A Biomimetic Approach for Designing a Full External Breast Prosthesis: Post-Mastectomy

applied sciences

Article A Biomimetic Approach for Designing a Full External Breast Prosthesis: Post-Mastectomy

Pedro Cruz 1,*, F. Josue Hernandez 1, Ma. Lourdes Zuñiga 2, Jose Maria Rodríguez 3, Rafael Figueroa 4, Antonio Vertiz 2 and Zaira Pineda 1 ID

1 Department of Mechanical Engineering, Autonomous University of San Luis Potosí, UASLP, 78700 San Luis Potosi, Mexico; [email protected] (F.J.H.); [email protected] (Z.P.) 2 Department of Nursing, Autonomous University of San Luis Potosí, UASLP, 78700 San Luis Potosi, Mexico; [email protected] (M.L.Z.); [email protected] (A.V.) 3 Department of Mechanical Engineering, National Center for Research and Technological Development, CENIDET, 62490 Cuernavaca, Mexico; [email protected] 4 Department of Engineering, Sonora Institute of Technology, 85130 Cd Obregon, Mexico; rafael.ﬁ[email protected] * Correspondence: [email protected]

Received: 4 January 2018; Accepted: 27 February 2018; Published: 1 March 2018

Abstract: This work presents the design of a new breast prosthesis using the biomimetic technique for cases of complete mastectomy to address the problem of the increasing number of women diagnosed with breast cancer in Mexico who are candidates for a mastectomy. The designed prosthesis considers the morphology of a real breast regarding its internal structure to obtain authentic mobility and feel. In order to accomplish this, a model was obtained in 3D CAD using a coordinate measuring machine (CMM) that can be scalable without losing its qualities, and which can be used in any type of patient; afterwards, a ﬁnite element model was developed and a static analysis performed with suggested load cases to evaluate the sensitivity and naturalness of the prosthesis; and ﬁnally, a modal analysis was conducted. The results obtained in displacements and in distribution of stress for the load cases assessed are consistent with those of a real breast: there were smooth contours and there was natural mobility in the prosthesis designed by means of the biomimetic technique.

Keywords: breast cancer; biomimetic design; breast prosthesis

1. Introduction Breast cancer is the accelerated, disorganized, and uncontrolled growth of cells in the mammary gland and it affects the entire population, although it is not significant in the male population [1,2]. In Mexico, breast cancer is one of the main causes of death, according to the records of INEGI for 2016. In women, incidence peaks in the group of 60 to 64 years of age and then drops in the group of 65 and older; the greatest increase was observed in women aged between 25 and 44 years old and between 45 and 49 [3]. For this reason, emphasis has been placed on awareness and on studies focused on this disease due to the importance of early-stage diagnosis and treatment of breast cancer. Unfortunately, this type of cancer is usually detected in advanced stages. The severity of this type of cancer can be classified into 5 stages, depending on the degree of invasion and the patient’s likelihood of survival: stage 0, I, II, III and IV. In Mexico, 90% of the cases are detected in stages III and IV, and as stated in 2014 by the National Center of Gender Equality and Reproductive Health (CNEGSR) the patient’s probability of survival is from 7 to 36%, where the main option for fighting breast cancer is surgery [4,5]. Surgery consists of extracting the tissue invading the mammary gland and the lymph nodes—“mastectomy”. The type of mastectomy depends on the degree of tumor advancement corresponding to the most drastic case, since the patient’s mammary gland is removed. Extirpation of

Appl. Sci. 2018, 8, 357; doi:10.3390/app8030357 www.mdpi.com/journal/applsci Appl. Sci. 2018, 8, 357 2 of 16 the cancerous tissue results in decreased physical and cognitive functioning, together with a lower perception of overall health in the individual. The patient experiences a curvature of the spine and shoulders due to the imbalance caused by the tendency to hide this part of her body. In addition, the person has muscle contractions, discomfort in the neck, back pain, a loss of tissue; her gait also becomes slower and less controlled, and her steps longer [5–9]. Psychologically, patients subjected to a mastectomy can experience a variety of ailments such as depression and anxiety, since the fear of social discrimination is one of the greatest problems after the surgery [10]. The methods of breast reconstruction after a mastectomy help to counteract these ailments. These methods consist of using tissue inserts (generally from different parts of the patient’s own body), internal implants (mainly bags with saline materials) or external breast prostheses [11,12]. However, post-mastectomy breast reconstruction methods present a series of conditions that can affect the patient’s health. In the case of reconstruction with a tissue implant, the patient will again need surgery, at the same time as another part of her body will be physically affected and altered; in the case of reconstruction by implants, there is the risk of a rupture of this bag, which contains materials that can cause allergic reactions, anaplastic lymphomas, and heterotopic ossifications [11,13–15]. Nanotechnology is currently also benefiting the development of implants and prostheses [16]. Nanotechnology has the potential to bring enormous changes to the fields of breast surgery. Breast implants with nanofiber coatings to deliver specific anti-cancer drugs are currently under study. In addition, the prostheses can also delivery drugs that help to treat the injury of the surgery and to avoid problems due to excessive heat or ventilation [17]. The use of external prostheses is a safer option, since they do not involve a surgical procedure and can be used by the patient at any time. There are external prostheses available on the local and world markets; nevertheless, their main problem is that they have crude and simple designs that are far from offering the natural performance and realistic sensation of a breast; that is, such prostheses have generic designs that do not match the culture and the size required according to the needs of each patient [7,12,18]. Using a breast prosthesis that is not suitable for the patient with regards to her weight, size, and sensitivity can have an impact on her health, provoking and aggravating physical problems such as muscle pain, hunched shoulders, curvatures, etc. The patient is also affected psychologically when using an unsuitable breast prosthesis, with problems such as insecurity and discomfort in carrying out her daily activities. Therefore, prostheses with better ergonomic designs are required for patients, not only to fulfill the person’s esthetical needs (which is the main reason), but also to fulfill the suitable weight, size, and sensitivity requirements [19]. The present document is aimed at the design and analysis of external breast prostheses As of the commercial and scientific research conducted, the following tendencies stand out regarding the design of breast prosthesis:

• Symmetry and balance. • Realism and sensitivity, analogous to a real breast. • Lightness, which helps avoid and alleviate lymphedemas. • Suitable for maintaining a comfortable environment in the scar region. • Safe and reliable when carrying out a range of activities. • Suitable for providing smooth adherence without pressure. • Reusable and accessible for any person.

