Predictors of Three-Dimensional Breast Kinematics during Bare-Breasted Running : Medicine & Science in Sports & Exercise

Journal Logo


Predictors of Three-Dimensional Breast Kinematics during Bare-Breasted Running


Author Information
Medicine & Science in Sports & Exercise 44(7):p 1351-1357, July 2012. | DOI: 10.1249/MSS.0b013e31824bd62c


Exercise-related breast pain is common in women (particularly those with larger breasts), and it has been associated with the motion of the breast (12,14,17). Consequently, breast motion has been suggested to restrict exercise participation (12,15), alter performance characteristics including kinematic and kinetic profiles during running (McGhee et al. (14) and White et al. (27), respectively), and increase internal breast forces exerted on the Cooper ligaments, pectoralis fascia, and ribs (6). Breast motion may also contribute to greater load on the thoracic and cervical spine (5,8). Previous studies on breast motion during exercise have reported large variations in vertical displacement of the bare-breast during running within the same breast cup size. Lorentzen and Lawson (12) reported that vertical breast displacement ranged from 3.94 to 7.58 cm in A cup participants, 4.07 to 7.91 cm in B cup participants, 4.79 to 8.31 cm in C cup participants, and 6.68 to 9.28 cm in D cup participants. More recently, three-dimensional displacement has been reported to vary by up to 48% during bare-breasted running in participants with the same (D) breast cup size (21). The factors that contribute to differences in breast motion during dynamic activity have not been evaluated. Such analysis would need to be undertaken on participants encompassing a wide range of breast cup, chest, and body size. Understanding differences in breast motion may aid the development of biomechanical breast models and facilitate the development of effective brassiere support (13,17,21).

Various physical characteristics may influence linear breast motion, for example, the acceleration of the breast will be affected by the inertia (mass) of the breast and the resultant forces acting on the breast. The inertia will be influenced by the volume and density of the breast, which will differ according to the ratio of fat to the glandular tissue, the ratio of fat to the connective tissue, and the distribution of these tissues (6). The mechanical properties of the breast will also influence its response to loading (19). These inertial and mechanical characteristics are not constant over time and may vary according to age, “physiological condition,” time point in the menstrual cycle, menopause, pregnancy, and postweaning (6,16,18,19). The forces acting on the breast have been modeled during dynamic activities and will vary depending on breast mass and weight, the angle of insertion of the breast, and the linear acceleration vectors of the breast’s center of mass (6). Considering all of these factors, variability in breast inertia between participants during exercise may be explained by anthropometric variations. “Local” and “global” anthropometric measurements may be used to represent breast size and body size, respectively. The latter reflecting, for example, nutritional status, level of physical activity, and ground reaction impact forces during weight bearing activity.

Breast size is typically represented by the conventional brassiere sizing system and involves measuring chest girth at the level of the inframammary fold and cup size, which is based on the difference between the chest girth and the girth around the fullest part of the breast (15). In addition, Turner and Dujon (24) provided data that could be used to predict breast mass based on this sizing system. These data were validated by measurements of the mass of breast tissue removed during reduction mammaplasty procedures. These estimates accounted for breast volume changes between chest sizes within a given cup size (15). This is known as the bra cross-grading system where both cup and chest size determine breast volume/mass (21). Estimation of breast mass using the quick and simple conventional sizing system has many advantages over other methods of representing breast size based on breast volume, which have included measurement of multiple anthropometric characteristics (suprasternal notch–manubrium to inframammary crease, manubrium to nipple, nipple to clavicle, nipple to nipple, areola–inframammary, horizontal measures of nipple width, nipple height, breast projection at 90° to chest wall, circum linear measurement inferior to nipple (26)), casting, water displacement, and various two- and three-dimensional imaging techniques (10).

The contribution of global body size measures to the explanation of variance in breast motion has yet to be investigated. The upper body forms >60% of total body mass (23) and can be modeled to apply a time-varying “driving force” on the breast during activity (9). This is supported by the observation of a time delay between the maximum displacement of the torso (represented by the suprasternal notch) and the breast during a running gait cycle (20). Breast tissue is intimately linked with the anatomy of the upper extremity, because the deep fascia to which the Cooper ligaments are attached also overlays the major and minor pectoralis muscles, the intercostals, serratus anterior, rectus abdominis, and external obliques (6,17,19). The effect of general body size measures including body mass, height, body mass index (BMI), and somatotype on breast characteristics have yet to be understood (4). Benditte-Klepetko et al. (3) observed significant correlations between breast mass and BMI in 50 women ages between 20 and 40 yr; however, breast kinematics were not examined.

