a study of postural changes after breast augmentation

8
ORIGINAL ARTICLE BREAST A Study of Postural Changes After Breast Augmentation Marco Mazzocchi Luca Andrea Dessy Pierpaolo Iodice Raoul Saggini Nicolo ` Scuderi Received: 18 August 2011 / Accepted: 10 October 2011 / Published online: 16 November 2011 Ó Springer Science+Business Media, LLC and International Society of Aesthetic Plastic Surgery 2011 Abstract Background A number of factors, including body mass and one’s mood, may influence posture. Breast augmentation results not only in a significant improvement in body image- related feelings and self-esteem but also in a sudden change in body mass. The aim of this study was to assess postural changes following breast augmentation by studying body position, orientation through space, and center of pressure. Methods Patients with breast hypoplasia who underwent breast augmentation were enrolled. Posture evaluation was performed before and 1, 4, and 12 months after surgery by quantifying the center of mass using the Fastrak TM system and the center of pressure using stabilometry. The Wilco- xon signed-rank sum test was used to compare value modifications. Results Forty-eight patients were enrolled in the study. A retropositioning of the upper part of the body, confirmed by baropodometric analysis, was evident in the early postopera- tive period. We subsequently observed a reprogramming of the biomechanical system, which reached a state of equilibrium 1 year after surgery, with a slight retropositioning of the head and a compensatory anterior positioning of the pelvis. Conclusion We believe that with respect to posture, the role played by psychological aspects is even more impor- tant than that played by changes in body mass. Indeed, hypomastia is often associated with kyphosis because patients try to hide what they consider a deficiency. Fol- lowing breast augmentation, the discovery of new breasts overcomes the dissatisfaction with the patient’s own body image, increases self-esteem, and modifies posture regardless of the changes in body mass due to the insertion of the implants. Keywords Breast augmentation Á Posture Á Fastrak TM Á Stabilometry Á Body image Many women seek breast augmentation because they are dissatisfied with the appearance of their breasts and, con- sequently, with their body image. Indeed, as reported in the literature, concern over physical appearance may be a defining characteristic of cosmetic surgery patients [15]. The mental representation of one’s physical appearance can be understood through the psychological construct of the body image, which is the construct that may best help us understand the motivations of cosmetic surgery candi- dates [6]. The dissatisfaction of such subjects with their body image can result in anxiety, reduced self-esteem, and altered interpersonal relationships. Moreover, they display a closed attitude suggestive of refusal and hide the breast by assuming the typical kyphotic posture. The literature contains numerous postaugmentation reports demonstrating patients’ overall satisfaction with their new breasts [710] and the feel of these new breasts [7, 10]. Moreover, patients do not regret the decision to M. Mazzocchi Department of Plastic Surgery, University of Perugia, Perugia, Italy M. Mazzocchi (&) Via Portuense 331, 00149 Rome, Italy e-mail: [email protected] L. A. Dessy Á N. Scuderi Department of Plastic Surgery, ‘‘La Sapienza’’ University of Rome, Rome, Italy P. Iodice Á R. Saggini Department of Neuroscience and Imaging, ‘‘G. d’Annunzio’’ University of Chieti, Chieti, Italy 123 Aesth Plast Surg (2012) 36:570–577 DOI 10.1007/s00266-011-9841-6

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Page 1: A Study of Postural Changes After Breast Augmentation

ORIGINAL ARTICLE BREAST

A Study of Postural Changes After Breast Augmentation

Marco Mazzocchi • Luca Andrea Dessy •

Pierpaolo Iodice • Raoul Saggini • Nicolo Scuderi

Received: 18 August 2011 / Accepted: 10 October 2011 / Published online: 16 November 2011

� Springer Science+Business Media, LLC and International Society of Aesthetic Plastic Surgery 2011

Abstract

Background A number of factors, including body mass and

one’s mood, may influence posture. Breast augmentation

results not only in a significant improvement in body image-

related feelings and self-esteem but also in a sudden change in

body mass. The aim of this study was to assess postural

changes following breast augmentation by studying body

position, orientation through space, and center of pressure.

Methods Patients with breast hypoplasia who underwent

breast augmentation were enrolled. Posture evaluation was

performed before and 1, 4, and 12 months after surgery by

quantifying the center of mass using the FastrakTM

system

and the center of pressure using stabilometry. The Wilco-

xon signed-rank sum test was used to compare value

modifications.