Some of the above points can be achieved by designing external prostheses tailored to the size and needs of each patient, naturally benefitting posture and the performance of daily activities (work, family, sports, etc.) [20]. There are diverse scientific and technological advances in the literature that provide computational models and finite element models focused on simulating the mammary gland for preclinical evaluation, prevention, training, diagnostic [21–31] or on analyzing the biomaterials used for implant reconstruction [14,15,32]. In the case of the most advanced computational models of a breast for the simulation of the anatomy is the anthropomorphic software breast phantom. The anthropomorphic Appl. Sci. 2018, 8, 357 3 of 16 Appl. Sci. 2018, 8, x FOR PEER REVIEW 3 of 16 mammographic imagines [33]. However, the use of finite element breast models in the design process software breast phantom simulates the skin, regions of adipose and fibroglandular tissue, and the and the analysis of breast prosthesis, considering the internal anatomy of the breast (biomimetics) or matrix of Cooper’s ligaments and adipose compartments using 3D breast and 2D mammographic the behavior of a prosthesis in a manner similar to a real breast has not been reported. In particular, imagines [33]. However, the use of finite element breast models in the design process and the analysis this work presents the design and the analysis of a breast prosthesis for cases of total mastectomy of breast prosthesis, considering the internal anatomy of the breast (biomimetics) or the behavior of a using computational methods (CAD, FEM) and the biomimetic technique. This last technique prosthesis in a manner similar to a real breast has not been reported. In particular, this work presents considers the morphological and physiological features of a real breast for the design of the external the design and the analysis of a breast prosthesis for cases of total mastectomy using computational breast prosthesis. It is expected that the prosthesis will perform similarly to the breast regarding methods (CAD, FEM) and the biomimetic technique. This last technique considers the morphological structure, symmetry, consistency, contour smoothness, mobility, and a sensation that is realistic to and physiological features of a real breast for the design of the external breast prosthesis. It is expected the touch. A prosthesis with such features would contribute significantly to the patient’s physical that the prosthesis will perform similarly to the breast regarding structure, symmetry, consistency, rehabilitation and social integration. contour smoothness, mobility, and a sensation that is realistic to the touch. A prosthesis with such features would contribute significantly to the patient’s physical rehabilitation and social integration. 2. Materials and Methods 2. MaterialsThe methodology and Methods proposed in this work covers the development of an external 3D breast prosthesisThe methodology model based proposedon the breast in thiscontour work of coversa medical the mannequin. development The of model an external was sized 3D in breast this prosthesismanner with model the objective based on of the having breast a contourdesign base of a that medical could mannequin. be analyzed The and model evaluated was sizedthrough in thisthe finitemanner elements with the method. objective Likewise, of having the a design 3D model base that will could allow be analyzedthe analysis and of evaluated the external through breast the prosthesisfinite elements to different method. Likewise,scales; that the is, 3D the model prosthesis will allow can the be analysis customized of the for external different breast users prosthesis while maintainingto different scales;its properties. that is, theThere prosthesis are different can betechniques customized for modeling for different mammary users while glands: maintaining magnetic resonance,its properties. RX, Thereinfrared are imaging, different photographs, techniques for 3D modeling laser scanning mammary or coordinate glands: measuring magnetic resonance, machines [20,34,35].RX, infrared These imaging, techniques photographs, are supported 3D laser by novel scanning complex or coordinate algorithms measuring for computer machines simulation [20,34 that,35]. Theseallow obtaining techniques computational are supported anthropomorphic by novel complex mode algorithmsls which for could computer feasibly simulation be replicated that in allow 3D print.obtaining In this computational work we sought anthropomorphic to apply a simple models and whichaccessible could technology. feasibly be Therefore, replicated a incoordinate 3D print. measuringIn this work machine we sought was to used apply (CMM) a simple for and modeling accessible the technology. breast contour Therefore, of the aprosthesis coordinate as measuring shown in Figuremachine 1. wasThe used breast (CMM) is definitely for modeling not consider the breasted contoura rigid oftissue the prosthesis as it can as deform shown during in Figure the1. Themeasurement breast is definitelyprocess. The not magnitude considered of athese rigid deform tissueations as it canis negligible deform duringbecause the the measurement contact force process.of the test The tip magnitude(probe) is regularly of these less deformations than 1 mN isand negligible can be adjusted because according the contact to forcethe desired of the testdegree tip (probe)of sensitivity. is regularly Some lesssuccess than cases 1 mN reported and can bein adjustedthe literature according are directed to the desired at nanoscale degree measurement of sensitivity. applicationsSome success [36], cases ultra-precision reported in the applications literature are [37] directed and atapplications nanoscale measurementof non-rigid applicationselements in [36the], automotiveultra-precision industry applications [38]. [37] and applications of non-rigid elements in the automotive industry [38]. To take thethe measurementsmeasurements on the medicalmedical mannequin, concentric circles were traced along the surface of the mannequin’s breast,breast, whichwhich were were distributed distributed uniformly uniformly [39 [39].]. The The measurement measurement time time for for a asingle single breast breast with with the the available available coordinate coordinate measuring measuring machine machine took took 5 min.5 min.

Figure 1. Random measurements on the co contourntour of the mannequin’s breast.

With the data obtained regarding the periphery of the circles, a point cloud was generated and contouring ofof the the prosthesis prosthesis was was performed performed via concentricvia concentric circles. circles. With this,With the this, skeleton the skeleton of the external of the externalstructure structure of the prosthesis of the prosthesis was formed, was which formed, also which has a also protuberance has a protuberance to emulate to a nippleemulate (Figure a nipple2). (Figure 2). Appl. Sci. 2018, 8, 357 4 of 16 Appl. Sci. 2018, 8, x FOR PEER REVIEW 4 of 16 Appl. Sci. 2018, 8, x FOR PEER REVIEW 4 of 16

Figure 2. Isometric view of the skeleton for the 3D model. Figure 2. Isometric view of the skeleton for the 3D model. Figure 2. Isometric view of the skeleton for the 3D model. With respect to affixing the prosthesis, which will be in contact with the wearer’s thoracic wall, spheresWith were respectrespect added toto afﬁxingaffixingto the back thethe prosthesis,ofprosthesis, the 3D model whichwhich to willwill allow bebe ininair contactcontact to circulate with thebetween wearer’s the thoracicthoracic wall, wall andspheres the wereprosthesis. added This to the prevents backback ofof the thethe increase 3D3D modelmodel of totemperatureto allowallow airair to toin circulate circulatethis part betweenbetween of the body thethe thoracicthoracicand reduces wallwall perspirationand the prosthesis.prosthesis. on the surfaceThis prevents where thethe surgerincrease y scar of temperatureis found, as shownin this in part Figure of the 3. body and reducesreduces perspirationperspiration onon thethe surfacesurface wherewhere thethe surgerysurgery scarscar isis found,found, asas shownshown inin FigureFigure3 .3.

