In patients with breast carcinoma, increasing tumor size has been

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1 20 Correlation of Tumor Volume and Surface Area with Lymph Node Status in Patients with Multifocal/Multicentric Breast Carcinoma Aleodor A. Andea, M.D. 1 David Bouwman, M.D. 2 Tracie Wallis, B.S. 3 Daniel W. Visscher, M.D. 4 1 Department of Pathology, Memorial Sloan-Kettering Cancer Center, New York, New York. 2 Department of Surgery, Harper Hospital, Karmanos Cancer Center, Wayne State University School of Medicine, Detroit, Michigan. 3 Department of Pathology, Harper Hospital, Karmanos Cancer Center, Wayne State University School of Medicine, Detroit, Michigan. 4 Department of Pathology, Mayo Clinic, Rochester, Minnesota. BACKGROUND. Multicentric breast carcinomas have a higher frequency of axillary lymph node metastasis than unifocal tumors of similar stage. It remains unclear whether this merely reflects larger tumor volumes or a different biologic behavior. The authors have shown previously that when aggregate tumor diameter are used for staging, unifocal and multifocal tumors have a similar frequency of axillary lymph node metastasis. However, summing diameter overestimates actual tumor volume because volume is proportional to the third power of the diameter. Therefore, the aim of the current study was to reanalyze the relation between size and axillary lymph node status by correcting for tumor volumes and surface areas. METHODS. Volumes and surface areas of 122 breast tumor specimens with multiple macroscopic nodules (two foci: n 95; three foci: n 22; three foci: n 5) were calculated by approximating the shape of each tumor nodule to an ellipsoid (for volume) or to a prolate spheroid (for area). For comparison, the authors used an internal control series, comprised of 469 macroscopic unifocal tumors. For all patients, multiple assessments of largest tumor size and combined size of all foci were correlated with the status of axillary lymph nodes. The associations between lymph node status, tumor volume or area, and multifocality were modeled using univariate and multivariate logistic regression. RESULTS. When either the largest or the aggregate tumor volume was used as a size estimate, tumor specimens with multiple nodules had a higher frequency of lymph node involvement compared with unifocal tumors of a similar volume or area. The odds ratio (OR) for having positive lymph nodes was 2.34 for aggregate volume measurement (P 0.001). Surface area estimates yielded similar results (OR 2.2, P 0.001). CONCLUSIONS. Breast tumors with multiple macroscopic nodules had a different biology, with a propensity to dissemination at smaller tumor volumes (i.e., there was another factor besides volume alone that accounted for the differences in behavior). Cancer 2004;100: American Cancer Society. Presented at the 91st Annual Meeting of the United States and Canadian Academy of Pathology, Chicago, Illinois, March Address for reprints: Aleodor A. Andea, M.D., Department of Pathology, Memorial Sloan-Kettering Cancer Center, 1275 York Avenue, New York, NY 10021; Fax: (212) ; andeaa@mskcc.org Received June 10, 2003; revision received September 24, 2003; accepted September 24, KEYWORDS: breast carcinoma, multifocal, multicentric, axillary lymph node metastasis. In patients with breast carcinoma, increasing tumor size has been reported to correlate strongly with a progressively greater frequency of lymph node involvement and with decreased survival. This finding constitutes the rationale for inclusion of tumor dimension in the American Joint Committee on Cancer (AJCC)/International Union Against Cancer (UICC) staging system. 1 8 The largest tumor diameter is used to approximate tumor size for staging purposes due to its relatively straight forward, direct measurement. However, theoretic models have shown that the propensity for 2003 American Cancer Society DOI /cncr.11880