Results Forty-eight patients were enrolled in the study. A

retropositioning of the upper part of the body, confirmed by

baropodometric analysis, was evident in the early postopera-

tive period. We subsequently observed a reprogramming of the

biomechanical system, which reached a state of equilibrium

1 year after surgery, with a slight retropositioning of the head

and a compensatory anterior positioning of the pelvis.

Conclusion We believe that with respect to posture, the

role played by psychological aspects is even more impor-

tant than that played by changes in body mass. Indeed,

hypomastia is often associated with kyphosis because

patients try to hide what they consider a deficiency. Fol-

lowing breast augmentation, the discovery of new breasts

overcomes the dissatisfaction with the patient’s own body

image, increases self-esteem, and modifies posture

regardless of the changes in body mass due to the insertion

of the implants.

Keywords Breast augmentation � Posture � FastrakTM �

Stabilometry � Body image

Many women seek breast augmentation because they are

dissatisfied with the appearance of their breasts and, con-

sequently, with their body image. Indeed, as reported in the

literature, concern over physical appearance may be a

defining characteristic of cosmetic surgery patients [1–5].

The mental representation of one’s physical appearance

can be understood through the psychological construct of

the body image, which is the construct that may best help

us understand the motivations of cosmetic surgery candi-

dates [6]. The dissatisfaction of such subjects with their

body image can result in anxiety, reduced self-esteem, and

altered interpersonal relationships. Moreover, they display

a closed attitude suggestive of refusal and hide the breast

by assuming the typical kyphotic posture.

The literature contains numerous postaugmentation

reports demonstrating patients’ overall satisfaction with

their new breasts [7–10] and the feel of these new breasts

[7, 10]. Moreover, patients do not regret the decision to

M. Mazzocchi

Department of Plastic Surgery, University of Perugia,

Perugia, Italy

M. Mazzocchi (&)

Via Portuense 331, 00149 Rome, Italy

e-mail: [email protected]

L. A. Dessy � N. Scuderi

Department of Plastic Surgery, ‘‘La Sapienza’’

University of Rome, Rome, Italy

P. Iodice � R. Saggini

Department of Neuroscience and Imaging, ‘‘G. d’Annunzio’’

University of Chieti, Chieti, Italy

123

Aesth Plast Surg (2012) 36:570–577

DOI 10.1007/s00266-011-9841-6

Page 2: A Study of Postural Changes After Breast Augmentation

undergo breast augmentation after surgery, stating that they

would repeat the procedure and recommend it to others

[7, 9, 10]. Patients also report significant improvements in

their own feelings of sexual attractiveness and self-esteem.

These high rates of patient satisfaction persist beyond the

immediate postoperative period, resulting in a constantly

improving body image.

Neuropsychological studies indicate that control of

posture and locomotion are interdependent at many levels

of the central nervous system (CNS), from the motor cortex

to the basal ganglia, the brain stem, and the spinal cord

[11]. These structures participate in postural control by

providing the appropriate spatial frameworks required to

incorporate postural adjustments [12, 13]. Moreover,

stimulation of specific areas of the hypothalamus or brain

stem has been shown to trigger changes in posture [14–17].

Interactions between the pathways that control posture and

walking exist, even at the level of spinal premotor inter-

neurons [18]. These afferent inputs are modulated by

numerous factors, including mood state and anxiety.

The position and orientation through space of body parts

can be assessed reliably by means of the FastrakTM

system

(Polhemus, Colchester, VT, USA), which is used for static

and dynamic biomedical evaluations. It is an electromagnetic

three-dimensional tracking system that locates the position

and orientation of up to four sensors placed on relevant body

parts. It provides real-time measurements, with six degrees of

freedom, that determine sensor position and orientation

through space. Each sensor can, therefore, measure joint

motion on three different planes, i.e., the primary movement

plane and two secondary planes, collecting data on range of

motion and speed over time. These data can be used to cal-

culate the center of mass (COM), which is a point equivalent

to the total body mass in the global reference system (GRS)

and is the average of each body segment COM in three-

dimensional (3D) space. The COM is a passive variable

controlled by the balance control system. The vertical pro-

jection of the COM onto the ground is often called the center

of gravity (COG). Its measurement unit is the meter (m).