Figure 3. 3D Designed prosthesis model: isometric and back view. Figure 3. 3D Designed prosthesis model: isometric and back view. In the inner part of the prosthesis, which is one of the main contributions of this work, an internal biomimeticIn the inner structure part ofwas the incorporated prosthesis, which (not consideredis one of the in main any contributions prosthesis); thatof this is, work,it resembles an internal the In the inner part of the prosthesis, which is one of the main contributions of this work, an internal internalbiomimetic structure structure of a realwas breast,incorporated since the (not internal considered structure in any directly prosthesis); affects the that mechanical is, it resembles behavior the biomimetic structure was incorporated (not considered in any prosthesis); that is, it resembles the ofinternal the prosthesis structure [15].of a realBiomimetic breast, since endeavors the internal to understand structure directlyhow life affects functi theons mechanical on different behavior levels, internal structure of a real breast, since the internal structure directly affects the mechanical behavior imitatingof the prosthesis the structures [15]. Biomimetic and organisms endeavors found into natu understandre with the how aim life of functicreatingons new on differentstructures, levels, new of the prosthesis [15]. Biomimetic endeavors to understand how life functions on different levels, materials,imitating theand structures new products-based and organisms mainly found on in nature nature [40–43]. with the There aim of are creating different new structures structures, in new the imitating the structures and organisms found in nature with the aim of creating new structures, new breastmaterials, that andprovide new support products-based to the mammary mainly ongland. nature A main [40–43]. structure There is are the differentglandular structures tissue, in whichin the materials, and new products-based mainly on nature [40–43]. There are different structures in the bundlesbreast that of providesmall bodies support known to the as mammary lobes are found, gland. as A willmain be structure explained is thein the glandular following tissue, section. in which breast that provide support to the mammary gland. A main structure is the glandular tissue, in which bundles of small bodies known as lobes are found, as will be explained in the following section. Morphologybundles of smalland Histology bodies known of the Female as lobes Mammary are found, Gland as will be explained in the following section. Morphology and Histology of the Female Mammary Gland MorphologyThe mammary and Histology gland of is the composed Female Mammary of 15 to Gland20 sections called lobes, which are arranged in the sameThe way mammary as the petals gland of ais daisy. composed The lobes, of 15 lobules,to 20 sections and the called bulbs lobes, are all which connected are arranged by thin intubes the The mammary gland is composed of 15 to 20 sections called lobes, which are arranged in the same calledsame wayducts, as whichthe petals connect of a indaisy. the nipple,The lobes, and lobules, fat fills theand spaces the bulbs between are all the connected lobules andby thinthe ductstubes way as the petals of a daisy. The lobes, lobules, and the bulbs are all connected by thin tubes called [44,45].called ducts, Figure which 4 shows connect a graphic in the diagram nipple, withand fatthe fills different the spaces structures between in a thereal lobules breast [46].and the ducts ducts, which connect in the nipple, and fat ﬁlls the spaces between the lobules and the ducts [44,45]. [44,45]. Figure 4 shows a graphic diagram with the different structures in a real breast [46]. Figure4 shows a graphic diagram with the different structures in a real breast [46]. Appl. Sci. 2018, 8, 357 5 of 16 Appl. Sci. 2018, 8, x FOR PEER REVIEW 5 of 16

Figure 4. Internal anatomy of the breast: A Lactiferous duct, B Lobules, C Cross section of lactiferous duct, D Nipple and Adipose tissue, tissue, F F Pectoralis Pectoralis ma majorjor muscle, muscle, G G Chest Chest wall, wall, H H Cooper’s Cooper’s ligaments, ligaments, I IRetromammary Retromammary space, space, J Jskin, skin, K K In Inframammaryframammary fold fold (Adapted (Adapted with with permission permission from [44], [44], Copyright Springer Nature, 2018).

This work sought to imitate the lobular arrangement in a real breast; consequently, a structure This work sought to imitate the lobular arrangement in a real breast; consequently, a structure was proposed that emulates the bundle of lobes found in the internal structure of the breast. was proposed that emulates the bundle of lobes found in the internal structure of the breast. In the internal structure of the prosthesis, several types of 2D geometry were considered In the internal structure of the prosthesis, several types of 2D geometry were considered according according to the manufacturing ability of the prosthesis and the stress distribution property during to the manufacturing ability of the prosthesis and the stress distribution property during application application of loads on the prosthesis model. The most relevant structures were: (a) Rectangular of loads on the prosthesis model. The most relevant structures were: (a) Rectangular structure; structure; (b) Rectangular structure with rounded corners and (c) Triangular or lobular structure. The (b) Rectangular structure with rounded corners and (c) Triangular or lobular structure. The results results showed that the triangular structure is the best choice to be used in the prosthesis. Once the showed that the triangular structure is the best choice to be used in the prosthesis. Once the type of type of internal structure has been defined, then the internal structure in the 3D model of the internal structure has been deﬁned, then the internal structure in the 3D model of the prosthesis prosthesis is done manually by using CAD in approximately 30 minutes, this time is determined by is done manually by using CAD in approximately 30 minutes, this time is determined by the the designer’s experience. designer’s experience. The distribution of lobes in the prosthesis was placed within a circular adjustment with the aim The distribution of lobes in the prosthesis was placed within a circular adjustment with the aim of of taking advantage of the qualities of this adjustment with respect to the deformation fields and to taking advantage of the qualities of this adjustment with respect to the deformation ﬁelds and to the the distribution of stress. The circumferential adjustment is used when it is necessary to obtain a distribution of stress. The circumferential adjustment is used when it is necessary to obtain a uniform uniform distribution of loads or stress in components. The lobular cavities gradually increase in size distribution of loads or stress in components. The lobular cavities gradually increase in size the closer the closer they are to the back part. This arrangement also has an element of connectivity with the they are to the back part. This arrangement also has an element of connectivity with the nipple, just nipple, just as in the real lobular arrangement—following the pattern of the petals of a daisy. Figure as in the real lobular arrangement—following the pattern of the petals of a daisy. Figure5 shows the 5 shows the complete 3D model; in this image, the placement of the lobular structure and the circular complete 3D model; in this image, the placement of the lobular structure and the circular adjustment adjustment in the inside of the prosthesis shell can be seen. in the inside of the prosthesis shell can be seen. Appl. Sci. 2018, 8, 357 6 of 16 Appl. Sci. 2018, 8, x FOR PEER REVIEW 6 of 16 Appl. Sci. 2018, 8, x FOR PEER REVIEW 6 of 16

Figure 5. 3D Model of breast prosthesis: isometric cutaway view. FigureFigure 5. 3D3D Model Model of of breast breast prosth prosthesis:esis: isometric isometric cutaway cutaway view. The circumferential adjustment and the design of the internal biomimetic structure based on the The circumferential adjustment and the design of the internal biomimetic structure based on the real anatomyThe circumferential of a female adjustment breast achieve and the designgreatest of approximation the internal biomimetic to the structure structure and based shape on of the a real anatomy of a female breast achieve the greatest approximation to the structure and shape of a real anatomybreast through of a female the breastshell or achieve delimiting the greatest surface approximation obtained. Consequently, to the structure the and behavior shape of of a realthe real breast through the shell or delimiting surface obtained. Consequently, the behavior of the externalbreast through prosthesis the is shell expected or delimiting to be similar surface to that obtained. of a real Consequently, breast. the behavior of the external external prosthesis is expected to be similar to that of a real breast. prosthesisWith isrespect expected to tothe be lightness similar to of that the of prosthes a real breast.is, the proposed prosthesis (with biomimetic With respect to the lightness of the prosthesis, the proposed prosthesis (with biomimetic technique)With respect for a patient to the lightnesswith a complete of the prosthesis, mastecto themy proposedwho used prosthesis a C cup has (with an biomimeticapproximate technique) mass of technique) for a patient with a complete mastectomy who used a C cup has an approximate mass of 0.7for akg patient (6.86 N), with which a complete is acceptable mastectomy considering who used that a Cshe cup uses has a anC approximatecup. Undoubtedly, mass of weight 0.7 kg (6.86is also N), a 0.7 kg (6.86 N), which is acceptable considering that she uses a C cup. Undoubtedly, weight is also a whichdetermining is acceptable factor consideringin the dynamic that sheand uses realistic a C cup. beha Undoubtedly,vior of the breast. weight In is th alsois sense, a determining the proposed factor determining factor in the dynamic and realistic behavior of the breast. In this sense, the proposed prosthesisin the dynamic improves and realisticthe mechanical behavior properties of the breast. of th Ine thissame sense, due theto its proposed internal prosthesisstructure. improvesTo verify prosthesis improves the mechanical properties of the same due to its internal structure. To verify dimensions,the mechanical geometry, properties adju ofstments, the same and due final to its finish internal of the structure. prosthesis, To verifya rapid dimensions, prototype geometry,was built dimensions, geometry, adjustments, and final finish of the prosthesis, a rapid prototype was built withadjustments, ABS material. and final The finish first ofprototype the prosthesis, of the adesign rapid is prototype shown in was Figure built 6 with and ABSit was material. confirmed The that first with ABS material. The first prototype of the design is shown in Figure 6 and it was confirmed that theprototype qualities of of the the design prosthesis is shown mean in that Figure it can6 and be it manufactured was confirmed simply that the and qualities economically. of the prosthesis themean qualities that it canof the be prosthesis manufactured mean simply that itand can economically.be manufactured simply and economically.

