Optimized table describing the relationship between breast volume and breast size used for implant size selecting in surgery

doi:10.21203/rs.3.rs-3770615/v1

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Optimized table describing the relationship between breast volume and breast size used for implant size selecting in surgery

https://doi.org/10.21203/rs.3.rs-3770615/v1

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The relationship between breast volume/mass and breast size helps surgeons choose implants with proper size. However, current breast volume/mass table is incomplete or inaccurate. This study aims to compare breast volumes obtained by two methods and achieve a complete relationship between breast volume/mass and breast size. Data of breast volume measured by water displacement method, breast mass predicted by breast tissue cut off in breast reduction surgery, and breast density was acquired by literature research. Breast volume was calculated by breast mass multiply breast density. The quantitative relationship between measured breast volume and calculated breast volume was analysed. It was found that exponential relationship exists between the two kinds of breast volumes. Breast volume table was supplemented according to this relationship and accurate breast mass table was calculated. In the future, more breast volume/mass studies with expanded breast size ranges should be explored to enrich the application group.

breast reconstruction

breast implant

breast volume

breast mass

Breast cancer is one of the most common diseases for women. The lifetime risk of breast cancer is up to 12%, and the risk of death is up to 5%[1]. Eighty percent of breast cancer patients can keep their breasts through breast-conserving surgery. In spite of this, 20% of breast cancer patients need to be treated with mastectomy [2–4]. For woman who has undergone a mastectomy, breast reconstruction helps rebuild confidence and offers significant quality-of-life benefits[5, 6].

Usually, two kinds of materials are used in breast reconstruction: autologous tissue and artificial implant. Artificial implant surgery, including a two-stage procedure that involves tissue expansion with a temporary expander and replacement with a permanent implant, is a safe and popular reconstruction method[7]. More than 300,000 women around the world accept breast implant surgery every year, either to reconstruct breasts because of breast cancer or to increase the size of healthy breasts[8]. Implant with the same size as the patient’s healthy breast helps the patient keep a good body balance, and in another, achieve a good cosmetic result.

Generally, breast volume measurement in pre-operation is a crucial factor in selecting implant size which should closely match patients’ healthy breasts [9]. However, the progress of measuring breast volume is too complex for patients. Implants can also be selected based on the removed breast mass. In this situation, however, patients would have to endure two surgeries. There is a potential need that breast implants can be chosen by volume/mass according to the patient’s breast size in advance. The relationships between breast size and volume [10]/mass [11], have been identified in previous research. Unfortunately, these relationships cannot be applied directly to clinical surgery. For example, the breast mass used in Turner et al.’s research was the mass of tissue cut off in breast reduction surgery instead of the mass of the whole breast cut off in mastectomy, so it may not be suitable to be directly used in breast reconstruction surgery. Meanwhile, the relationship concluded in Turner et al.’s research was obtained by predicting through a formula instead of measuring the real breast. Conversely, breast volume obtained by the water-displacement method has been repeatedly documented to be accurate [12–14]. However, the correspondence between breast size and breast volume is not explicit and breast volumes corresponding to some breast sizes have not been measured. Therefore, supplementing the vacant volume data and concluding a relationship between breast size and volume/mass may offer important considerations for surgeons when assessing implant size for breast reconstruction according to patients’ breast sizes.

Volume can be calculated using mass and density, which is a feasible method to supplement breast volume data. Considering breast mass predicted in Turner et al.’s research was obtained by a large amount of data, the relationship between breast mass and breast size should be reliable. Therefore it is possible to connect the predicted breast mass to real breast volume in the same breast size.

To identify a new method of selecting implant with suitable size according to breast volume or mass for breast reconstruction, the aim of our study was to (1) confirm whether the breast volume data calculated by mass was consistent with those measured by the water-displacement method, (2) explore the link between breast volumes obtained by two methods, and obtain a more intact relationship between breast size and volume/mass. The first hypothesis stated that the breast volume calculated through predicted breast mass by removed tissue during breast reduction surgery is significantly different from the breast volume measured by the water-displacement method for the same breast size. It was also hypothesized that an explicit reasonable quantitative relationship exists between breast volume calculated from breast tissue mass and breast volume directly measured by the water-displacement method.

