Radiol Oncol 1995; 29: 44-6. Determination of the breast volume after breast conservating surgery Liliane Demange1 and Jean Tisnes2 1 Department of Radiotherapy and Oncology, Institut Jean-Godinot, Reims Cedex 2 Société de Fabrication d'Instruments de Mesure, Massy Cedex, France A mathematical description has been developed to estimate the difference in volume between the breasts after breast conservating surgery. This method can help the physician to evaluate the cosmetic results after treatment. It is a simple method for the radiotherapist who routinely uses a simulator. Key words: mastectomy; mammography-methods; breast conservating therapy, cosmetic evaluation, breast volume Introduction The patient with a diagnosis of early breast cancer can now be successfully treated by conservative techniques. Studies results have demonstrated that for small tumors (Tl and small T2) lumpectomy followed by radiotherapy is a valid alternative to mastectomy. 1 Today, the physician tries not only to cure the patient but to achieve the best possible cosmetic results.2 In the breast the cosmetic outcome is generally evaluated by the difference in size between the two breasts, teleangiectasia and fibrosis. Measurement of the size of the breast is somewhat subjective. We describe in this paper a more objective method of measuring breast size. Correspondence to: Liliane Demange MD, Institut Jean Godinot, 1, rue du Général Koenig, 51056 Reims Cedex, France. UDC: 618.19-006.6-089.87:618.19-073.75 Method Theory Breast is a region bounded by the chest wall on one side and by the skin on the other. This could be schematized by regarding the breast as a segment of a sphere, with the pectoral muscle being a second segment of a sphere within the first. The volume of interest is represented by the difference between the two spherical domes. The problem can now be resolved mathematically. The common base of the two segments is a circle of radius R. The outer segment is bounded by the skin (height H); the inner segment is defined by the fascia of the pectoral muscle (height h) from the chest wall. The volume of the breast (v) can be assimilated to the difference in volume of these two spherical domes mathematically expressed as: V = | (H3 - h3) + i R2 (H - h) Determination of the breast volume after breast conservating surgery 45 However, it appears more suitable to the geometry encountered in most of the patients to consider the base of the segments as elliptical (Figure la, lb). The maximum and minimum radii need to be defined. The maximum radius is in the transverse axis (R) and the minimum in the cranio caudal axis (r). We can now use the ratio (r/R) to modify the above equation V = 5 (H3 - h3) + 5 R2 (H - h) Ro 2 V = volume of the breast. R = half the maximum transverse "width" of the breast. r = half the maximum cranio caudal "length" of the breast. H = elevation of the breast. h = elevation of the chest wall. We have used this formula to calculate the volume of the breast in this study. Measurement of the geometrical dimensions of the breast With the patient in the supine position, using a conformator (or a CT-scan if available), we drew the contours of the thorax including the breast at two different levels. The first contour CMed is taken at the level of the two nipples, the second at the level of the inframammary fold. The cranio caudal diameter (2 r) of the breast is measured directly on the patient as shown on the picture. The most medial limit (A) and the most lateral limit (B) of the breast tissue are located clinically on the patient and are indicated by the conforma-tor on the median contour (CMcd). The "width" (2R) of the breast is equal to the distance AB. The height H of the external segment of a sphere (to which the breast can be assimilated) is the maximal distance (h) between the median contour CMcd and the AB line. The height of the inner segment of a sphere (to which the chest wall is approximated) can only be estimated, as the conformator cannot Figure la. Representation of the base of the breast as an ellipse of which the great radius R is half the width of the breast and small radius r is half its height. H ^—— Figure lb. Representation of the volume of the breast as being the difference between two domed segments of heights H and h and of which the base is an ellipses of radiuses R and r. Figure 2. Measurement of the cranial caudal diameter 2 r. trace its contour. We can consider that the maximal distance (h) between the contour CInf at the level of the inframammary fold and the AB line represents its best approximation and can be easily measured on the drawing. All the measurements required for the calculation of the volume of the breast are then available. 46 Demange L and Tisnes ] Application We have measured the volume of the breast of 22 women who had been treated by lumpectomy for breast cancer prior to radiation. Table l compares the volumes of the treated breast and of the other breast: 1) the volume of the other breast ranges from 169 cm3 to 846 cm3, with an average of 435 cm3. 2) the volume of the treated breast ranges from 163 cm3 to 799 cm3, with an average of 405 cm3. 3) the difference between the volume of the Table 1. Comparison of the volumes of the treated breast and of the other breast. N° of cases Volume (cm3) Difference in volume between the two breasts Treated breast Other breast 3 cm % 1 166 169 3 1,8 2 163 190 27 14,2 3 226 244 18 7,4 4 230 251 21 8,4 5 200 275 75 27,3 6 256 280 24 8,6 7 272 288 16 5,5 8 254 304 50 16,4 9 298 319 21 6,6 10 309 348 39 11,2 11 388 397 9 2,3 12 380 411 31 7,5 13 432 448 16 3,6 14 450 463 13 2,8 15 490 540 50 9,3 16 546 572 26 4,5 17 562 578 16 2,7 18 498 608 110 18 19 604 628 24 3,8 20 647 660 13 2 21 742 763 21 2,75 22 799 846 47 5,5 treated breast and the volume of the other breast ranges from 2 % to 27 % , due mainly to variation of the difference H-h between treated breast and other breast. The same method could be used to measure the difference in volume between the breast as it appears just after radiotherapy and as it becomes after months or years. The study of a greater number of cases should enable us to establish a correlation between the calculated difference of volume and the qualitative assessment (minor, marked or major difference), and to derive an objective assessment of one of the factors of the aesthetic result of a conservative treatment of breast cancer. Acknowledgment The authors wish to thank Janet Armstrong for her help in the translation, Michel Demange for the graphical work and Jeannine Prieur for typing the manuscript. References 1. Veronesi V, Saccozi R, Banfia Del V. Comparing radical mastectomy with quadrantectomy, axillary dissection and radiotherapy in patients with small cancers of the breast. N Engl J Med 1981; 305; 6-11. 2. Limbergen E, Schueren E, Tongelen K. Cosmetic evaluation of breast conservating treatment for mammary cancer. 1. Proposal of qualitative scoring system. Radiother Oncol 1989; 16; 159-244.