The aim of this study was to examine differences in breast displacement, velocity, and acceleration across participants with varying breast cup size during bare-breasted running. The ability of measurements of breast and body size to explain differences in multiplanar breast kinematics during running, across a range of breast cup sizes, was then examined using allometric scaling. It was hypothesized that, during bare-breasted running: 1) breast motion would significantly increase with an increase in breast cup size; 2) of all the breast and body size variables examined, estimates of breast mass would be the most significant predictors of differences in breast motion between breast cup sizes; and 3) differences in breast motion across participants with varying breast cup sizes would be reduced when breast motion was scaled using breast mass.


Forty-eight women (mean ± SD: age = 26.0 ± 6.0 yr, stature = 1.667 ± 0.064 m, and mass = 62.78 ± 8.24 kg) volunteered to take part in the study that was approved by the institutional ethics committee. Participants were excluded if they had experienced any surgical procedures to the breasts, if they had given birth or breastfed within the last year, if they were not physically active (exercising for >30 min on more than three occasions in a week), or if they were <18 yr or >39 yr. Written informed consent was obtained before the recording of anthropometric measurements and breast kinematics during running. A restricted anthropometric profile was undertaken by a level 1 ISAK (International Society for the Advancement of Kinanthropometry)–accredited anthropometrist. This included measurement of stretch stature, body mass, skinfolds (triceps, thigh, subscapular, biceps, medial calf, iliac crest, supraspinale, abdominal), girths (waist, hip, arm relaxed, arm flexed and tensed), and bone breadths (wrist and femur). BMI (body mass (kg) divided by stature2 (m)) and somatotype (endomorphy, mesomorphy, and ectomorphy using the Heath Carter method) were also calculated.

The participants’ breast size was measured by a trained bra fitter (Table 1), with participants standing naked on the top half and with their arms relaxed by their side. Chest girth was measured after expiration with a metal anthropometric tape placed underneath the breasts in line with the inframammary fold. To specify cup size, a second girth measurement was recorded over the fullest part of the breast. A chest girth of 26–28, 28–30, 30–32, and 32–34 inches corresponded to chest sizes of 32, 34, 36, and 38 inches, respectively (20). The difference between the chest and breast girths was used to calculate cup size (15). Breast mass was estimated using guidelines presented by Turner and Dujon (24). These estimates were based on chest size and cup size, with 115 g per cup size for chest girths 32–34 inches and 215 g per cup size for chest girths 36–38 inches.

Number of participants across breast cup and chest size.

Participants completed a treadmill warm-up at a self-selected pace. After this, upper body clothing was removed, and 5-mm-radius retroreflective markers were positioned on the right nipple, the suprasternal notch, and the left and right anterior inferior aspect of the 10th rib (Fig. 1).

Marker positioning and axes of the laboratory coordinate systems and the local coordinate system (LCS).

Owing to discomfort during bare-breasted running, trials began with a 2-min familiarization period at 1.4 m·s−1. After this, treadmill speed was steadily increased during a 2-min period to 2.8 m·s−1 (7,12), where marker coordinates were recorded for ten running gait cycles. This was the maximum duration and maximum running speed that some participants could manage without breast support. Three-dimensional displacement of the markers were tracked using eight 200-Hz calibrated Oqus Infrared cameras (Qualisys, Gothenburg, Sweden) positioned around the treadmill, markers were identified, and three-dimensional data were reconstructed in the Qualisys Track Manager Software (Qualisys) using the methods outlined by Scurr et al. (20). Relative breast kinematics were established independent to the six degrees-of-freedom movement of the trunk (20), and gait events were identified using the instant that the anterior–posterior (a/p) velocity vector of the heel marker changed from positive to negative (heel strike) and then negative to positive (toe-off) (28). The relative vertical, medial–lateral (m/l), and a/p breast displacement during the 10 running gait cycles were then filtered using a 10-Hz low-pass Butterworth filter. Data were then time-normalized across gait cycles. Instantaneous first (velocity, m·s−1) and second (acceleration, m·s−2) derivatives were calculated for each sample (0.01 s) for five gait cycles. Consecutive maxima and minima points were identified to establish peak displacement, velocity, and acceleration within each gait cycle. The minimum value during each gait cycle was subtracted from the maximum values to give a range of peak displacement, velocity, and acceleration during each gait cycle (21). These data were then averaged across five gait cycles (21). In addition, a static capture of each participant in the anatomical reference position was used to calculate the vertical (26) and resultant distance from the suprasternal notch to the right nipple.