Data acquisition

Breast volume can be speculated by its relationship with breast size, or calculated by other parameters such as breast mass and density. Therefore, we conducted a literature search for data on breast volume, mass, and density.

Breast volume

The most advisable way to measure breast volume is the water-displacement method [15], which measures breast volume by calculating the volume of water discharged after the breast was put into a special device with full water.

In McGhee et al.’s article [10], 104 women, who were not breastfeeding or pregnant and had no breast surgery before, were chosen to take part in their study. Breast volume and standardized bra size including both cup size and band size (Australian bra size) was connected. Ranges of breast volume and the corresponding professionally-fitted bra sizes for the participants were reported.

Breast mass

Seventy-five consecutive patients who were undergoing bilateral breast reduction mammoplasty at the Northern General Hospital were invited in Turner et al.’s study, and then a modified formula of breast size and the removed weight of the breast was concluded.

Breast density

Sanchez et al.[16] retrospectively analyzed 99 studies spanning 26 years, and obtained 111,123 measurements about breast density of women aged from 18 to 90 years. It was assumed that the breast consists of fat and glandular tissue entirely, and other tissues such as skin and suspensory ligaments were ignored. Breast mass-density (ρ_B) was calculated using ${\rho }_{B}=A{\rho }_{F}+\left(1-A\right){\rho }_{G}$, where A was the proportion of fat in breast (fat: ρ_F = 900kg/m³; glandular tissue: ρ_G = 1057 kg/m³). Sanchez et al.[16] found that the mass-density ranged from 911 kg/m³ to 999 kg/m³.

Data processing

Before comparing breast volume through two methods, being measured by water-displacement method or being calculated from breast mass, pre-processing is conducted to ensure breast volume data from these two methods were comparable, including eliminating data with a small sample, bra sizing system transformation, sorting out breast volume range corresponding to single breast size, and calculating breast volume from breast mass. After identifying the quantitative relationship between breast volumes obtained by the two methods, mean volume data corresponding to missing breast size were calculated according to this relationship. The breast volume range corresponding to each missing breast size was replenished if mean volume data was proven reasonable. The breast mass range was amended according to the new relationship between breast sizes and volume in order to obtain an accurate mass range corresponding to each breast size which can be used in breast reconstruction directly. It was assumed in this study that professionally-fitted bra size was equal to breast size.

Pre-processing of data

The data of 24DD/H in McGhee’s research were discarded due to their small sample, otherwise, they might cause errors. The difference between the Australian breast size system for breast volume data and the UK breast size system for breast mass data makes it difficult to correlate the two kinds of data. Therefore, the breast size in the Australian system was transformed into breast size in the UK system according to the conversion table reported in previous research [17, 18]. After that, the volume range corresponding to each existing breast size was sorted out since one breast volume range corresponds to several breast sizes in McGhee et al.’s research (Table 1).

Table 1

Breast volume measured by water-displacement method (ml)
Cup size	Volume range
Cup size	32	34	36	38	40
A	150–249	--	--	--	--
B	150–299	250–299, 350–399	--	--	--
C	250–349	250–349	300–349, 500–699	500–599	-
D	350–399	300–699	500–599	700–899	1000–1099
DD	400–499, 600–699	400–699	700–799	--	1100–1499
E	500–599	500–699	800–899, 1000–1099	1100–1499	1000–1099
F	--	700–899, 1000–1099	800–899, 1000–1099	--	1100–1499
G	1000–1099	1100–1499	--	1500–2000+	1100–1499
H	--	--	1500–2000+	--	--
-- indicates no data

Calculating breast volume by breast mass

Except for being measured directly, breast volume can also be calculated through breast mass according to formula $Volume = Mass ÷ Density$. This paper calculated breast volume by multiplying breast mass and breast density range (911–999 kg/m³) (Table 2). All data were retained in two decimal places.

