S Bianchin

C Sfienti

J Lukasik

A Le Fèvre

W Trautmann

P Adrich

T Aumann

C O Bacri

T Barczyk

R Bassini

C Boiano

A S Botvina

A Boudard

J Brzychczyk

A Chbihi

J Cibor

B Czech

M De Napoli

J. -E Ducret

H Emling

J Frankland

M Hellström

D Henzlova

K Kezzar

G Immè

I Iori

H Johansson

A Lafriakh

E Le Gentil

Y Leifels

W G Lynch

J Lühning

U Lynen

Z Majka

M Mocko

W F J Müller

A Mykulyak

H Orth

A N Otte

R Palit

P Paw Lowski

A Pullia

G Raciti

E Rapisarda

H Sann

C Schwarz

H Simon

K Sümmerer

M B Tsang

G Verde

C Volant

M Wallace

H Weick

J Wiechula

A Wieloch

B Zwieglinski

Mass measurement and isoscaling in 124 Sn+Sn and 107 Sn+Sn reactions at 600 AMeV

Isotopic effects in projectile spectator fragmentation at 600 AMeV have been investigated using data collected in recent experiments with SIS beams at the GSI laboratory and with the ALADiN forward-spectrometer. For this purpose, primary beams of 124 Sn, as well as secondary beams of 124 La and 107 Sn produced at the FRS fragment separator have been used. Isoscaling in 124,107 Sn+Sn reactions is investigated and results are compared with data taken with the INDRA multidetector for 12 C+ 112,124 Sn reactions.

Introduction

The growing interest in isospin effects in nuclear reactions is motivated by an increasing awareness of the importance of the symmetry term in the nuclear equation of state, in particular for astrophysical applications. Supernovae simulations or neutron star models require inputs for the nuclear equation of state at extreme values of density and asymmetry for which the predictions differ widely [1,2]. Fragmentation reactions are, therefore, a very interesting tool because they permit the production of nuclear systems with subnuclear densities and temperatures which, e.g., largely overlap with those expected for the explosion stages of core-collapse supernovae [3]. Laboratory studies of the properties of nuclear matter in the hot environment, similar to the astrophysical situation, are thus becoming feasible, and an active search for suitable observables is presently underway. Of particular interest is the density-dependent strength of the symmetry term which is essential for the description of neutron-rich objects up to the extremes encountered in neutron stars. In a very recent experiment with the ALADiN spectrometer, the possibility of using secondary beams for reaction studies at relatistic energies has been explored. Beams of 107 Sn, 124 Sn, 124 La, and 197 Au as well as Sn and Au targets were used to investigate the mass and isospin dependence of projectile fragmentation at 600 MeV per nucleon. The neutron-poor radioactive projectiles 107 Sn and 124 La were produced at the Fragment Separator FRS.

The present contribution will show results obtained from an isoscaling analysis with the collected data. A comparison will be made with data obtained with the 4π multidetector INDRA and the relation between isoscaling and the coefficient γ of the symmetry-energy term E sym = γ(A -2Z) 2 /A will be discussed.

The S254 experiment

The S254 experiment has been devoted to the investigation of isotopic effects in the decay of projectile spectators at relativistic energies. For this purpose, fragment decays of 197 Au, 124 Sn, 107 Sn and 124 La projectiles in collisions with nat Sn and Au targets at an incident energy E=600 AMeV have been studied with the ALADiN (A large Acceptance Dipole magNet) forward-spectrometer at SIS.

Production of secondary beams

In order to extend the range of isotopic compositions of the excited spectator systems, four different projectiles, all with incident energy of 600 MeV per nucleon, have been investigated allowing a study of various combinations of masses and N/Z ratios in the entrance channel: 124 Sn, 197 Au, 124 La and 107 Sn. The two latter beams have been delivered by the FRagment Separator (FRS) of the GSI laboratory as products of the fragmentation of primary 142 Nd beams at 895 and 875 AMeV on a 9 Be production target with a density of 4009 mg/cm 2 . The separation and the focusing of the fragments produced by the reaction take place in the four different parts of the fragment separator. Each of these parts is composed of a dipole magnet used to separate the different ion species as a function of their A/Z ratio and two quadrupole magnets used for focusing (Fig. 1). Although the fragment separator is able to provide an isotopically pure secondary beam using a wedge-shaped degrader to select the charge of the desired beam, we have chosen not to use it, in order to maintain a beam intensity of approximately 2000 particles/sec. The position measurement at the dispersive mid-plane and the measurement of the flight time during the 80 m passage from the FRS to the ALADiN spectrometer permit the reconstruction of the A/Z ratio of the selected projectiles with high precision. A discriminant analysis using information from all upstream detectors permits a selection of Z proj with good resolution, if necessary. As an illustration, the composition of the beam delivered by the fragment separator is shown in Fig. 2. In the present analysis, the secondary beam delivered by the fragment separator is used without any further selection.