Univariate ANOVA analyses were used to determine differences in breast kinematic variables (relative a/p, m/l, and vertical breast displacement, velocity, and acceleration-dependent variables) across cup sizes (P < 0.05). Post hoc analyses were undertaken as appropriate using multiple independent sample comparisons with the significance level adjusted using the Bonferroni method (P < 0.005). Only A to DD breast cup sizes (n = 47) were included in these analyses because there was only one participant with an E and G breast cup size (Table 1).

Allometric scaling was used to investigate the relationship between multiplanar relative breast displacement/velocity/acceleration (dependent variables) and each of the anthropometric measures (independent variables): chest size, breast mass, body mass, stature, sum of eight skinfolds, endomorphy, ectomorphy, mesomorphy, BMI, suprasternal notch to nipple resultant/vertical distance, and age. Breast cup size (A to G) was used as a fixed factor because this allowed the ability of anthropometric variables to explain variation in breast motion across cup sizes to be explored. All variables were natural log-transformed (ln) and examined for normality of distribution and homogeneity of variance. The intercept (a) and slope (b) parameters expressed in the linear form of the allometric equation: lnY = lna + blnX were solved using ANCOVA (where Y represented the dependent variable and X represented the independent variable (25)). The assumption of a common b exponent across cup sizes was verified by a nonsignificant (P > 0.05) breast cup × independent variable interaction effect. The common b exponents were used to calculate power function ratios Y/Xb. Comparison of breast motion with the effect of the breast/body size variable covaried out using ANCOVA allows the contribution of these variables to be assessed. Individuals can then be compared without the confounding influence of differences in breast and body size. Every model was checked for potential misspecification according to Batterham and George (1). This included checking the following regression diagnostics; normality of distribution of the model residuals, the assumption of homoscedasticity via correlations between the absolute residual and the independent (anthropometric) variable, analysis of raw residuals plotted against the natural log-transformed independent variable, and plots of the scaled variable (power function ratio against the independent variable). In cases where the models were found to be incorrectly specified, second-order polynomial equations were found to scale the data appropriately.

After scaling, the univariate ANOVA or Kruskal–Wallis tests were repeated, this time using breast kinematic data scaled for breast mass to determine whether there were any significant differences across A to DD cup sizes (P < 0.05). Post hoc analyses were undertaken as appropriate using multiple independent sample comparisons with the significance level adjusted using the Bonferroni method (P < 0.005).


The mean relative a/p, m/l, and vertical displacement, velocity, and acceleration (before scaling) of the right breast during running across cup sizes are presented in Figure 2A. Univariate ANOVA (excluding E and G cups) identified significant differences in displacement across breast cup sizes in all movement axes (P < 0.05), with displacement increasing with cup size. Breast velocity and acceleration (a/p, m/l, and vertical) also significantly increased with breast cup sizes (P < 0.05). The results of the post hoc analyses are presented in Figure 2A.

Mean anterior–posterior (white), medial–lateral (light gray), and vertical (dark gray) breast displacement, velocity, and acceleration during bare-breasted running at 2.8 m·s−1 across cup sizes before (A) and after scaling for breast mass (B). *Brackets denote which differences were significant for a given direction (P < 0.05).