The FastrakTM

system is based on two modalities for

posture evaluation, i.e., the visualization of the relative

angles and the study of COM, the latter being the best

parameter for comparison over time. It has been used to

assess the reproduction of a neutral lumbopelvic position

following flexion movements [19], primary and coupled

rotations of the thoracic spine [20], and the reproducibility

of spine position sense measurements [21].

Stabilometry is a method that reliably quantifies the

position of the body’s center of pressure (COP). COP is

defined as the coordinates of the resultant force applied

through the feet on the force plate. It is the point of the

vertical ground reaction force vector. It represents the

average of all the pressures over the surface that are in

contact with the ground. If only one foot is on the ground,

the COP lies within that foot. If both feet are in contact

with the ground, the COP lies somewhere between the two

feet, depending on the relative weight borne by each foot.

This method has been used extensively in both normal

subjects and patients and thus has established normality

ranges [22–24].

The use of mammary implants to increase breast volume

produces a sudden change in body mass. This increased

body mass may play an important role in modulating body

sway amplitude and frequency, reflecting specific strategies

for maintaining upright standing posture.

To our knowledge, no studies have investigated postural

sway changes after breast augmentation. The aim of this

study was to assess the entity of postural changes after

breast augmentation by using the methods described above,

i.e., stabilometry and the FastrakTM

system.

Materials and Methods

Patients affected by breast hypoplasia and due to undergo

breast augmentation in the Department of Plastic and

Reconstructive Surgery of ‘‘La Sapienza’’ University of

Rome between January 2008 and March 2010 were

enrolled in the study. Participants were informed about the

study and provided written informed consent.

Inclusion criteria were the positioning of the implant in

a subglandular pocket, to ensure that pectoralis major

muscle function was unimpaired, and good general health.

Exclusion criteria were the presence of any muscular or

bone trauma and neurological disorders. Posture was

evaluated before surgery (T0), and after 1 (T1), 4 (T2),and

12 months (T3) by measuring the COM with the FastrakTM

system and the COP with stabilometry.

All measurements were performed in the absence of a

magnetic field and with a constant temperature of

23 ± 1�C; furthermore, care was taken to ensure that

patients were not wearing any metal objects.

Different COMs were calculated to evaluate the body’s

position and orientation through space, with the patient

standing upright. Four functional systems were considered:

the head, the sternum-clavicle, the pelvis, and the knees.

An anatomical landmark was marked on each functional

system with an adhesive marker (Figs. 1, 2).

The spatial points were obtained by means of the

FastrakTM

system, with a root-mean-square (RMS) error of

0.08 mm, which indicates sampling precision. The system

was composed of a transmitting antenna and four remote

sensors. The antenna was placed on a wooden support,

while one sensor was placed on the 4th lumbar vertebra and

the others on marked body points. The data were analyzed

using dedicated software (Polhemus ViewTM

, Polhemus,

Aesth Plast Surg (2012) 36:570–577 571

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Page 3: A Study of Postural Changes After Breast Augmentation

Colchester, VT, USA) that allowed 3D visualization

(Fig. 3). A Matlab program (MathWorks Inc., Natick, MA,

USA) was used to identify a mathematical relationship

between different anatomical points and different joints,

which in turn yielded different COM subsystems. Postural

changes over time were evaluated on the basis of variations

in space of the COM.

The inclinations of the head, shoulders, pelvis, and knees

were calculated. Every pair (brace) of points were considered

when calculating the angles. In particular, the zenith and

azimuth were calculated to evaluate the posture and its

changes over time. The first measurement (T0) was taken as

the reference value, while subsequent variations were mea-

sured in centimeters on the different spatial plans (x, y, z).

x indicated anterior (?) or posterior (-) movements, y indi-

cated laterolateral movements (right ?, left -), and z indi-

cated movements in height (increment ?, decrement -).

The stabilometric analysis was performed with the heels

joined and an angle of 30� between the feet, with the eyes first

open and then closed (Fig. 4). The analysis time was

51 s. Any deflections in the COP along the lateral and

anterior/posterior axes were recorded (sampling rate =

50 Hz) using a custom force platform developed according to

the specifications provided by the French Association of

Posturology [25, 26]. The area encompassed by the COP was

analytically evaluated as an ellipse, whose principal axes

were estimated through principal component analysis (PCA)

[24, 27].