Table 2

Breast volume calculated through mass and density
Bra size		Breast mass [g]	Breast density [kg/m³]	Breast volume (calculation result) [ml]
Band size [inch]	Cup size	Breast mass [g]	Breast density [kg/m³]	Breast volume (calculation result) [ml]
32	A	115	911–999	120.65 ± 5.55
	B	230		241.35 ± 11.15
	C	345		362.03 ± 16.68
	D	460		482.70 ± 22.24
	DD	575		603.38 ± 27.80
	E	690		724.05 ± 33.36
	F	805		844.73 ± 38.92
	G	920		965.40 ± 44.48
	H	1035		1086.08 ± 50.04
34	A	115		120.65 ± 5.55
	B	230		241.35 ± 11.15
	C	345		362.03 ± 16.68
	D	460		482.70 ± 22.24
	DD	575		603.38 ± 27.80
	E	690		724.05 ± 33.36
	F	805		844.73 ± 38.92
	G	920		965.40 ± 44.48
	H	1035		1086.08 ± 50.04
36	A	215		225.61 ± 10.39
	B	430		451.20 ± 20.80
	C	645		676.80 ± 31.20
	D	860		902.45 ± 41.55
	DD	1075		1128.05 ± 51.98
	E	1290		1353.66 ± 62.37
	F	1505		1579.27 ± 72.76
	G	1720		1804.88 ± 83.16
	H	1935		2030.49 ± 93.55
38	A	215		225.61 ± 10.39
	B	430		451.20 ± 20.80
	C	645		676.80 ± 31.20
	D	860		902.45 ± 41.55
	DD	1075		1128.05 ± 51.98
	E	1290		1353.66 ± 62.37
	F	1505		1579.27 ± 72.76
	G	1720		1804.88 ± 83.16
	H	1935		2030.49 ± 93.55
40	A	315		330.55 ± 15.25
	B	630		661.05 ± 30.45
	C	945		991.64 ± 45.69
	D	1260		1322.18 ± 60.92
	DD	1575		1652.73 ± 76.15
	E	1890		1983.27 ± 91.38
	F	2205		2313.82 ± 106.61
	G	2520		2644.36 ± 121.84
	H	2835		2974.90 ± 137.06

Exploring the link between breast volumes obtained by two methods

The breast volume range calculated through breast mass and density range was defined as RV₁, and the mean of RV₁ was defined as V₁. The breast volume range measured by the water-displacement method in McGhee et al.’s study was defined as RV₂, and the mean of RV₂ was defined as V₂. Given that the water-displacement method has been repeatedly reported to be accurate to measure breast volume, RV₂ and V₂ were assumed as standardized. If there were two different RV₂ corresponding to the same breast size, the one which was closer to RV₁ of the same breast size was retained and the other was discarded.

All data of V₁ and V₂ were checked for normality using the Shapiro - Wilk test (V₁: p = 0.072 > 0.05, V₂: p = 0.074 > 0.05). Pearson rank correlation coefficient (correlation coefficient = 0.866**, p < 0.001) demonstrated a highly significant correlation between V₁ and V₂. Paired samples t-tests were employed to determine significant differences between V₁ and V₂ (p = 0.003 < 0.05). All the procedure was conducted using the SPSS version 25 statistical software (IBM Corp., Armonk, NY, USA).

Then all the data of V₁ and V₂ were divided into 5 groups according to their band size (32, 34, 36, 38, and 40), with each group being fitted with exponential curves respectively. The results of a one-way ANOVA repeated test were used to evaluate the significant differences between the predicted volume and V₂. All analyses were essentially explorative with p ≤ 0.05(*). The coefficient of determination (R²) was calculated to evaluate the effectiveness of fitting. R² for perfect effect would therefore be equal to 1, which means that the predicted volume through V₁ by fitting equation equals to V₂. The function shows disproportionate increases between V₁ and V₂, as well as the extent to which individual values deviate from the curve. All the exploring curving procedure was conducted using the OriginPro 2021b software (OriginLab Crop., Northampton, Massachusetts, USA).

Supplementing missing breast volume and amending breast mass

The mean volume data which have not been collected for some breast sizes in each group were predicted by V₁ through the fitting equation. If the predicted volume was between the known volumes corresponding to the smaller and the larger size, it can be considered as reasonable. After confirming that each missing mean volume data was reasonable, corresponding missing volume ranges were calculated by RV₁ and the fitting equation. Finally, a complete relationship between breast size and volume can be obtained.

Since the breast mass used in this research was breast tissue cut off during breast reduction surgery, it should be amended when being used to select implant size for breast reconstruction. The corresponding breast mass range was computed by breast volume measured by the water-displacement method or supplemented in this research (mean breast volume data multiply density range).

