length, area and elasticity. These values are deﬁned for each element based on the material properties of the simulated tissue. An equilibrium equation is deﬁned for each radial element relating its stress (internal and external pressures) to its strain, or deformation (change in length). The static equilibrium condition states that the forces, or pressures, inside the element should be equal to the external forces, or pressures, applied externally. Using this equation we can estimate the change in length (the deformation) of the long element when a stress exists. The set of radial elements used to ﬁll an object deﬁne a set of equations. To correlate these equations 3 global conditions are considered: surface tension, the Pascal principle and volume conservation. The meshing of an object using radial elements reduces the number of elements on the model in one order of magnitude for the same granularity if compared to a standard tetrahedral or cubic meshing. This reduction enables the simulation of more complex ob- jects with less computational effort. The combination of the state-less and the dynamic approaches improves the compliance of the simulation. Deformations are simulated using a state-less solution for elastic deformations of objects ﬁlled with uncompressible ﬂuid. Movements in space, energy and gravity are simulated separately on a dynamic engine. Large deformations that rapidly change the entire shape of the object can be stably sim- ulated in just one time step because of this separation. The simplicity of the method, its reduced number of elements and the fact that no matrix inversions are needed (only mul- tiplications of matrices by vectors), result in a simulation that is fast and scalable, while enabling a full simulation of deformations and dynamics. It is important to stress that the REM model can simulate not only deformations caused by touch and gravity but also dynamic effects like the breast movements caused by walking and jumping. Figure 5 shows the breast simulated on different body postures and the effect of gravity applied on the volume. Figure 5. The breast in different body postures. The volume conservation property of the method enhances the accuracy and re- alism of the simulation. Large deformations, caused by touch and gravity acting on the breast, represent a difﬁcult challenge for other simulation methods, but can be stably sim- ulated by the REM. 3. Experimental Results Our prototype was implemented in C++ and OpenGL and runs on a standard PC at rates compatible with real time graphic and haptic interaction. To test and validate this prototype we acquired a number of 3D scans from a patient using a laser range scanner and deﬁned the elasticity constants of the REM model based on breast tissue properties. Figure 3 shows the 3D scan of the patient’s torso. Using a 3D editor each breast is delimited on the torso and a REM mesh is built. Figure 1 shows the REM breast model being touched using a haptic interface. It is important to stress that the REM model can simulate not only deformations caused by touch and gravity but also dynamic effects like the breast movements caused by walking and jumping. Figure 5 shows the breast simulated on different body postures and the effect of gravity applied on the volume. The same breast can be simulated with an implant inside in order to show the likely outcomes of a cosmetic surgery. Figure 6 compares the breast model with and without an implant. Again, the model can simulate deformations and dynamics and the patient is able to see the likely shape and behavior of her breast after surgery. Figure 6. The breast with and without an implant. 4. Future directions The implemented breast simulator still requires a number of improvements in order to become an usefull tool. The ”surgical interface” is being implemented, where the surgeon can choose the type, shape and volume of the implant to be used, the plane of tissue dissection as well and the exact location where the implant will be inserted. Nevertheless, the major challenge of this project is the breast model acquisition. We are implementing the model acquisition module based on the following protocol. • Step 0: We start designing a 3D generic model based on atlas images of the breast. The model represents the external surface and the main internal tissue layers. A REM simulation model is built for the generic breast. For each patient the following steps are performed: • Step 1: We estimate the rate between fat and tissue inside the patient’s breast. • Step 2: We perform the 3D scanning of the patient’s torso as well as the estimation of the volume and the mass of the breast. • Step 3: The volume of the real breast and its rate between fat and tissue are used to scale the generic model and the different tissue layers inside it. • Step 4: The shape of real breast and the location of external reference points are used to estimate a geometric correction ﬁeld to be applied to the generic model. The geometry of the patient’s breast model is settled. • Step 5: The last step in tuning the reference model is to adapt the REM model to ﬁt the physical properties of the patient’s breast. Our major concern is to ﬁt the elasticity of the real tissue. The breast tissue being non-isotropic we need to compare the simulation model and the real breast in a number of different postures: upright, supine, lateral, etc. The deformation caused by the action of gravity on the patient’s breast is compared to the simulated deformation and correction factors are estimated for the model spring constants. As part of the project development, we also work with plastic surgeons to get reg- ular feedback on various aspects of the software development: Accuracy of the modeling based on their experience, critical features to include in the prototype development, user interface considerations, etc. This feedback loop helps ensure the research is producing a valuable tool for plastic surgeons. 5. Conclusion In this paper we discussed how 3D simulation can be helpful for analysing Reconstructive Breast Surgery and presented our ongoing project where medical expertise and Virtual Reality technology are put together in order to develop a useful application to simulate the outcomes of breast augmentation procedures. References  Balaniuk, R. and Costa, I. F. ”LEM - An approach for physically based soft tissue simulation suitable for haptic interaction”. Conf. Paper, Fifth PHANTOM Users Group Workshop - PUG00, Aspen, USA, Oct. 2000.  Balaniuk, Remis and Salisbury, Kenneth, ”Soft-tissue simulation using the Radial Elements Method”, Balaniuk, R. and Salisbury, K. Conference Paper, IS4TM - International Symposium on Surgery Simula- tion and Soft Tissue Modeling, Juan-les-Pins, France, June 12-13 2003.  Jacobs RA, ”Three-dimensional photography”. Plastic Reconstructive Surgery. 2001 Jan;107(1):276-7.  Malata CM, Boot JC, Bradbury ET, Ramli AR, ”Sharpe DT, Congenital breast asymmetry: subjective and objective assessment.” Br J Plast Surg. 1994 Mar;47(2):95-102.  Kanhai , R., and Hage , J. ”Bra cup size depends on band size.” Plast. Reconstr. Surg. 104: 300, 1999.  Pechter , E. ”Reply: Bra cup size depends on band size.” Plast. Reconstr. Surg. 104: 300, 1999.  Meyer L, Ringberg A, ”Augmentation mammaplasty-psychiatric and psychosocial characteristics and outcome in a group of Swedish women.” Scand J Plast Reconstr Surg Hand Surg. 1987;21(2):199-208.  Vandeweyer E, Hertens D, ”Quantiﬁcation of glands and fat in breast tissue: an experimental determi- nation” Ann Anat 2002 Mar;184(2):181-4.  Katch VL, Campaigne B, Freedson P, Sady S, Katch FI, Behnke AR, Contribution of breast volume and weight to body fat distribution in females. Am J Phys Anthropol. 1980 Jul;53(1):93-100.  Rohrich , R. J. The increasing popularity of cosmetic surgery procedures: A look at statistics in plastic surgery. Plast. Reconstr. Surg. 106: 1363, 2000.  Galdino GM, Nahabedian M, Chiaramonte M, Geng JZ, Klatsky S, Manson P, Clinical applications of three-dimensional photography in breast surgery. Plast Reconstr Surg. 2002 Jul;110(1):58-70.  Hamas , R. S. The comparative dimensions of round and anatomic saline-ﬁlled implants. Aesthetic Surg. J. 20: 281, 2000.  Stephane Cotin and Herve Delingette and Nicholas Ayache, ”Real-Time Elastic Deformations of Soft Tissues for Surgery Simulation”, IEEE Transactions on Visualization and Computer Graphics, num 1, pages 62-73, vol. 5, 1999.