Spectral analysis was applied for each stabilometric test

in both the x and y directions using Burg’s autoregressive

method [23], with order 100 and decimation to 10 Hz. Total

power (TP) was calculated separately for each direction, i.e.,

mediolateral (ML) or anterior–posterior (AP), to obtain a

global measure of COP sways, which corresponds to its

variance. Only the frequencies encompassed within the

0–2-Hz band were included in the TP calculation, since very

little activity was observed above this limit.

The Wilcoxon signed-rank sum test was used to com-

pare value modifications. The level of significance was set

at P \ 0.05.

Results

Forty-eight patients were enrolled in the study. The patients’

age ranged between 20 and 32 years (mean = 24.7), their

Fig. 1 Anatomical landmarks of each functional system marked with

an adhesive marker

Fig. 2 Scheme of the anatomical landmarks of each functional system

572 Aesth Plast Surg (2012) 36:570–577

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Page 4: A Study of Postural Changes After Breast Augmentation

weight between 53.1 and 62.6 kg (mean = 56.7 kg), their

height between 164 and 178 cm (mean = 168.8 cm), and

their body mass index (BMI) between 19.8 and 23.6 kg/m2

(mean = 21.4). All the patients were right-handed, were in

good health, and had not suffered any muscular or bone

trauma or neurological disorder. Implants were placed in a

subglandular pocket in all patients. Textured round implants

(Mentor Corporation, Santa Barbara, CA, USA) were used

in all cases (size from 200 to 325 cc).

The mean value, standard deviation (SD), and statistical

significance of the changes in COM over time are sum-

marized in Table 1.

Head COM displayed a significant variation (P \ 0.05)

on the x plane from T0 to T1; this variation, which indi-

cated the retroposition of the head at T0, decreased at T2

and stabilized at T3. A nonsignificant variation toward the

right was observed on the y plane from T0 to T2, though

this variation decreased at T3. A significant variation

(P \ 0.01) emerged on the z plane from T0 to T1; this

variation also decreased at T2 and stabilized at T3 (Fig. 5).

Shoulder COM displayed a significant variation

(P \ 0.01) on the x plane from T0 to T1. This variation,

which indicated the retroposition of the head at T0,

decreased at T2 and disappeared at T3. No significant

variations were present on the y plane. A significant vari-

ation (P \ 0.05) that emerged from T0 to T1 on the z plane

progressively decreased at T2 and at T3.

No significant variations were detected in pelvis COM

on any of the planes considered. A nonsignificant 0.5-cm

retropositioning observed at T1 on the x plane decreased at

T2 and subsequently displayed a slight degree of anterior

positioning at T3.

Significant variations were detected in knee COM on the

y plane at T2 (P \ 0.01) and at T3 (P \ 0.05). A nonsig-

nificant 0.4-cm anterior positioning was detected in knee

COM on the x plane at T1; this variation increased at T2

but subsequently decreased at T3, when it displayed a

slight degree of retropositioning.

The COP values, expressed as a percentage of the body

weight distribution in the anteroposterior and laterolateral

directions, are summarized in Table 2. A nonsignificant

Fig. 3 Screen image of the

PolhemusView software

Fig. 4 Stabilometric analysis performed with heels joined and an

angle of 30� between the feet

Aesth Plast Surg (2012) 36:570–577 573

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reduction in the anterior weight distribution emerged in

the anteroposterior direction at T1; this variation became

significant at T2 (P \ 0.001) with the eyes open, and at

T3 (P \ 0.001) with the eyes both open and closed.

Moreover, a significant increase in the right weight

distribution in the laterolateral direction was observed at

all the time intervals, regardless of whether the eyes were

open or closed.