The ALADiN spectrometer

A schematic layout of the experimental setup is shown in Fig. 3. For each beam particle, its arrival time and its position in a plane perpendicular to the beam direction are measured upstream of the target with two thin plastic scintillators. The geometric acceptance of the spectrometer is θ lab ≈ ±9.2 • horizontally and ±4.3 • vertically. It is matched by the dimensions of the Time Projection-MUltiple Sampling Ionization Chamber TP-MUSIC IV and by the timeof-flight (TOF) wall. At E=600 AMeV, the angular distributions of some lighter fragments extend beyond the acceptance of the spectrometer and are detected in the CsI(Tl) hodoscope array that surrounds the entrance of the magnet. The Large Area Neutron Detector LAND [4], used to determine the neutron multiplicity, is positioned close to zero degrees with respect to the incident beam direction.

The atomic numbers Z and the velocities of nuclear fragments are determined with the TOF wall, located at the end of the ALADiN spectrometer and extending over 2.4 m in horizontal and 1.0 m in vertical directions. It consists of two layers of vertically mounted scintillator strips of 2.5 cm width and 1.0 cm thickness, viewed by photomultiplier tubes at both ends [5]. The two layers are offset by half a width with respect to each other. The primary beam is directed through a hole of 4.8 × 6.0 cm 2 cut into the middle sections of the central scintillator modules. An overall time resolution of about 400 ps and 120 ps (FWHM) for fragments with Z=2 and Z ≈ Z proj , respectively, is achieved. The TP-MUSIC IV detector used to measure the charge and to reconstruct the trajectory of the projectile fragments, is divided into two parts separated by a cathode plane. On each side of the detector, three ionisation chamber sections (each with 8 anodes) and four proportional counters are used. Using charge-division and pads techniques, the TP-MUSIC IV allows the recontruction of the trajectories of the fragments.

Trajectory reconstruction

Isoscaling requires the knowledge of the isotopic composition of the fragments produced in the collisions. It is, therefore, necessary to determine precisely the mass of each of these fragments, which is achieved by reconstructing their trajectory through the known field of the ALADiN magnet. This procedure allows us to determine the magnetic rigidity of the reaction products and, with the measured charge and velocity, their mass.

The reconstruction is based on the so-called backtracking method. The trajectories of the fragments inside the TP-MUSIC IV are deduced from their positions measured with the proportional counters. With an assumed starting value for the rigidity, this trajectory is followed back through the magnet. In an iterative procedure, the fragment rigidity is varied until the reconstructed intersection with the target plane coincides with the intersection of the projectile, measured with an accuracy of about 1 mm. A fragment entering in the acceptance of a magnet is deflected along a trajectory of radius ρ (in unit of meter) given by:

| R| = Bρ = p 0.3q (1)
where the magnetic field B, the charge of the fragment q and its momentum p are given in units of Tesla, electron charge and GeV /c, respectively. Since the momentum of the fragment is given by:

p = m 0 βγA = m 0 βA 1 -β 2 (2)
with m 0 =0.935 GeV/c 2 , the mass number A and β = v/c, it follows that:

A = 0.3Z| R| 1 -β 2 m 0 β (3)
The rigidity | R| is measured with a resolution of ∼ 1 % for Z = Z proj through the trajectory reconstruction procedure, the charge Z is measured by both the TP-MUSIC IV detector and the TOF-wall and the velocity β is obtained measuring the time-of-flight with the TOF-wall knowing the path length from the reconstruction of the trajectory. Fig. 4 shows mass spectra obtained for light fragments (2≤ Z ≤10) produced by the fragmentation of 124 Sn (upper panels) and 107 Sn (lower panels) projectiles on a nat Sn target. The mass resolution obtained for fragments entering into the acceptance of the ALADiN spectrometer is about ∆A/A = 3 % (FWHM) for fragments with Z=2 and decreases to 1.5 % for Z ≥8. Masses are thus individually resolved for fragments with atomic number Z ≤10. The dominant contribution to the uncertainty of the mass measurement: is caused by the mass-dependent error for the time measurement which is amplified by the factor γ 2 (for 600 MeV/nucleon, γ 2 =2.6 ). Assuming that the rigidity resolution is about 1 % for Z proj , a time resolution of ∆t ≈280 ps (FWHM) can be deduced for the light fragments and ∆t ≈120 ps (FWHM) for the projectile. By inspection of the mass spectra, first-order isotopic effects can be observed: higher yields are obtained for neutron-rich isotopes in the case of the neutron-rich system.