2 Multifocal/Multicentric Breast Ca/Andea et al. 21 metastases depends on the total number of cells of a given tumor combined with the probability of each individual cell to disseminate. 9,10 The number of cells is better estimated by three-dimensional parameters such as tumor volume (or possibly surface area, if we consider that only cells located at the advancing front of the tumor have a significant probability for dissemination), then by a linear measurement. Multifocal/multicentric (MF/MC) breast tumors are defined by the presence of two or more clearly separated tumors in the same breast (in the same quadrant for multifocal tumors and different quadrants for multicentric tumors). Compared with unifocal lesions, MF/MC carcinomas have a higher frequency of lymph node metastasis and a less favorable patient outcome. 17 However, it is still unclear whether this difference merely reflects larger tumor burden or a different biologic behavior (which could be responsible for the multifocality as well). The current recommendation of the AJCC/UICC TNM classification for staging MF/MC breast tumors is to use the diameter of the largest tumor nodule, regardless of the number or size of additional tumor nodules As a result, these criteria underestimate the total tumor dimension because additional nodules, which are often sizable, are not included in the T classification. This system is based on the assumption that the metastatic potential of MF/MC carcinomas is determined reasonably well by the size of the largest nodule. A previous study showed that if the stage of MF/MC tumors is corrected by summing to provide an aggregate tumor diameter, their metastatic behavior approximates that of similar-stage unifocal tumors. 13 Even though using the largest diameter alone underestimates the total MF/MC tumor size, summing diameters will overestimate the total tumor volume/surface area because they are proportional to the third and second power of the diameter, respectively. In other words, MF/MC tumors with aggregate diameters equal to those of unifocal tumors will have a significantly lower volume or surface area. We explored the relation between lymph node involvement and total tumor volume/surface area in MF/MC and in unifocal breast carcinomas. Our objective was to determine whether the observed higher metastatic frequency of MF/MC compared with unifocal tumors reflects a different biologic behavior or merely a larger aggregate tumor volume/surface area (as appears to be the case for tumor diameter). MATERIALS AND METHODS Selection of Patients and Specimens Our study population was comprised of 122 patients selected from the files of Karmanos Cancer Center/ Harper University Hospital (Detroit, MI) covering the period from 1984 to Of this group of patients, 101 patients were also reported in a previous study. 13 The criteria for inclusion were the presence of macroscopically measurable and clearly separated tumor nodules in the same or different quadrants of the breast. Only patients with invasive carcinoma were considered. The pathologic lymph node status was known for all patients. We excluded patients who had diffuse breast involvement or microscopic multifocal tumors for which an accurate size could not be assessed. To compare MF/MC tumors with unifocal tumors, we used a control series of 469 consecutive patients with unifocal invasive breast carcinome obtained from our files between 1992 and The pathologic lymph node status was also known for these patients. Data Collection After reviewing the pathology reports, we recorded the location of all tumor nodules, as well as the status of the axillary lymph nodes. When available, three perpendicular diameter of every tumor nodule were recorded. Three-dimensional measurements were available for all tumor nodules in 67 specimens and for some tumor nodules in 36 specimens. In 19 specimens, only the largest diameter of each nodule was recorded. In the control series, three perpendicular diameter were recorded for tumor nodules in 398 specimens (85%). Data Analysis and Statistical Methods For volume computation, the shape of the tumor nodules was approximated to an ellipsoid when three diameter were available and to a sphere when only the largest diameter was recorded. For surface area estimation, we approximated the tumors with prolate spheroids. The volume was computed using the following formula: V 1 a b c 6 The surface area was approximated by the following formula: A 0.5 z z a arcsin e e ; z b c ;e 2 a2 z 2 2