The stabilometric data are given in Table 3. The sway

area, with the eyes both open and closed, revealed a

Table 1 Mean value, standard deviation (SD), and statistical significance of the changes in center of mass over time

Plane T0 T1 T2 T3

X Y Z X Y Z X Y Z X Y Z

Head

Mean 0 0 0 -1.20667 -0.16933 0.999333 -0.234 0.424667 0.239333 -0.20188 0.19625 0.524375

SD 0 0 0 1.837086 1.334581 1.188033 1.081296 0.736562 2.583316 1.172832 0.61857 1.5396

P – – – \0.05 [0.05 \0.01 [0.05 [0.05 [0.05 [0.05 [0.05 [0.05

Shoulders

Mean 0 0 0 -1.03313 -0.06938 0.745625 -0.222 0.118667 0.270667 0.029375 0.025 0.25375

SD 0 0 0 1.434861 1.58745 1.121323 1.465841 1.390118 2.509023 0.542335 0.934183 1.977329

P – – – \0.01 [0.05 \0.05 [0.05 [0.05 [0.05 [0.05 [0.05 [0.05

Pelvis

Mean 0 0 0 -0.54688 -0.22063 0.31125 -0.19267 -0.24733 0.198667 0.238125 -0.13375 0.411875

SD 0 0 0 1.544076 1.297117 1.072826 1.31972 0.899878 3.452286 0.836505 0.5633 1.034918

P – – – [0.05 [0.05 [0.05 [0.05 [0.05 [0.05 [0.05 [0.05 [0.05

Knee

Mean 0 0 0 0.396875 -0.1325 0.392 0.650625 -0.445 -0.34544 -0.385 -0.35688 0.086875

SD 0 0 0 1.557085 1.297723 1.870343 1.618725 0.750638 3.487074 0.85785 0.536402 1.379884

P – – – [0.05 [0.05 [0.05 [0.05 \0.01 [0.05 [0.05 \0.05 [0.05

Fig. 5 Pre- and postoperative posture measurements of a patient who underwent breast augmentation. Left posture before surgery. Centerposture 1 month after surgery. Right posture 1 year after surgery

574 Aesth Plast Surg (2012) 36:570–577

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significant increase in area at T1 (P \ 0.01) that persisted

at T2 (P \ 0.001). By T3, the sway area values had

dropped, almost returning to the T0 values. The surface

ellipse with eyes open revealed a significant increase at T1

(P \ 0.05) that persisted at T2 (P \ 0.01); by T3, this

value had dropped, almost returning to the T0 values. The

surface ellipse with the eyes closed displayed a significant

increase at T2 (P \ 0.05), only to decrease at T3, when it

became nonsignificant.

No major complications related to the breast augmen-

tation procedure were observed, either in the postoperative

period or during follow-up.

Discussion

Human postural control depends on central processing of

labyrinth, retinal, and somatosensory information (the

sensory afferent system), which can be modulated by

numerous factors, including mood state, anxiety, and self-

esteem. This results in adaptive and compensatory activi-

ties of the antigravity muscles whose aim, during the static

upright position, is to maintain the COM inside an area

roughly corresponding to the surface of the feet.

Many studies based on posturography have shown that

an increase in body sway is the result of either sensory

Table 2 Center of pressure

expressed as a percentage of the

body weight distribution in the

anteroposterior and laterolateral

directions

OE open eyes, CE closed eyes

T0 T1 T2 T3

Anteroposterior direction—OE

Mean Ant. 46.98000 43.16667 36.42667 34.40667

SD 6.886654 11.09837 7.917834 7.018493

P [0.05 \0.0001 \0.0001

Anteroposterior direction—CE

Mean Ant. 47.14000 45.09333 37.94667 34.86667

SD 6.993242 9.780043 8.494525 8.197183

P [0.05 [0.05 \0.0001

Laterolateral direction—OE

Mean Right 46.91333 51.79333 49.15333 49.62000

SD 3.641794 3.607426 5.320294 3.530925

P \0.01 \0,05 \0.01

Laterolateral direction—CE

Mean Right 47,62000 51,90667 49,68667 50,66667

SD 3,560136 3,571608 4,248002 2,912207

P \0.01 \0.05 \0.01

Table 3 Stabilometric data

OE open eyes, CE closed eyes

T0 T1 T2 T3

Sway area (mm2)—OE

Mean 5258.827 8307.347 9751.98 6286.847

SD 2227.750 3193.075 2682.173 1894.782

P \0.01 \0.0001 \0.05

Sway area (mm2)—CE

Mean 6287.760 9790.947 11096.91 6962.413

SD 2402.350 4438.207 4101.96 1558.047

P \0.01 \0.001 [0.05

Surface ellipse (mm2)—OE

Mean 16.6468 32.53193 34.37853 15.32533

SD 12.28584 28.45718 21.63079 8.140124

P \0.05 \0.01 [0.05

Surface ellipse (mm2)—CE

Mean 13.46633 13.66853 23.9766 9.792

SD 17.69077 11.89038 13.94486 5.013033

P [0.05 \0.05 [0.05

Aesth Plast Surg (2012) 36:570–577 575

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failure, such as visual impairment [28], peripheral vestib-