When examining multiplanar breast displacement and acceleration, breast mass was the only covariate that was both significant (P < 0.05) and that rendered the differences between cup sizes as nonsignificant. For a/p breast displacement, body mass and BMI also rendered variations between breast cup sizes nonsignificant. In contrast to the breast displacement and acceleration data, some variations between cup sizes remained significant when breast mass was included as a covariate in the ANCOVA models for vertical and m/l breast velocities but not for a/p breast velocity. The suprasternal notch to nipple vertical distance was also a significant covariate for the vertical and m/l velocities; however, similar to breast mass, this distance could not account for variation in the velocities between cup sizes.

Based on the finding that breast mass was the only variable that consistently explained variation in multiplanar breast displacement, velocity, and acceleration, breast mass was subsequently used to scale these measurements (Fig. 2B). Although other covariates also contributed to the explanation of variance for certain dependent variables, significant pairwise correlations (Pearson r) between these covariates (breast mass, body mass, endomorphy, BMI, and suprasternal notch to right nipple vertical distance) indicated colinearity. If these variables were to be included together in ANCOVA, inaccurate exponents may be obtained (2). Therefore, ANCOVA were only computed with a single covariate (breast mass).

An example of the effect of breast mass on breast displacement across cup sizes is provided for the m/l displacement of the breast in Figure 3. In accordance with the other a/p, m/l, and vertical kinematic variables examined, Figure 3 highlights that, although the breast motion variables increased with an increase in cup size, increases in breast mass result in greater breast motion (regardless of cup size). This was emphasized by the nonsignificant cup size × breast mass interaction effects.

Breast mass and relative medial–lateral breast displacement during bare-breasted running at 2.8 m·s−1 across cup sizes.

After assessment of the regression diagnostics for the ANCOVA, a/p and vertical breast displacement; a/p, m/l, and vertical velocity; and m/l and vertical accelerations were found to be incorrectly specified. These variables were subsequently scaled using second-order polynomials. The common b exponents for the variables scaled using allometric equations are presented in the Supplemental Digital Content 1 ( The second-order polynomial equations used to scale the remaining variables are described in the Supplemental Digital Content 2 (

Scaling the dependent variables using either the power function ratios or the second-order polynomial coefficients resulted in a reduction of the number of significant differences in breast motion observed between cup sizes (Fig. 2B). There were no significant differences in a/p, m/l, or vertical displacement between breast cup sizes, no significant differences in vertical breast velocity, and no significant differences in a/p or vertical breast acceleration between cup sizes (P > 0.05). An example of m/l breast displacement scaled using the power function ratio is presented in Figure 4. Scaling m/l breast displacement for breast mass removed the positive association between breast mass and breast displacement seen in Figure 3.

Relative medial–lateral breast displacement during bare-breasted running at 2.8 m·s−1 when scaled using a power function ratio (BM = breast mass).


The purposes of this study were to analyze differences in breast motion during bare-breasted running across breast cup sizes and to examine the ability of breast and body size measurements to explain these differences. The results showed that, during running, all breast kinematic variables significantly increased with increasing breast cup size, which accepts hypothesis 1. In addition, after individual consideration of all the local and global body size measures, breast mass was the most significant predictor of multiplanar breast motion—consistently rendering differences between cup sizes as nonsignificant. However, differences in vertical and m/l breast velocities across cup sizes could not be explained by breast mass; therefore, hypothesis 2 could only be partially accepted. Finally, after allometric/polynomial scaling of the breast motion variables using estimates of breast mass, the number of significant differences between breast cup sizes reduced from 40 (prescaling) to only 4. Consequently, the final hypothesis that differences in breast motion across participants with varying breast cup sizes would be reduced when breast motion was scaled using breast mass was therefore accepted.

Mean relative breast displacement, velocity, and acceleration significantly increased with cup size before scaling these data in relation to breast mass. The range of vertical displacement values (0.042–0.099 m) is comparable to that reported by Lorentzen and Lawson (12) for A to D breast cup sizes (0.039–0.0928 m) during treadmill running. In addition, during bare-breasted running in D cup participants, Scurr et al. (21) reported maximum relative breast displacements to be 0.051 ± 0.034 m (a/p), 0.048 ± 0.034 m (m/l), and 0.086 ± 0.052 m (vertical), which are toward the upper range of the values obtained for A to G breast cup participants in this study (ranges of 0.030–0.059 m (a/p), 0.018–0.062 m (m/l), and 0.042–0.099 m (vertical)). Although previous studies have mostly examined vertical breast motion (12,13), the results of the current study support recent three-dimensional studies that have shown significant a/p and m/l breast motion in addition to vertical motion (20,21). The results also extend previous studies by the inclusion of multiplanar velocity and acceleration data across breast cup sizes.