Comparison between breast volumes obtained by two methods

A total of 29 comparison cases between V₁ and V₂ were paired according to breast size. The statistical analysis results of paired sample t-tests showed that there was a significant difference between V₁ and V₂. Paired breast volume obtained by two methods was presented in Table 3.

Table 3

Paired breast volumes obtained in two methods (ml)
Cup size	32		34		36		38		40
Cup size	V₁	V₂	V₁	V₂	V₁	V₂	V₁	V₂	V₁	V₂
A	120.65	200	120.65	--	225.61	--	225.61	--	330.55	--
B	241.35	225	241.35	275	451.20	--	451.20	--	661.05	--
C	362.03	300	362.03	300	676.80	600	676.80	550	991.64	--
D	482.70	375	482.70	500	902.45	550	902.45	800	1322.18	1050
DD	603.38	650	603.38	550	1128.05	750	1128.05	--	1652.73	1300
E	724.05	600	724.05	600	1353.66	1050	1353.66	1300	1983.27	1050
F	844.73	--	844.73	800	1579.27	1050	1579.27	--	2313.82	1300
G	965.40	1050	965.40	1300	1804.88	--	1804.88	1750	2644.36	1300
H	1086.08	--	1086.08	--	2030.49	1750	2030.49	--	2974.90	--
-- indicates no data

The mean breast volume calculated by breast mass ranged from 120.65 ml to 1086.08 ml in 32 or 34 band size, 225.61 ml to 2030.49 ml in 36 or 38 band size, and 330.55 ml to 2974.9 ml in 40 band size, indicating a wide range in each band size group and obvious overlap between the three groups.

The quantitative relationship between breast volumes obtained by two methods

Through the curve fitting of an exponential function, the corresponding curve equations in different breast size groups were obtained respectively (Fig. 1). Predicted volumes were calculated according to the equations (Table 4 - Table 7).

More fitting details can be concluded as follows.

(Ⅰ) The high coefficient of determine (R² = 0.94994, p = 0.00001 < 0.05) for 32 band size group indicates that the fitting results can be accepted. The nonlinear fitting equation of predicting volume through V₁ was shown by Eq. (1).

$${V}_{2}={e}^{5.06188+(1.97\times {10}^{-3}){V}_{1}}$$

Table 4

Predicted volume for 32 band size group (ml)
Bra size		V₁	V₂-known	V₂-predicted
Band size [inch]	Cup size	V₁	V₂-known	V₂-predicted
32	A	120.65	200	200.25
	B	241.35	225	254.00
	C	362.03	300	322.17
	D	482.70	375	408.63
	DD	603.38	650	518.29
	E	724.05	600	657.38
	F	844.73	--	833.80
	G	965.40	1050	1057.56
	H	1086.08	--	1341.38
-- indicates no data

In the 32 band size group, breast volume for F and H cup sizes was vacant. The predicted volume for F cup size was 833.80 ml, which was in the range of V₂-known of E and G cup size (600–1050 ml), indicating that V₂-predicted for F cup size was reasonable. The predicted volume of H cup size can be accepted as well, because its predicted volume (1086.08 ml) was larger than 1050 ml (the known volume range of G cup size).

(Ⅱ) High coefficient of determine (R² = 0.92897, p = 0.00002 < 0.05) proved that the fitting results for 34 band size group can be accepted. The nonlinear fitting equation of predicting volume through V₁ was shown by Eq. (2).

$${V}_{2}={e}^{4.9009+(2.27\times {10}^{-3}){V}_{1}}$$

Table 5

Predicted volume in 34 band size group (ml)
Bra size		V₁	V₂-known	V₂-predicted
Band size [inch]	Cup size	V₁	V₂-known	V₂-predicted
34	A	120.65	--	176.76
	B	241.35	275	232.47
	C	362.03	300	305.73
	D	482.7	500	402.07
	DD	603.38	550	528.78
	E	724.05	600	695.40
	F	844.73	800	914.55
	G	965.40	1300	1202.74
	H	1086.08	--	1581.77
-- indicates no data

In the 34 band size group, the volume of A and H cup sizes was missing. The predicted volume of A cup size (176.76 ml) was smaller than the known volume for B cup size (275 ml), and the predicted volume of H cup size (1581.77 ml) was larger than the known volume of G cup size (1300 ml). Therefore the predicted volumes of A and H cup sizes can be confirmed as reasonable.