3 22 CANCER January 1, 2004 / Volume 100 / Number 1 Where a, b, and c are perpendicular diameter of tumor foci a b c. For every MF/MC tumor specimen included in the current study, we computed six tumor size estimates: volume, surface area, and diameter of the largest tumor nodule and the aggregate volume, surface area, and diameter of all tumor nodules. To stage tumor specimens based on their volume or surface area, we used a modification of the current T classification system. The cutoff values for the T classification were the volume and surface area of two spheres with diameters of 2 cm and 5 cm, respectively. We assigned T1 to tumor specimens with volume 4.2 cm 3 or area 12.6 cm 2, T2 to tumor specimens with volume cm 3 or area cm 2, and T3 to tumor specimens with volume 65.4 cm 3 or area 78.5 cm 2. Individual Student t test and P values were obtained to assess the differences in the mean values of the continuous variables. Separate chi-square tests were performed to compare the frequency of axillary lymph node metastasis in multifocal versus unifocal tumors of the same T classification. A logistic regression method 21 was used for each of the size estimates to model the odds of axillary lymph node metastasis as a function of volume, surface area, or diameter. The same method was used to model the relation between lymph node status and tumor volume, area, and diameter in the unifocal series as well. To evaluate the influence of multicentricity on lymph node status while controlling for tumor size (estimated as either volume or surface area), we used a multivariate logistic regression model. Tumor size and multicentricity were the independent variables and the logit of lymph node status was the dependent variable. RESULTS Of 122 patients with MF/MC tumors, 95 presented with 2 tumor nodules, 22 with 3 tumor nodules, and 5 with 4 tumor nodules. The clinicopathologic and morphologic characteristics of the cases are presented in Table 1. Overall, MF/MC tumors had a higher frequency of positive axillary lymph nodes compared to patients with unifocal tumors (71.3% vs. 55%, P 0.01). MF/MC tumors did not differ significantly from unifocal tumors in the distribution of various individual histologic subtypes. Also, the mean age of the patients was similar. Ductal carcinoma in situ (DCIS) was present in 76 MF/MC tumor specimens (62.3%) and constituted 30% of tumor volume in 18 tumor specimens (14.75%). This value was significantly higher than the DCIS occurrence in the unifocal series (i.e., 16.3%, P 0.001). Angiolymphatic invasion was identified in 38 patients (31.1%) and was extensive in 6 (4.9%). TABLE 1 Clinicopathologic and Morphologic Characteristics of Multifocal and Unifocal Tumors Characteristics Multifocal tumors (n 122) (%) Unifocal tumors (n 469) (%) P value Mean age (yrs) (range) 56.6 (26 95) 57 (27 92) 0.7 a Histology b,c Invasive ductal 103 (84.4) 418 (89.6) 0.15 d Lobular 5 (4) 27 (5.7) 0.47 d Other types 8 (6.5) 15 (3.2) 0.36 d Medullary 1 (0.9) 4 (0.85) Mucinous 1 (0.9) 7 (1.5) Metaplastic 2 (1.9) 1 (0.2) Papillary 3 (2.4) 3 (0.64) Tubular 1 (0.9) 0 (0) Mixed ductal and lobular 6 (4.9) 6 (1.3) 0.01 d Grade e 1 8 (7.6) 2 49 (46.7) 3 48 (45.7) DCIS f 76 (62.3) 76 (16.3) d Angiolymphatic invasion 38 (31.1) Axillary lymph node positivity 87 (71.3) 258 (55) d DCIS: ductal carcinoma in situ. a A Student t test was used for comparison. b Histology of multifocal index lesions. c Histologic type was available for 466 unifocal tumors. d A chi-square test was used for comparison. e Multifocal tumors (n 105) were graded using the modified Scarf Bloom Richardson grading system. The grade was available for 274 unifocal tumors. Because grading was not performed uniformly for unifocal tumors, a comparison with multifocal tumors was not possible. f Data regarding ductal carcinoma in situ were available for 465 unifocal tumors. Figure 1A C shows the distributions of aggregate tumor surface areas, volumes, and diameter, respectively. Median values for various aggregate tumor size estimates show that, on average, MF/MC tumors have lower aggregate tumor volumes than unifocal tumors (median volume 4.5 cm 3 vs. 5.2 cm 3, P 0.02) and similar aggregate surface areas (median area 16.8 cm 2 vs cm 2, P 0.1). However, MF/MC tumors are characterized by significantly higher aggregate diameter measurements than unifocal tumors (median aggregate diameter 4 cm vs. 2.5 cm, P ). Therefore, the use of aggregate diameter estimates could create the false impression that MF/MC tumors have a larger tumor burden than unifocal tumors. The frequencies of axillary lymph node metastases for each T classification group (based on volume and surface area measurements) are illustrated in Table 2. The results show that when either volume or surface area estimates are used to assign cases into T classifications, the incidence of positive lymph nodes is significantly higher in multifocal compared with unifocal tumors of the same stage. The only exception is T2 for aggregate surface area measurements in