Figure 6. Printed model of the designed biomimetic prosthesis. Figure 6. Printed model of the designed biomimetic prosthesis. The use of 3D printing in the development of functional prototypes is well known, as it is the The use ofof 3D3D printingprinting in in the the development development of of functional functional prototypes prototypes is wellis well known, known, as itas is it the is usethe use of stereolithography printers for additive manufacturing. This type of printer allows the useof stereolithography of stereolithography printers printers for additive for additive manufacturing. manufacturing. This type This of printer type allowsof printer the combinationallows the combination of materials that can give specific properties for each working condition. Currently, 3D combinationof materials thatof materials can give that specific can give properties specific forproperties each working for each condition. working condition. Currently, Currently, 3D printing 3D printing of polymers such as silicone is well placed for rapid test models and small-scale printingof polymers of polymers such as silicone such as is wellsilicone placed is well for rapid placed test for models rapid and test small-scale models and manufacturing small-scale manufacturing (ears, noses, etc.). In the future, there is no doubt that 3D printing of polymers such manufacturing(ears, noses, etc.). (ears, In thenoses, future, etc.). there In the is nofuture, doubt ther thate is 3D no printingdoubt that of polymers3D printing such of aspolymers silicone such will as silicone will have radical advantages for the breast prosthesis proposal presented in this ashave silicone radical will advantages have radical for the breastadvantages prosthesis for proposalthe breast presented prosthesis in thisprop manuscript,osal presented in addition in this to manuscript, in addition to the possibility of printing a prosthesis specific for each patient. In the case manuscript,the possibility in ofaddition printing to a the prosthesis possibility specific of printing for each a patient. prosthesis In the specific case of for large-scale each patient. manufacturing, In the case of large-scale manufacturing, it is possible to take advantage of standard silicone-based methods and ofit islarge-scale possible tomanufacturing, take advantage it ofis possible standard to silicone-based take advantage methods of standard and molding silicone-based systems. methods and molding systems. molding systems. 3. Model FEM: Modeling and Analysis in Finite Element 3. Model FEM: Modeling and Analysis in Finite Element 3. ModelDifferent FEM: breast Modeling models and have Analysis been developed in Finite Element using finite elements in particular cancer detection studiesDifferent or in the breast design models of brassieres have been with developed different using uses. finite The modelselements are in solidparticular volumes cancer without detection any Different breast models have been developed using finite elements in particular cancer detection studiesfrills in theor in inner the part.design The of modelbrassieres developed with diff inerent this work uses. specifies The models the inner are solid part ofvolumes the prosthesis without using any studies or in the design of brassieres with different uses. The models are solid volumes without any frillsthe biomimetic in the inner technique. part. The In model the different developed geometries in this work of the specifies designed the breast inner prosthesis part of the model, prosthesis three frills in the inner part. The model developed in this work specifies the inner part of the prosthesis usingstructure the typesbiomimetic were considered:technique. In the the outer different shell, geom the internaletries of structure, the designed and thebreast spaces prosthesis formed model, by the using the biomimetic technique. In the different geometries of the designed breast prosthesis model, three structure types were considered: the outer shell, the internal structure, and the spaces formed three structure types were considered: the outer shell, the internal structure, and the spaces formed by the former two. Figure 7 shows the structure and the interaction of elements considered for the by the former two. Figure 7 shows the structure and the interaction of elements considered for the Appl. Sci. 2018, 8, 357 7 of 16 Appl. Sci. 2018, 8, x FOR PEER REVIEW 7 of 16 Appl. Sci. 2018, 8, x FOR PEER REVIEW 7 of 16 formerprosthesis two. model, Figure7 such shows as solid the structure elements and (skin the and interaction tissue) and of elementsthe fluid consideredzones. Different for the breast prosthesis models prosthesismodel,have been such model, developed as solid such elements as using solid (skinfinite elements and elements tissue)(skin andin and part tissue) theicular fluid and cancer zones. the fluid Differentdetection zones.breast Differentstudies models or breast the have design models been of havedevelopedbrassieres been usingdevelopedwith different finite using elements uses. finite The in particularelements models arein cancer partsolidicular detection volumes cancer studieswithout detection or any the frillsstudies design in theofor brassieres innerthe design part. with Theof brassieresdifferentmodel developed uses. with The different models in this uses. are work solidThe modelsspecifies volumes are withoutthe solid inner volumes any part frills ofwithout in the the prosthesis inner any part.frills in Theusing the model innerthe developedbiomimetic part. The modelintechnique. this workdeveloped specifies in thethis inner work part specifies of the prosthesisthe inner usingpart theof the biomimetic prosthesis technique. using the biomimetic technique.