(Ⅲ) The fitting results of the 36 band size group could be accepted as well because of its high coefficient determination (R² = 0.95316, p = 0.00003 < 0.05). The nonlinear fitting equation of predicting volume through V₁ was shown by Eq. (3).

$${V}_{2}={e}^{5.64298+(8.91348\times {10}^{-4}){V}_{1}}$$

Table 6

Predicted volume in 36 band size group (ml)
Bra size		V₁	V₂-known	V₂-predicted
Band size [inch]	Cup size	V₁	V₂-known	V₂-predicted
36	A	215.22	--	345.18
	B	451.20	--	422.06
	C	676.80	600.00	516.07
	D	902.45	550.00	631.04
	DD	1128.05	750.00	771.60
	E	1353.66	1050.00	943.47
	F	1579.27	1050.00	1153.62
	G	1804.88	--	1410.58
	H	2030.49	1750.00	1724.78
-- indicates no data

Data of three cup sizes (A, B, and G cup size) in 36 band size group should be added by predicted volume. All predicted volumes can be regarded as acceptable after comparing them with the known volume of their adjacent cup sizes (345.18 ml (predicted A cup) < 422.06 ml (predicted B cup) < 600ml (known C cup), 1050 ml (known F cup) < 1410 ml (predicted G cup) < 1750 ml (known H cup)).

(Ⅳ) In 38 band size group, the coefficient of determine (R² = 0.96005, p = 0.004 < 0.05) is high so that the fitting results can be accepted. The nonlinear fitting equation of predicting volume through V₁ was shown by Eq. (4).

$${V}_{2}={e}^{5.84879+(9.10773\times {10}^{-4}){V}_{1}}$$

Table 7

Predicted volume in 38 band size group (ml)
Bra size		V₁	V₂-known	V₂-predicted
Band size [inch]	Cup size	V₁	V₂-known	V₂-predicted
38	A	215.22	--	425.93
	B	451.2	--	523.08
	C	676.8	550.00	642.39
	D	902.45	800.00	788.96
	DD	1128.05	--	968.93
	E	1353.66	1300.00	1189.95
	F	1579.27	--	1461.39
	G	1804.88	1750.00	1794.76
	H	2030.49	--	2204.17
-- indicates no data

When band size increases to 38, up to 5 cup sizes need to be predicted for their corresponding volumes. All their predicted volumes can be retained after comparing them with the known volume of contiguous cup sizes. The predicted volumes of the A cup (425.93 ml) and B cup size (523.08 ml) were both smaller than the known volume of the C cup (550 ml). Similarly, the predicted volume of DD and F cup size all stay in reasonable range (800 ml < 968.93 ml < 1300 ml, 1300 ml < 1461.39 ml < 1750 ml). Consistent with the criterion for being acceptable, the predicted volume of H cup size (2204.17 ml) was larger than the known volume of G cup size (1750 ml).

(V) However, the low coefficient of determine (R² = 0.111, p = 0.0006 < 0.05) group demonstrated that the fitting results of 40 band size cannot be accepted. The nonlinear fitting equation of predicting volume through V₁ was shown by Eq. (5).

$${V}_{2}={e}^{6.83833+(1.26062\times {10}^{-4}){V}_{1}}$$

Final relationship between breast size and volume/mass

Given that predicted mean volumes for 32–38 band size groups through fitting equations are all reasonable, it can be confirmed that the equations between V₁ and V₂ in these band size groups are acceptable. This consistency indicates that the predicted volume range corresponding to each missing breast size can also be calculated by these equations. After supplementing vacant breast volume data, the final relationship between breast size and volume was shown in Table 8. The relationship between breast size and mass was shown in Table 9.