4 Multifocal/Multicentric Breast Ca/Andea et al. 23 which the difference in axillary lymph node status between unifocal and MF/MC tumors approaches significance. However, if combined diameters are used as size estimates for MF/MC tumors, the frequency of metastasis is not significantly different from the unifocal tumors within the same T classification groups (Table 3). A continuous model describing the relation between aggregate tumor volume or surface area and lymph node status using logistic regression is presented in Figure 2. The curves depicted in Figure 2A,B reveal that MF/MC tumors exhibit a higher incidence of axillary lymph node metastases than unifocal tumors of similar total volume or surface area. To verify whether these differences are statistically significant, we analyzed a multivariate logistic regression model investigating the influence of multifocality versus unifocality on lymph node status, controlling for tumor volume or surface area (they were included as covariates in the model). The results (Table 4) show that multifocality has a statistically significant influence on lymph node status when aggregate tumor volume or surface area is used as size estimates. The odds ratio (OR) for having positive lymph nodes in MF/MC versus unifocal tumors of the same size was 2.34 (P ) when aggregate volume was used and 2.2 (P ) when total surface area was considered. For comparison, the logistic regression model of the relation between aggregate tumor diameter and lymph node status is depicted in Figure 2C. The curves for the multifocal and unifocal series are very close and even superimposed for diameters 2 cm. A multivariate logistic regression model shows that there are no significant differences in frequency of positive lymph nodes between multifocal and unifocal tumors of the same aggregate diameter (OR 1.4, P 0.18). FIGURE 1. (A) Distribution of aggregate surface area. (B) Distribution of aggregate tumor volume. (C) Distribution of combined diameter. DISCUSSION The incidence of multifocality or multicentricity in breast carcinoma varies from 13% to 70%, depending mainly on the sampling method employed in the study. 11,14,17,22 33 These figures are significant enough to justify a separate analysis of the metastatic potential and behavior of multifocal tumors. Accurate staging of MF/MC breast carcinomas is also emerging as a practical issue in patient management due to increased utilization of diagnostic imaging in patients undergoing breast-conserving therapy. We did not attempt to differentiate between multifocal tumors, defined as the presence of multiple foci of the same tumor, and multicentric carcinomas, defined as multiple primary carcinomas in the same breast. Even with molecular studies it can be difficult to separate them and many times the distinction is arbitrary. Moreover, the distinction is not incorporated in the TNM staging scheme. However, the finding that MF/MC tumors have a significantly higher incidence of DCIS than unifocal tumors (62.3% vs. 16.3%, P 0.001) favors the hypothesis that multiple tumors

5 24 CANCER January 1, 2004 / Volume 100 / Number 1 TABLE 2 Lymph Node Status and Tumor Classification in the Multifocal and Unifocal control Series Using Volumes and Surface Areas as Size Estimates Volume Surface area Unifocal tumors positive/total (%) Aggregate positive/total (%) a P value b MF tumors Largest positive/total (%) c P value b Unifocal tumors positive/total (%) Aggregate Positive/total (%) a P value b MF tumors Largest Positive/total (%) c P value b T1 79/207 (38.2) 35/58 (60.3) /67 (61.2) /203 (37.9) 30/51 (58.8) /67 (61.2) T2 132/204 (64.7) 44/56 (78.6) /49 (81.6) /208 (63.9) 46/60 (76.7) /49 (81.6) 0.01 T3 47/58 (81) 8/8 (100) 0.3 d 6/6 (100) 0.24 d 48/58 (82.8) 11/11 (100) 0.3 d 6/6 (100) 0.5 d MF: multifocal tumors. a Aggregate size of all tumor nodules. b A comparison was performed between multifocal and unifocal tumors using the chi-square test. c Size of the largest nodule. d The Fisher exact test was performed because one cell had 0% frequency. TABLE 3 Lymph Node Status and Tumor Classification in the Multifocal and Unifocal control Series Using Diameters as Size Estimates Unifocal tumors Positive/total (%) Aggregate Dimension MF tumors Largest Positive/tot (%) a