FigureFigure 7. 7.Structure Structure and and the the interaction interaction of of elements elements considered considered for for the the prosthesis prosthesis model. model. Figure 7. Structure and the interaction of elements considered for the prosthesis model. In the external structure, 2 mm of thickness with a Young modulus of 10 Kpa, Poisson modulus In the external structure, 2 mm of thickness with a Young modulus of 10 Kpa, Poisson modulus of of 0.4In andthe external damping structure, ratio (ζ) of2 mm0.05 ofwere thickness considered, with thesea Young properties modulus are of very 10 Kpa, close Poisson to those modulus of human 0.4 and damping ratio (ζ) of 0.05 were considered, these properties are very close to those of human ofskin. 0.4 and For dampingthe internal ratio structure, (ζ) of 0.05 a hyper were elasticconsidered, nonlinear these material properties (Neo-Hookea are very closen) was to those considered of human with skin. For the internal structure, a hyper elastic nonlinear material (Neo-Hookean) was considered skin.a Young For the modulus internal of structure, 15 Kpa, Poisson a hyper modulus elastic no ofnlinear 0.4 and material damping (Neo-Hookea ratio valuesn) (ζ was) of 0.06,considered similar withto the with a Young modulus of 15 Kpa, Poisson modulus of 0.4 and damping ratio values (ζ) of 0.06, a propertiesYoung modulus of glandular of 15 Kpa, tissue. Poisson In addition, modulus properties of 0.4 and ofdamping fatty tissue ratio ofvalues 2.5 Kpa, (ζ) of Poisson 0.06, similar modulus to the of similar to the properties of glandular tissue. In addition, properties of fatty tissue of 2.5 Kpa, Poisson properties0.499 and of damping glandular ratio tissue. values In addition, (ζ) of 0.06 properties were considered of fatty tissue for the of 2.5interior Kpa, [13,15,23,47,48].Poisson modulus These of modulus of 0.499 and damping ratio values (ζ) of 0.06 were considered for the interior [13,15,23,47,48]. 0.499properties and damping can be obtained ratio values using ( ζmedical) of 0.06 grade were silico consideredne with fordifferent the interior configurations [13,15,23,47,48]. spaces (SoftgelThese These properties can be obtained using medical grade silicone with different conﬁgurations spaces propertiesA-341C—DC can be200 obtained silicone); using silicone medical has been grade widely silico neused with for different the development configurations of prostheses spaces (Softgel because (Softgel A-341C—DC 200 silicone); silicone has been widely used for the development of prostheses A-341C—DCit is not toxic, 200 and silicone); it is biocompatible silicone has been with widely the human used for body, the development withstanding of common prostheses sterilization because because it is not toxic, and it is biocompatible with the human body, withstanding common sterilization it methods.is not toxic, In addition, and it is this biocompatible silicone has witha hardness the human between body, 10 andwithstanding 90 (degrees common Shore A). sterilization With this, a methods. In addition, this silicone has a hardness between 10 and 90 (degrees Shore A). With this, methods.3D finite In elements addition, model this siliconewas developed has a hardness with 273,9 between65 5-node 10 and tetrahedral 90 (degrees elements Shore measuringA). With this, 1.98 a × a 3D ﬁnite elements model was developed with 273,965 5-node tetrahedral elements measuring 3D10 finite−5 m, aselements shown modelin Figure was 8. developed The size of with the 273,9mesh65 was 5-node optimized tetrahedral using elements diverse meshmeasuring criteria 1.98 until × 1.98 × 10−5 m, as shown in Figure8. The size of the mesh was optimized using diverse mesh criteria 10the−5 m, optimal as shown size inwas Figure reached. 8. The size of the mesh was optimized using diverse mesh criteria until theuntil optimal the optimal size was size reached. was reached.

Figure 8. Type and size of mesh for the model. Figure 8. Type and size of mesh for the model. Figure 8. Type and size of mesh for the model. In the boundary conditions, the back part of the prosthesis was considered, fixed to the patient’s thoracicIn the wall, boundary completely conditions, fixed, the and back the part other of eltheements prosthesis free. wasThe considered,model was fixedsubjected to the to patient’s different thoracicload cases wall, to completely analyze its fixed, behavior and andthe otherfunctionality elements [31,49]. free. The The model most wascommon subjected load tocases different are for loadpostures: cases tostanding analyze upright, its behavior prone and (on functionality all fours) and [31,49]. lying The supine. most Additionally,common load newcases cases are for are postures: standing upright, prone (on all fours) and lying supine. Additionally, new cases are Appl. Sci. 2018, 8, 357 8 of 16

In the boundary conditions, the back part of the prosthesis was considered, ﬁxed to the patient’s thoracic wall, completely ﬁxed, and the other elements free. The model was subjected to different load Appl. Sci. 2018, 8, x FOR PEER REVIEW 8 of 16 cases to analyze its behavior and functionality [31,49]. The most common load cases are for postures: standingproposed upright, in this work prone to (on evaluate all fours) the andsensitivity lying supine. and naturalness Additionally, of the new prosthesis, cases are termed proposed inspection in this workor palpation to evaluate load the cases. sensitivity These cases and naturalness are shown ofin theFigure prosthesis, 9 below, termed where inspection the palpation or palpation force applied load cases.was 5 TheseN. cases are shown in Figure9 below, where the palpation force applied was 5 N.

FigureFigure 9.9. Different load load cases cases proposed proposed to to ev evaluatealuate the the finite ﬁnite element element model: model: (a) (standinga) standing person, person, (b) (positionb) position prone prone (on (onall allfours), fours), (c) (lyingc) lying supine, supine, (d) (horizontald) horizontal force force applie appliedd to the to thenipple nipple region, region, (e) (combinese) combines the the effects effects of ofgravity gravity with with a apoint point lo loadad in in the the upper upper part part of of the the prosthesis prosthesis and (ff)) combinescombines thethe effectseffects ofof gravitygravity withwith aa pointpoint loadload placedplaced inin thethe lowerlower partpart ofof thethe prosthesis.prosthesis.

OneOne ofof thethe mainmain aimsaims ofof thisthis workwork isis toto analyzeanalyze thethe displacementsdisplacements andand thethe distributiondistribution ofof thethe stressstress thatthat cancan occuroccur inin thethe designeddesigned prosthesisprosthesis inin thethe differentdifferent loadload casescases proposed.proposed. Finally,Finally, aa staticstatic andand dynamicdynamic (modal)(modal) analysis analysis was was performed performed to to know know the the behavior behavior and and evaluate evaluate the the performance performance of theof the prosthesis. prosthesis.

4.4. ResultsResults andand DiscussionDiscussion TheThe finitefinite elementelement modelmodel breastbreast prosthesisprosthesis waswas subjectedsubjected toto thethe proposedproposed loadload cases.cases. TheThe firstfirst casecase “a”,“a”, involvesinvolves thethe conditioncondition ofof aa standingstanding person,person, wherewhere onlyonly thethe gravitygravity isis affected.affected. FigureFigure showsshows thethe displacementsdisplacements andand stressstress generatedgenerated byby thisthis condition.condition. TheThe casecase forfor aa standingstanding personperson isis oneone ofof thethe mostmost importantimportant becausebecause itit isis oneone ofof thethe predominantpredominant positionspositions in daily daily life. life. Figure Figure 10 10shows shows displacement displacementss in the in range the range of 0 to of 26 0 mm, to 26 with mm, the with greatest the greatestmagnitude magnitude of displacement of displacement found in found the nipple. in the nipple.Likewise, Likewise, the distribution the distribution of displacements of displacements in the inprosthesis the prosthesis is symmetrical is symmetrical and with and good with trajecto good trajectory;ry; it does itnot does present not present punctual punctual stress (stress stress (stressconcentration) concentration) and its andmaximum its maximum stress is stress approx is approximatelyimately 7 Kpa. 7The Kpa. prosthesis The prosthesis does not does present not presentdefects defectsin its form in its or form contour or contour or on its or onsurface its surface for this for load this case. load case.The results The results are consistent are consistent with with that thatof the of theprofile profile of deformation of deformation and and magnitude magnitude of ofdi displacementsplacement reported reported by by [50,51], [50,51], similar to thethe deformationdeformation ofof aa realreal breastbreast underunder thethe effectseffects ofof gravity.gravity. CasesCases ““bb”” andand ““cc”” representrepresent thethe positionspositions prone (on all fours) and lying supine. These are the most frequent in a person’s daily life. Figure 11 shows the results obtained under these load cases for displacements and stress. Appl. Sci. 2018, 8, 357 9 of 16

prone (on all fours) and lying supine. These are the most frequent in a person’s daily life. Figure 11 Appl.Appl. Sci. Sci. 2018 2018, 8,, x8 ,FOR x FOR PEER PEER REVIEW REVIEW 9 of9 of16 16 shows the results obtained under these load cases for displacements and stress.