Table 8

Volume range in different bra sizes (ml)
Cup size	Breast volume
Cup size	32 band size group	34 band size group	36 band size group	38 band size group
A	150.00-249.00	174.54-179.00^a	342.00-348.40^a	412.92-429.98^a
B	150.00-299.00	250.00-299.00	414.31-429.96^a	513.26-533.08^a
C	250.00-349.00	250.00-349.00	500.00-699.00	500–599
D	350.00-399.00	300.00-699.00	500.00-599.00	700–899
DD	600.00-699.00	400.00-699.00	700.00-799.00	924.12-1015.90^a
E	500.00-599.00	500.00-699.00	1000.00-1099.00	1100–1499
F	772.26-900.25^a	700.00-899.00	1000.00-1099.00	1367.69-1561.52^a
G	1000.00-1099.00	1100.00-1499.00	1309.80-1519.11^a	1500–2000+
H	1215.46-1480.35^a	1411.93-1772.05^a	1500.00-2000.00+	2024.14-2400.20^a
^a indicates volume replenished by calculating

Table 9

Mass range in different bra sizes (g)
Cup size	Breast mass
Cup size	32 band size group	34 band size group	36 band size group	38 band size group
A	182.20-199.80	161.03-176.58	314.46-344.83	388.02–425.50
B	204.98-224.78	250.53-274.73	384.50-421.64	476.53-522.56
C	273.30-299.70	273.30-299.70	546.60-599.40	501.05-549.45
D	341.63-374.63	455.50-499.50	501.05-549.45	728.80-799.20
DD	592.15-649.35	501.05-549.45	683.25-749.25	882.70-967.96
E	546.60-599.40	546.60-599.40	956.55-1048.95	1184.30-1298.70
F	759.59-832.97	728.80-799.20	956.55-1048.95	1331.33-1459.93
G	956.55-1048.95	1184.30-1298.70	1285.04-1409.17	1594.25-1748.25
H	1222.00-1340.04	1440.99-1580.19	1594.25-1748.25	2008.00-2201.97

Breast reconstruction plays an important role in operation treatment for mastectomy patients. Implants of the right sizes during breast reconstruction help to achieve good function and cosmetic results for patients. The purpose of this study was to develop a new method, which supplements the vacant volume and provides a complete relationship between breast size and breast volume or mass, to help surgeons select implant with a suitable size for breast reconstruction according to breast volume/mass.

It can be easily found in Table 3 that V₁ and V₂ were not equal to each other for most bra sizes. The result of paired sample t-tests (p = 0.003 < 0.05) supports the first hypothesis that there is a significant difference between the two volumes which are obtained by calculating through predicted breast mass, and by measuring through the water-displacement method. Previous research has found diverse breast volumes measured by different methods as well [19]. The disparity between breast volumes by two methods demonstrates that the first hypothesis can be accepted, implying that surgeons should be careful when using the present predicted breast mass system to select implants because it may be different from the real breast mass needed.

Several quantitative relationships in the form of exponential functions with high correlations were found to explain the relation between calculated breast volume from predicted mass and measured breast volume for each band size group, which means that hypothesis two can be accepted. The high coefficients of determination, from 0.93 to 0.96, indicate that for breast sizes with vacant volume data in Table 3, their corresponding breast volume can be accurately calculated by predicted breast mass with the same size through the obtained exponential functions. Interestingly, these quantitative relationships were disparate for different band size groups, indicating that band size can be used as a standard of classification for surgeons to estimate the implant volume.

Perfect exponential fitting functions were found to describe the quantitative relationship between predicted breast volume from mass (V₁) and measured breast volume by water-displacement method (V₂) for each band size group in ranges from 32 to 38. Particularly, the relationship between the volumes obtained by the two different methods was found to be nonlinear. It is acknowledged that breast volume increment between adjacent cup sizes increases as cup size increases within the same band size group. For example, breast volume increment from 34E to 34F is greater than that from 34A to 34B. However, breast mass used to compute V₁ increases evenly as cup size increases, resulting in an even increase in predicted breast volume from the mass. The nonlinear relationship between breast volumes obtained by the two methods may be caused by the even increase in V₁ and uneven increase in V₂. This phenomenon also implies that breast mass calculated by Turner et al. according to breast tissue cut off in breast reduction surgery may be different from the real breast mass data with the same breast size.

Unexpectedly, no reasonable fitting curve was found in the 40 band size group, which may be caused by concentrated samples or small sample size in this group, or changed quantitative relationship between breast volumes achieved by two methods for large breasts. This finding indicates either that larger-sized dispersive samples should be used to predict the relationship between two kinds of breast volumes, or that different quantitative relationships may be drawn for large breasts. Accurate fitting curves for large breasts should be explored in a future study to ensure scientific implant selection for women with large breasts, especially given the larger breast volume range for this cohort.