This article identified breast mass as the strongest predictor of differences in breast motion between breast cup sizes during bare-breasted running. Greater breast mass corresponded to greater a/p, m/l, and vertical breast displacement, velocity, and acceleration. This finding supports previous research on vertical breast displacement; for example, Haake and Scurr (9) predicted that an increase in breast mass from 100 to 700 g would lead to a 70% increase in vertical breast displacement. Using data from the current study, increases in breast mass from 120 to 690 g, resulted in increases in vertical displacement of the breast from 0.0435 to 0.0856 m, representing an approximately 100% increase in vertical breast displacement. After the application of allometric or polynomial models to scale each of the breast kinematic variables for breast mass, the number of significant differences between cup sizes was reduced. However, estimated breast mass did not explain differences in vertical and m/l breast velocities across cup sizes. It should be recognized that the lower number of participants in some of the cup size groups might have led to inaccuracies in the equations generated. However, all models were screened for misspecification, which included checking the regression diagnostics—normality of distribution of the model residuals and assumption of homoscedasticity. The different participant numbers across cup sizes may be one reason why some models were incorrectly specified and, consequently, more appropriately represented by polynomial equations. Irrespective of this limitation, the finding that breast mass was the strongest predictor of differences in breast motion can be explained by its influence on the forces acting on the breast during running and by breast stiffness and damping (6,9). Further studies are required to corroborate and develop multiplanar models of the breast during exercise to aid understanding of other variables that may contribute to the explanation of differences in breast kinematics (especially for breast velocity).

The results showed nonsignificant cup size × breast mass interactions, meaning that the gradient or the change in breast kinematics for a given change in breast mass was consistent across cups sizes. This suggests that the level of breast support should be based on estimates of breast mass, irrespective of cup size. For example, the breast mass of a 32/34 B cup (230 g) is similar to a 36/38 A cup (215 g), and likewise, the breast mass of a 36/38 C cup (645 g) is similar to a 40/42 B cup (630 g). This confirms reports of breast volume varying between individuals of the same cup size (15), which has implications for bra manufacturers. First, previous studies have suggested that different support/design requirements may be required for different breast cup size groups (11,22). Second, scaling offers a method of reducing the confounding influence of breast size on breast motion, enabling a more effective analysis of varying breast support designs. Further studies should seek to corroborate these findings with more participants and participants with more diverse breast sizes, particularly different chest sizes within a given cup size.

In conclusion, during bare-breasted running, this study identified increases in mean relative breast displacement, velocity, and acceleration with increases in breast cup sizes A to G. Allometric and polynomial models provided a method to account for differences in breast kinematics between breast cup sizes. Of all the breast and body size measurements taken during this study, the results suggest that breast mass is the strongest predictor of breast kinematics across cup sizes during bare-breasted running. The application of this technique reduced differences in breast displacement, velocity, and acceleration between A to G cup sizes. This procedure may be useful in assessing the effect of sports bra design on breast kinematics while eliminating the large between-cup-size differences in breast kinematics observed both in the current study and in previous literature (21).

The authors thank the University of Portsmouth for funding this study.

There are no conflicts of interest associated with this study.

The results of the present study do not constitute endorsement by the American College of Sports Medicine.