FigureFigureFigure 10. 10. 10. DisplacementDisplacement Displacement and and and Von Von Von Mises Mises Mises stress stress stress contour contour contour plots plots plots for for for case case case “ “aa ”.“”.a ”. b b

c c

Figure 11. Displacement and Von Mises stress contour plots for case “b” and “c”, respectively. FigureFigure 11. 11. DisplacementDisplacement and and Von Von Mises Mises stress stress contour contour plots plots for for case case “ “bb”” and and “ “cc”,”, respectively. respectively.

Maximum displacement of 11 mm and a stress of 4.1 Kpa were obtained for both weight MaximumMaximum displacementdisplacement ofof 11 11 mm mm and and a stress a stress of 4.1 of Kpa 4.1 were Kpa obtained were obtained for both weightfor both conditions; weight conditions; although the magnitudes are the same, the distribution fields show variations in the conditions;although the although magnitudes the magnitudes are the same, are the the distribution same, the ﬁeldsdistribution show variationsfields show in thevariations interior in of the the interior of the prosthesis. The prosthesis shows a symmetrical contour without any problems and the interiorprosthesis. of the The prosthesis. prosthesis The shows prosthesis a symmetrical shows a symmetrical contour without contour any without problems any and problems the form and agrees the form agrees with that reported by other works on breasts [21,30,52,53]. Table 1 shows the comparison formwith agrees that reported with that by reported other works by other on breasts works [21 on,30 breasts,52,53 ].[21,30,52,53]. Table1 shows Table the comparison1 shows the betweencomparison the between the obtained displacements and those reported in the literature. In addition, the prosthesis betweenobtained the displacements obtained displacements and those reported and those in the reported literature. in the In addition,literature. the In prosthesisaddition, the shows prosthesis a good shows a good distribution of stress. showsdistribution a good of distribution stress. of stress.

TableTableTable 1. 1. 1.ComparisonComparison Comparison of of ofobtained obtained obtained displacements displacements displacements with with with those those those reported. reported. reported.

BreastBreast Position Position Maximum Maximum Displacement Displacement Obtained Obtained (mm) (mm) Maximum Maximum Displacement Displacement Reported Reported (mm) (mm) Breast Position Maximum Displacement Obtained (mm) Maximum Displacement Reported (mm) StandingStanding 26 26 27.5 27.5 [22], [22], 30 30[50], [50], 20 20[31] [31] Standing 26 27.5 [22], 30 [50], 20 [31] ProneProne 11.06 11.06 15.6 15.6 [53], [53], 24 24[27]] [27]] ProneSupine 11.06 11.06 15.6 11 [[44],53], 24 14 [ 27[24]]] SupineSupine 11.06 11.06 11 11 [44], [44], 14 14 [24] [24]

It Itcan can be be observed observed that that the the displacement displacement valu valueses (in (in the the proposed proposed prosthesis) prosthesis) are are within within the the It can be observed that the displacement values (in the proposed prosthesis) are within the results resultsresults reported reported by by similar similar research. research. The The differences differences presented presented in inthe the values values are are due due to tothe the reported by similar research. The differences presented in the values are due to the dimensions, dimensions,dimensions, materials materials and and conditions conditions of ofeach each comp computationalutational model model or or experimental experimental model model that that were were used.used. Load Load cases cases “ d“”,d ”,“ e“”e ”and and “ f”“ f”are are suggested suggested for for this this work work with with the the aim aim of ofevaluating evaluating the the sensitivitysensitivity of ofthe the prosthesis; prosthesis; these these cases cases consist consist of ofthe the combined combined effect effect of ofgravity gravity and and a palpationa palpation force force appliedapplied in inthe the model. model. Case Case “d “”d presents” presents a horizontala horizontal force force of of5 N5 Napplied applied to tothe the nipple nipple region; region; the the results,results, seen seen in inFigure Figure 12, 12, demonstrate demonstrate that that th the combinatione combination of ofthese these weights weights achieves achieves a uniforma uniform Appl. Sci. 2018, 8, 357 10 of 16 materials and conditions of each computational model or experimental model that were used. Load cases “d”, “e” and “f” are suggested for this work with the aim of evaluating the sensitivity of the prosthesis; these cases consist of the combined effect of gravity and a palpation force applied in the model.Appl. Sci. Case 2018, “8,d x” FOR presents PEER REVIEW a horizontal force of 5 N applied to the nipple region; the results,10 seenof 16 in Figure 12, demonstrate that the combination of these weights achieves a uniform distribution in the distribution in the lower part of the prosthesis. This quality in the prosthesis translates into a natural lowerbehavior part ofand the a prosthesis.good response This qualityto touch, in thepreventi prosthesisng undesirable translates intobehaviors a natural such behavior as collapses and a or good responseruptures to of touch, the material preventing and a undesirablebad buffering behaviors against exerted such as pressure. collapses The or results ruptures obtained of the for material weight and a badcase buffering“e”, which against combines exerted the effects pressure. of gravity The resultswith a point obtained load forin the weight upper case part “ eof”, the which prosthesis, combines thedemonstrating effects of gravity that withthe shape a point of loadthe inprosthesis the upper is partsuitable, of the and prosthesis, the distribution demonstrating of stress that is the shapesymmetrical. of the prosthesis For the last is case, suitable, “f” combines and the distributionthe effects of gravity of stress with is symmetrical. a point load placed For the in lastthe lower case, “f” combinespart of the the prosthesis. effects of These gravity last with three a pointcases (cases load placed“d”, “e in” and the “ lowerf”), termed part ofpalpation the prosthesis. cases, obtained These last threedisplacements cases (cases in “thed”, range “e” and of 12 “f to”), 70 termed mm and palpation magnitudes cases, of obtainedstress of 4 displacements Kpa to 31 Kpa making in the range case of 12“ tod” 70the mm most and critical magnitudes with the of greatest stress of values 4 Kpa obtained. to 31 Kpa The making results case obtained “d” the with most respect critical to with the the greatestmagnitudes values of obtained. stress are The congruent results obtained with those with re respectported to thecase magnitudes studies of ofcancer stress detection are congruent or withevaluation those reported of brassier toes case for studiesbreasts of[54,55]. cancer detection or evaluation of brassieres for breasts [54,55].

d e

Figure 12. Displacement and Von Mises stress contour plots for case “d”, “e” and “f”, respectively. Figure 12. Displacement and Von Mises stress contour plots for case “d”, “e” and “f”, respectively.