The current study showed that the mean of breast volume increases as band size or cup size increases in most conditions. For example, breast volume becomes greater as cup size increases from A (176.76 ml) to H (1581.77 ml) in the 34 band size group. A similar trend was found as band size increased from 32 (322.17 ml) to 38 (642.39 ml) in the C cup size group. This indicates that band size and cup size may both cause a change of breast volume. It has been reported that breast volume varies between individuals with the same cup size due to changes in band size [17], which was consistent with this research. However, in Brown et al.’s study, it was reported that cup size, as opposed to band size, is the more discerning of the two measures in relation to breast volume [20], which was not consistent with this study. Likewise, a similar trend was also observed for breast mass in the same band size but increased cup size, which was consistent with the results reported in Malter et al.’s study [21], where a significant correlation between the resected breast tissue and the implant volume was found.

Another interesting observation is that the range of breast volume was wider as cup size increased. Given that a larger breast involves more uncertainty than a smaller one, this finding was reasonable. A broader breast volume range for larger breast sizes means surgeons should be more careful when choosing implants for women with large breasts. For example, if a patient is a larger-breasted woman, whose breast volume range is so wide that accurate volume range cannot be ensured according to this new relationship between breast size and volume, other measurements of breast volume, such as standardized distance measurements, impression procedure or radiological imaging procedure, should be considered as well, to further determine her breast volume.

Additionally, breast mass in different sizes was amended according to breast volume measured by the water-displacement method. The new relationship between breast size and breast mass allows surgeons to estimate breast mass preoperatively based on breast size. This means that not only breast volume range but also breast mass range can help surgeons select implants with the suitable size before operation. Unlike Turner et al.'s research, this relationship is more appropriate for breast reconstruction surgery, and could provide surgeons with another indicator when choosing an implant with the right size.

Considering positive results for limited band sizes (only from 32–38 band size groups), a limitation was that the method used in this research might not be suitable for breasts with large band sizes (40 and 40 + band size group). Volume data by two methods for breasts with band sizes smaller than 32 were not evaluated in this research, either. Despite the aforementioned limitations, this study holds much merit as an investigation into how surgeons select implants with suitable volume/mass according to patients’ breast size. One advantage of this method is that it can be accompanied with other pre-operation volume measurements, such as mammography and computer tomography, to improve the accuracy of estimating breast volume. Using the accomplished relationship between breast size and breast volume, a more precise implant volume can be predicted according to breast size, which would be more convenient for surgeons to select implants. Furthermore, this method is the first to compare the volumes directly measured by the water-displacement method and calculated through breast mass, providing a bridge to correlate breast data in different forms. In addition, this relationship can also be applied in the plastic surgery area, because previous studies have shown that breast volume may be a useful metric for plastic surgery. This relationship can help surgeons to predict the aesthetic effect of various breast surgeries on women and offer the most appropriate treatment decision [22].

In conclusion, the overall picture that emerges from this study is that a more complete and accurate relationship between breast size and volume/mass was obtained. Knowledge of this comprehensive relationship aids surgeons to choose implants with suitable volume/mass for patients based on their breast sizes. This method reduces the time to select implant size, so surgeons can pay more attention to considering other implant parameters, such as shape or materials. In the future, more data for smaller-breasted women whose band size is smaller than 32 and larger-breasted women whose band size is larger than 38 should be collected to improve the application range of this method.

Conflict of interest

The authors have no relevant financial or non-financial interests to disclose.

Author Contribution

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Xiaona Chen, Yaya Lu, Guangwu Sun and Tiantian Sun. The first draft of the manuscript was written by Xiaona Chen and Yaya Lu and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Data availability

The datasets used and/or analyzed during the current study are available on request.

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No competing interests reported.

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Optimized table describing the relationship between breast volume and breast size used for implant size selecting in surgery

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Abstract

Figures

Introduction

Materials and Methods

Data acquisition

Breast volume

Breast mass

Breast density

Data processing

Pre-processing of data

Calculating breast volume by breast mass

Exploring the link between breast volumes obtained by two methods

Supplementing missing breast volume and amending breast mass

Results

Comparison between breast volumes obtained by two methods

The quantitative relationship between breast volumes obtained by two methods

Final relationship between breast size and volume/mass

Discussion

Declarations

Author Contribution

Data availability

References

Additional Declarations

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