1. Batterham AM, George KP. Allometric modelling does not determine a dimensionless power function ratio for maximal muscular performance. J Appl Physiol. 1997; 83 (6): 2158–66.
2. Batterham AM, Tolfrey K, George KP. Nevill’s explanation of Kleiber’s 0.75 mass exponent: an artefact of collinearity problems in least squares models? J Appl Physiol. 1997; 82 (2): 693–7.
3. Benditte-Klepetko H, Leisser V, Paternostro-Sluga T, et al.. Hypertrophy of the breast: a problem of beauty or health? J Womens Health. 2007; 16 (7): 1062–9.
4. Byrne C, Spernak S. What is breast density? Breast Cancer Online [Internet]. 2005 [cited 2005 November 11];8(10). Available from: doi:10.1017/S1470903105003093.
5. Corion LUM, Smeulders MJC, van der Horst CMAM. Correctly fitted bra. Br J Plast Surg. 2004; 57: 588.
6. Gefen A, Dilmoney B. Mechanics of the normal woman’s breast. Technol Health Care. 2007; 15: 259–71.
7. Gehlsen G, Albohm M. Evaluation of sports bras. Phys Sports Med. 1980; 8 (10): 89–96.
8. Greenbaum AR. Badly drawn bra. Br J Plast Surg. 2004; 57: 743.
9. Haake S, Scurr J. A dynamic model of the breast during exercise. Sports Eng. 2010; 12 (4): 189–97.
10. Kovacs L, Eder M, Hollweck R, et al.. Comparison between breast volume measurement using 3D surface imaging and classical techniques. Breast. 2006; 16 (2): 137–45.
11. Lawson L, Lorentzen D. Selected sports bras: comparisons of comfort and support. Cloth Text Res J. 1990; 8 (4): 55–60.
12. Lorentzen D, Lawson L. Selected sports bras: a biomechanical analysis of breast motion while jogging. Phys Sports Med. 1987; 15 (5): 128–39.
13. Mason BR, Page KA, Fallon K. An analysis of movement and discomfort of the female breast during exercise and the effects of breast support in three cases. J Sci Med Sport. 1999; 2 (2): 134–44.
14. McGhee DE, Power BM, Steele JR. Does deep water running reduce exercise-induced breast discomfort. Br J Sports Med. 2007; 41: 879–83.
15. McGhee DE, Steele JR. How do respiratory state and measurement method affect bra size calculations? Br J Sports Med. 2006; 40: 970–4.
16. Milligan D, Drife JO, Short RV. Changes in breast volume during normal menstrual cycle and after oral contraceptives. BMJ. 1975; 29 (4): 494–6.
17. Page K-A, Steele JR. Breast motion and sports brassiere design. Sports Med. 1999; 27 (4): 205–11.
18. Palomar AP, Calvo B, Herrero J, López J, Doblaré M. A finite element model to accurately predict real deformations of the breast. Med Eng Phys. 2008; 30: 1089–97.
19. Rajagopal V, Nielsen PMF, Nash MP. Modeling breast biomechanics for multi-modal image analysis—successes and challenges. Wiley Interdiscip Rev Syst Biol Med. 2010; 2: 293–304.
20. Scurr J, White J, Hedger W. Breast displacement in three dimensions during the walking and running gait cycles. J Appl Biomech. 2009; 25: 322–9.
21. Scurr J, White J, Hedger W. Supported and unsupported breast displacement in three dimensions across treadmill activity levels. J Sports Sci. 2011; 29 (1): 55–61.
22. Starr C, Branson D, Shehab R, Farr C, Ownbey S, Swinney J. Biomechanical analysis of prototype sports bra. J Textile Appar Technol Manag. 2005; 4 (3): 1–14.
23. Syczewska M, Öberg T, Karlsson D. Segmental movements of the spine during treadmill walking with normal speed. Clin Biomech. 1999; 14 (6): 384–8.
24. Turner AJ, Dujon DG. Predicting cup size after reduction mammaplasty. Br J Plast Surg. 2005; 58: 290–8.
25. Welsman JR, Armstrong N. Statistical techniques for interpreting body size–related exercise performance during growth. Pediatr Exerc Sci. 2000; 12: 112–27.
26. Westreich M. Anthropometric breast measurement: protocol and results in 50 women with aesthetically perfect breasts and clinical application. Plast Reconstr Surg. 1997; 100 (2): 468–79.
27. White JL, Scurr JC, Smith NA. The effect of breast support on kinetics during overground running performance. Ergonomics. 2009; 52 (4): 492–8.
28. Zeni JA, Richards JG, Higginson JS. Two simple methods of determining gait events during treadmill and overground walking using kinematic data. Gait Posture. 2008; 27: 710–4.


Supplemental Digital Content

©2012The American College of Sports Medicine