ular disorders [29], and somatosensory loss [30], or of

neurological disorders of the central nervous system [31,

32]. Nevertheless, a discrepancy between the clinical

assessment and subjective symptomatology is often

observed in patients who complain of postural unsteadiness

in the absence of neurosensory impairment. This has led to

the hypothesis of psychopathological interference between

perceived and actual equilibrium disturbance [33].

Mechanisms of sensorimotor feedback and central inte-

gration processes that control posture have been the object

of numerous studies, the majority of which were based

on the removal, or limitation, of one particular sensory

modality and the subsequent measurement of sway changes.

These simulated changes were used to determine the

importance of sensory information in the control system.

In one study conducted on a healthy adult population,

the removal of sensory information resulted in an increase

in body oscillation amplitude [34], though this result was

not confirmed in other types of study populations (e.g.,

children) [35]. A reduction in the amount of sensory

information reaching the CNS also reduces the ability to

accurately estimate the COM dynamics, which in turn

impairs oscillation control. However, the methods adopted

by previous studies were not designed to shed light on the

mechanisms underlying posture. In this regard, the litera-

ture contains various descriptions of models that can be

used to predict the relationship between sensory informa-

tion and oscillation amplitude [6, 36, 37].

In this study we assessed postural changes after breast

augmentation. Our results show that breast augmentation

unexpectedly induced a retropositioning of the head and

shoulder COM (Table 3). We instead expected the increase

in the anterior body mass to have the opposite effect. Our

result may, however, be explained through the psycho-

logical aspects of posture, which are clearly explained in

the literature [25]. Hypomastia is, in fact, often associated

with kyphosis, with patients trying to hide what they con-

sider a defect. The discovery of new breasts appears to

eliminate the patient’s dissatisfaction with her body image,

thereby reducing anxiety and increasing self-esteem.

According to our data, the improvement in body image

corrects this postural dysmorphic disorder by opening the

shoulders, and shifting the head backward and the pelvis

forward, the latter being a compensatory mechanism for the

retropositioning of the head. More studies on larger num-

bers of subjects are warranted to shed more light on this

phenomenon.

Since body dissatisfaction is not exclusive to eating

disorders [38], we tested the hypothesis that posture in

healthy subjects without a diagnosable psychiatric disorder

may be affected not only by anxiety and depression, but

even by feelings linked to changes in body image.

In the early postoperative phase, we observed that

patients had difficulty in perceiving their body in space, as

demonstrated by an increased oscillating phase. This dif-

ficulty persisted for more than 4 months after surgery.

Indeed, the 3D spatial representation of the body shows

that the patients returned to their preoperative biome-

chanical equilibrium 1 year after surgery.

It is noteworthy that the postural oscillations followed a

similar course regardless of whether the patients’ eyes were

open or closed, which rules out the possibility that postural

control was temporarily impaired owing to a reduction in

visual sensory information.

One explanation for the increased oscillation observed in

our study is the long time required for tonic adaptation as a

result of the change in the COMs in the first phase. Fur-

thermore, the persistence of postural instability 4 months

after surgery is not related exclusively to a sensorimotor

phenomenon but even to psychological aspects. The central

nervous system requires a long time to redesign body image

and to reconstitute a series of automatisms that reduce,

through cascade activation, the perception, analysis, and

motor feedback times. It is likely that the system controlling

posture cannot reach an equilibrium of forces, whether they

be gravitational or compensatory, that are required to

maintain the upright position, until a biomechanical equi-

librium of the various subsystems is re-established and a

psychological readjustment has been achieved.

In conclusion, we believe that the role played by psy-

chological aspects in the control of posture is even more

important than that related to changes in the distribution of

body mass. This phenomenon is particularly evident in the

first period following surgery, when the emotional com-

ponent is most marked. Subsequently, as the emotional

component diminishes and the psychological component of

postural control becomes more stable, the patient’s posture

tends to return to its presurgical status.

Disclosure None of the authors has a financial interest in any of the

products, devices, or drugs described in this article.

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