AA good good distribution distribution ofof loadsloads is observed in in the the simulation simulation results results obtained obtained from from the the load load cases cases sincesince the the stress stress are are distributed distributed in in a a greater greater area, area, indicating indicating that that a a movement movement andand aa naturalnatural responseresponse are generatedare generated in the in prosthesis. the prosthesis. On theOn otherthe other hand, hand the, internalthe internal structure structure presents presents stress stress along along its entireits contour,entire contour, due to the due implementation to the implementation of lower of density lower density solid between solid between the spaces the spaces (ﬂuid) (fluid) and the and spherical the adjustmentspherical adjustment adapted for adapted this design. for this design.

ModalModal Analysis Analysis ModalModal analysis analysis depends depends onon the material properties. properties. Unfortunately, Unfortunately, only only a few a few studies studies reporting reporting thethe mechanical mechanical properties properties of of real real breast breast tissue tissue are are available available in thein the literature, literature, commonly commonly ignoring ignoring tissue damping.tissue damping. However, However, it is difﬁcult it is difficult to take ato damping take a damping value as value a standard as a standard because because the damping the damping of human tissueof human depends tissue on depends its location, on its the loca worktion, itthe does work and it does the amountand the amount of collagen of collagen present present in each in patient each 's tissue.patient's The tissue. damping The directly damping affects directly the magnitudeaffects the ofmagnitude the displacements of the displacements and in a small and proportion, in a small the proportion, the vibration frequency. It can be observed that the tendency is to consider the breasts as under-damped systems [25,56,57]. With the aim of evaluating the behavior dynamic of the prosthesis model a modal analysis was performed within the frequency range of 0 to 6 Hz. This range was considered because people who Appl. Sci. 2018, 8, 357 11 of 16 vibration frequency. It can be observed that the tendency is to consider the breasts as under-damped systems [25,56,57]. Appl. Sci.With 2018 the, 8, aimx FOR of PEER evaluating REVIEW the behavior dynamic of the prosthesis model a modal analysis11 wasof 16 performed within the frequency range of 0 to 6 Hz. This range was considered because people who walk or run run have have a afrequency frequency of ofstep step of 1.5 of 1.5to 4.5 to Hz 4.5 [25,53]. Hz [25 ,In53 ].the In simulation the simulation results results shown shownin Figure in Figure13, the 13prosthesis, the prosthesis presented presented 4 natura 4l natural frequencies frequencies and 4 modal and 4 modalforms. forms.

Figure 13. Displacement contour plots for modal analysis. Figure 13. Displacement contour plots for modal analysis.

The ﬁrstfirst mode shown in Figure 13 represents thethe displacementdisplacement generated above and below the prosthesis in resonance to a frequency of 3.59 Hz—predominantHz—predominant for the case of gravity. The other modes of vibration are 3.64, 5.05 and 5.84 Hz, respectively. The movements of the prosthesis in resonance do not manifest strange movements or behaviors beyond the naturalne naturalnessss of the same. Table 22 shows shows thethe comparison of the the obtained obtained natural natural frequenc frequenciesies with with those those reported reported in in the the literature. literature.

Table 2. Comparison of the obtained naturalnatural frequencies with those reported.reported.

ModeMode Frequency Frequency Obtained Obtained (Hz) (Hz) Frequency Frequency (Hz) (Hz) [25 ][25] 1 3.59 4.87 1 3.59 4.87 2 3.64 4.91 2 3.64 4.91 3 5.05 4.99 3 5.05 4.99 4 4 5.845.84 5.02 5.02

The frequency values obtained are very close to the values reported in the literature. Variations to theseThe values frequency may values be caused obtained by the are properties very close of to the the materials values reported used. in the literature. Variations to these values may be caused by the properties of the materials used. 5. Discussion 5. Discussion The main hypothesis approached in this work is that the internal biomimetic structure and the The main hypothesis approached in this work is that the internal biomimetic structure and the circumferential adjustment in the prosthesis would generate a natural behavior in daily activities and circumferential adjustment in the prosthesis would generate a natural behavior in daily activities realistic to the touch for people who use the prosthesis. The above qualities are not present in any and realistic to the touch for people who use the prosthesis. The above qualities are not present commercial product and in the scientific literature no advancement is reported in this field. For this in any commercial product and in the scientific literature no advancement is reported in this field. purpose, a biomimetic model in 3D was developed that includes a lobular configuration in its internal For this purpose, a biomimetic model in 3D was developed that includes a lobular configuration in its structure and a circumferential adjustment. The model can be scalable for any type of patient. The internal structure and a circumferential adjustment. The model can be scalable for any type of patient. circumferential adjustments are used to obtain better distributions of stress in some engineering The circumferential adjustments are used to obtain better distributions of stress in some engineering applications. Therefore, a finite element model was generated, which was evaluated with different applications. Therefore, a finite element model was generated, which was evaluated with different load cases: standing upright, facing down on all fours, facing up and the cases of palpation proposed, load cases: standing upright, facing down on all fours, facing up and the cases of palpation proposed, and a modal analysis. The results obtained in terms of displacements and stress are within the results and a modal analysis. The results obtained in terms of displacements and stress are within the results presented in works that use FEM models for cancer diagnosis or detection and for brassiere design. presented in works that use FEM models for cancer diagnosis or detection and for brassiere design. The deformation of the prosthesis contours is symmetrical and smooth; likewise, it does not present The deformation of the prosthesis contours is symmetrical and smooth; likewise, it does not present irregularities on the surface and has natural deformation patterns, resembling a real breast. The fields irregularities on the surface and has natural deformation patterns, resembling a real breast. The fields of stress indicate that the loads are distributed uniformly due to the contour and prosthesis structure; of stress indicate that the loads are distributed uniformly due to the contour and prosthesis structure; that is, the loads are not concentrated on a particular point, which means that the person will have that is, the loads are not concentrated on a particular point, which means that the person will have the the sensation of consistency to the touch without feeling great opposition to the palpation force sensation of consistency to the touch without feeling great opposition to the palpation force applied, applied, giving the prosthesis a great feeling of realism and belonging. The biomimetic lobular structure remained stable and without any problems during the evaluation of the prosthesis for the load cases posed. In cases “b” and “c”, the same magnitudes of displacements were obtained, as shown in the cutaway section of the models (Figure 14), where although the magnitude is the same, the distribution within the structure is different. Appl. Sci. 2018, 8, 357 12 of 16 giving the prosthesis a great feeling of realism and belonging. The biomimetic lobular structure remained stable and without any problems during the evaluation of the prosthesis for the load cases posed. In cases “b” and “c”, the same magnitudes of displacements were obtained, as shown in the cutawayAppl. Sci. 2018 section, 8, x FOR of the PEER models REVIEW (Figure 14), where although the magnitude is the same, the distribution12 of 16 Appl. Sci. 2018, 8, x FOR PEER REVIEW 12 of 16 withinAppl. Sci. the 2018 structure, 8, x FOR PEER is different. REVIEW 12 of 16 b c bb cc