P value b Positive/tot (%) c P value b T1 56/159 (35.2) 7/19 (36.8) /54 (59.3) T2 135/225 (60) 43/59 (72.9) /54 (77.8) 0.01 T3 67/85 (78.8) 37/44 (84.1) /14 (93) 0.3 d MF: multifocal tumors. a Aggregate size of all tumor nodules. b A comparison was performed between multifocal and unifocal series using the chi-square test. c Size of the largest nodule. d The Fisher exact test was performed because one cell had 0% frequency. present in the same breast are generally a manifestation of intramammary spread of one tumor (via the ductal system), i.e., they are multifocal. In agreement with previous studies, we found that, as a group, MF/MC carcinomas have a significantly elevated incidence of positive lymph nodes compared with unifocal tumors. 11,12,14 16 Theoretically, this difference in behavior may be a reflection of either the increased intrinsic aggressiveness of multifocal tumors or their larger tumor size. We assessed some of the intrinsic parameters, such as histologic type, which in our series was not significantly different from unifocal tumors. The distribution of Scarf Bloom Richardson tumor grades in the multifocal series (Grade I, 7.6%; Grade II, 46.7%; Grade III, 45.7%) is within the limits reported in the literature We found an incidence of angiolymphatic invasion of 31.1%, which was again similar to previous reports. 38,40 44 Evaluating the size of breast carcinomas is subject to several problems. Routinely, we use the diameter of tumor nodules, primarily for practical reasons. However, tumors are variably and irregularly shaped tridimensional objects. Therefore, diameters inaccurately reflect their real size. Moreover, adding diameters of MF/MC tumor nodules in an attempt to estimate total tumor bulk results in a consistent error because volumes and areas are proportional to the third and second power of the diameter, respectively. Therefore, summing diameter of tumor nodules will overestimate total tumor volume and, to a lesser extent, area. This is confirmed by our results showing that multifocal tumors have a lower median volume then unifocal tumors of similar stage (4.5 cm 3 vs. 5.3 cm 3 ) and a similar distribution of tumor surface area (16.8 cm 2 vs cm 2 ), but they have a significantly larger aggregate diameter (4 cm vs. 2.5 cm). Aggregate diameter measurements overestimate the total volume of MF/MC tumors and create the appearance that they have the same metastatic potential as unifocal tumors of similar size. For example, an MF/MC tumor with an aggregate diameter of 2 cm composed of two nodules with a diameter of 1 cm

6 Multifocal/Multicentric Breast Ca/Andea et al. 25 FIGURE 2. Correlation between lymph node status and tumor size in a unifocal and multifocal series using (A) aggregate tumor volume size estimates, (B) aggregate surface area size estimates, and (C) combined diameter size estimates. Solid dark line: unifocal tumors; light line: multifocal tumors. each will have a frequency of positive lymph nodes of 54% based on our regression model. Similarly, a unifocal tumor with a diameter of 2 cm will have 46% occurrence of positive lymph nodes. However, the MF/MC tumor described actually has a much lower volume than the unifocal tumor (1.8 cm 3 vs. 4.2 cm 3 ). Therefore, summing diameters of multifocal tumors creates the impression of a similar propensity for metastasis as unifocal tumors by overcorrecting for volume and, therefore, inadvertently accounting for their

7 26 CANCER January 1, 2004 / Volume 100 / Number 1 TABLE 4 Multivariate Analysis of Lymph Node Status Correlation with Aggregate Tumor Size and Multifocality Characteristics Aggregate tumor size estimates in multifocal cancers Volume Surface area Diameter Odds ratio a % CI of odds ratio P value for odds ratio Overall GOF b % CI: 95% confidence interval; GOF: goodness of fit. a Odds ratios of lymph node positivity in multifocal versus unifocal tumors controlling for tumor size. b The Hosmer and Lemeshow goodness-of-fit test was used. increased biologic aggressiveness. In addition, MF/MC tumors with the same combined diameter may have different aggregate volumes. For example, an MF/MC tumor composed of two nodules with diameters of 2 cm and 1 cm, respectively, and another MF/MC tumor composed of two nodules of 1.5 cm diameter each will have a volume of 4.7 cm 3 and 3.5 cm 3, respectively, but the same aggregate diameter (i.e., 3 cm). 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