Figure 14. Displacement contour plots (cutaway) for case “b” and “c”, respectively. Figure 14. Displacement contour plots (cutaway) for case “b” and “c”, respectively. FigureFigure 14.14. DisplacementDisplacement contourcontour plotsplots (cutaway)(cutaway) forfor casecase ““bb”” andand ““cc”,”, respectively.respectively. The internal internal biomimetic biomimetic structure structure of the of prosthesis the prosthesis behaves behaves satisfactor satisfactorilyily for the load for cases theload evaluated, cases The internal biomimetic structure of the prosthesis behaves satisfactorily for the load cases evaluated, evaluated,as shownThe internal in asFigure shown biomimetic 15. In in this Figure structurefigure 15 can. of In be the thisobserved prosthesis ﬁgure at canbehavesthe displacement be observed satisfactor contour atily thefor the displacementplots load for cases cases evaluated, “ contoura”, “d”, as shown in Figure 15. In this figure can be observed at the displacement contour plots for cases “a”, “d”, plots“ase ”shown and for “f casesin” thatFigure “thea”, 15.displacement “d In”, this “e” figure and values “canf” thatbe are observed thewithin displacement the at theresults displacement reported values areby contour similar within plots research. the for results cases reported“a”, “d”, by““ee”” similar andand ““ff”” research. thatthat thethe displacementdisplacement valuesvalues areare withinwithin thethe resultsresults reportedreported byby similarsimilar research.research. a d e f aa dd ee ff

Figure 15. Displacement contour plots for cases “a”, “d”, “e” and “f”. FigureFigure 15.15. DisplacementDisplacement contourcontour plotsplots forfor casescases ““aa”,”, ““dd”,”, ““ee”” andand ““ff”.”. Likewise, in modal analysis, the prosthesis presentspresents the behavior of the internal biomimetic Likewise,Likewise, inin modalmodal analysis,analysis, thethe prosthesisprosthesis prespresentsents thethe behaviorbehavior ofof thethe internalinternal biomimeticbiomimetic structure, as shown in Figure 1616.. structure,structure, asas shownshown inin FigureFigure 16.16.

Figure 16. Displacement contour plots for modal analysis. Figure 16. Displacement contour plots for modal analysis. FigureFigure 16.16. DisplacementDisplacement contourcontour plotsplots forfor modalmodal analysis.analysis. As can be appreciated in the above figure, in no modal form does the proposed prosthesis As can be appreciated in the above figure, in no modal form does the proposed prosthesis presentAs irregularitiescan be appreciated or bad behain thevior. above These figure, results in ensureno modal good form functioning does the when proposed the prosthesis prosthesis is present irregularities or bad behavior. These results ensure good functioning when the prosthesis is subjectedpresent irregularities to dynamic orperturbations. bad behavior. The These analysis results of ensurethe results good obtained functioning in terms when of the displacements prosthesis is subjected to dynamic perturbations. The analysis of the results obtained in terms of displacements andsubjected stress, to lie dynamic within the perturbations. results reported The inanalysis the literature of the results that use obtained FEM models in terms for ofcancer displacements diagnosis and stress, lie within the results reported in the literature that use FEM models for cancer diagnosis orand detection stress, lie and within for brassiere the results design. reported The deformation in the literature of the that contours use FEM of the models prosthesis for cancer is symmetrical diagnosis oror detection detection and and for for brassiere brassiere design. design. The The deformation deformation of of the the contours contours of of the the pr prosthesisosthesis is is symmetrical symmetrical Appl. Sci. 2018, 8, 357 13 of 16

As can be appreciated in the above ﬁgure, in no modal form does the proposed prosthesis present irregularities or bad behavior. These results ensure good functioning when the prosthesis is subjected to dynamic perturbations. The analysis of the results obtained in terms of displacements and stress, lie within the results reported in the literature that use FEM models for cancer diagnosis or detection and for brassiere design. The deformation of the contours of the prosthesis is symmetrical and smooth, as well. There are no irregularities on the surface, and it has natural deformation patterns to resemble a real breast. The ﬁelds of stress indicate that the loads are distributed uniformly due to the contour and structure of the prosthesis; that is, the loads are not concentrated on a particular point, which means that to the touch, the person will have the sensation of consistency without feeling much resistance to the palpation force applied, giving the prosthesis a great feeling of realism and belonging. The lobular biomimetic structure remained stable and without any problems during the evaluation of the prosthesis for the load cases posed. In the future we intend to develop a hybrid system that considers all the components of the design process or the development of a program in the “deep-knowledge and models” philosophy that would help us in measurement, scaling, modeling and manufacturing for prostheses similar to those presented in [58]. This methodology reduces the process input variables and generates results for decision making or manufacturing design plans [59]. Software of this type predicts magnitudes from the measurement—model by involving static and dynamic behavior of the design parts.

6. Conclusions In this paper, the biomimetic technique was used for the design of a breast prosthesis for cases of complete mastectomy. The prosthesis considers the morphology of the breast for the configuration of its internal structure. This configuration will give the prosthesis the naturalness and behavior of a real breast. Hence, a 3D prosthesis model was built, which can be easily scalable without affecting its functionality and it was assigned silicone-based materials with properties very similar to those of a real breast (fat and glandular tissue). With the model obtained in CAD, a finite element model was developed to perform a static analysis with load cases that simulate the daily activities of a person, analyzing the displacements and the distribution of stress. Finally, a modal analysis was performed in the frequency range of 0 to 6 Hz. The main conclusions obtained from theoretical studies and experimental tests are listed below:

• We successfully biomimetize the internal structures of a real breast to design and analyze a breast prosthesis for cases of complete mastectomy. With the biomimetic technique, a realistic model of the prosthesis can be easily obtained. • The lobular (biomimetic) geometry used for the design and the spherical adjustment that was adapted to define the internal structure of the prosthesis proposed in this work properly distributes the stress generated by the loads it was subject to. In addition, it can be concluded that the qualities and functioning of the prosthesis designed in this work will allow it to be adapted to different body types, by scaling the model, without affecting its functionality. • The load cases considered for the prosthesis study do not show irregularities in contour or shape on their surface nor in the internal structure. The displacements and stress found in the prosthesis analysis are within the ranges reported in works related to diagnosis, detection, and evaluation of brassieres. • Regarding final dimensions, finish, and manufacturability, the model was printed using ABS material. With this, it is possible that the prosthesis can be printed in 3D in an easy and uncomplicated way with the appropriate technology. • With the dynamic analysis performed in the prosthesis model the fundamental frequencies were obtained. This will prevent reaching conditions of resonance (critical deformations) during use that can affect the natural behavior of the prosthesis or damage its structure. The above ensures that the proposed prosthesis design will not fail and can be used for a variety of activities. Appl. Sci. 2018, 8, 357 14 of 16

As a conclusion, it can be veriﬁed that the prosthesis has realism in mobility and touch.

Acknowledgments: We thank the Department of Nursing at Autonomous University of San Luis Potosí. Furthermore, the authors wish to thank Jose María Rodriguez Lelis for all constructive discussions and their technical support. Author Contributions: Pedro Cruz and F. Josue Hernandez, conceived and wrote the paper together; Ma. Lourdes Zuñiga, Antonio Vertiz and Jose Maria Rodríguez contributed the medical and biomedical area; Rafael Figueroa, Zaira Pineda and Jose Maria Rodríguez contributed materials and analysis tools. All the co-authors contributed to the discussion of the results and preparation of the manuscript. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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