∆A A = ∆R R 2 + γ 2 ∆t t 2 (4)

Isoscaling and symmetry energy

Isotopic scaling, also called isoscaling, has been shown to be a phenomenon common to many different types of heavy-ion reactions [6][7][8][9]. It is observed by comparing products yields Y i from reactions which differ only in the isotopic composition of the projectiles or targets or both but are otherwise identical. Isoscaling refers to an exponential dependence of the measured yield ratios R 21 (N, Z) on the neutron number N and the proton number Z of the detected products. The scaling expression

R 21 (N, Z) = Y 2 (N, Z)/Y 1 (N, Z) = Cexp(αN + βZ) (5)
describes rather well the measured ratios over a wide range of complex particles and light fragments [10]. For illustration, the yield ratios R(Sn124/Sn107) obtained for the fragmentation of the 124 Sn and 107 Sn projectiles in the Z bound = 10 -20 and Z bound = 20 -30 intervals, covering the region of maximum fragment production, are plotted in Fig. 5 as a function of the neutron number. Isotopes of the same elements are plotted with the same symbols. Odd-Z nuclei are represented by open symbols while even-Z nuclei are represented by closed symbols (helium isotopes are represented by a cross). The dashed lines are best fits to the data points with one common pair of values α and β for elements with 3≤ Z ≤10. In the case of Fig. 5, α=0.397 and α=0.476 for Z bound = 10 -20 and Z bound = 20 -30, respectively. The fit values for other centrality selections are reported in Table 1. The observable Z bound , defined as the sum of the charges of the projectile fragments (Z ≥2) and used to sort the collisions according to their centrality, is related to the impact parameter and, thus, to the excitation energy. The accuracy of the isoscaling described by Eq. ( 5) can be compactly displayed, and then more easily judged, by plotting the scaled isotopic ratio, as a function of the neutron number N ,

S(N ) = R 12 (N, Z)exp(-βZ) (6)
Z bound α β 0-10 0.320 ± 0.005 -0.343 ± 0.001 10-20 0.397 ± 0.001 -0.416 ± 0.001 20-30 0.476 ± 0.001 -0.497 ± 0.001 30-40 0.633 ± 0.002 -0.648 ± 0.002 40-50 0.826 ± 0.082 -0.888 ± 0.039 Table 1: Parameters obtained from fitting the measured isotopic yield ratios with the scaling function given by Eq. ( 5) as a function of the Z bound selection (i.e. of the excitation energy). The first and last intervals are fitted for 3≤ Z ≤8, whereas the other ones are fitted for 3≤ Z ≤10.

For all elements, S(N) should lie along a straight line on a semilog plot when Eq. ( 5) accurately describes the experimental data.

The scaled isotopic ratio S(N) for different centrality selections obtained for the S254 experiment is shown in Fig. 6 (left panel). For a comparison, data obtained with the INDRA 4π detector for 12 C on 112,124 Sn reactions at incident energies of 300 and 600 MeV per nucleon are also plotted [11]. The difference between the isotopic compositions of the two systems being smaller in the case of the INDRA experiment, the value of the scaling parameter α, for a given centrality, is, as expected, smaller than in the present experiment. However, normalized by the difference of the squared Z/A values (see below), we obtain for the most peripheral bins α/∆(Z 2 /A 2 )=14.1 and α/∆(Z 2 /A 2 )=15.8 for the INDRA and the present experiments, respectively. This represents an agreement within ∼ 10 %. The slope parameter α decreases strongly with the centrality of the collision, extending from α=0.826 to α=0.320 for the most central event group (Table 1). The 12 C induced reactions cover the rise of fragment production over the range up to Z bound ≈ Z proj /2, whereas for collisions with the Sn target (in inverse kinematics) this range extends to very small Z bound . Moreover, in the INDRA case, the centrality selection was based on charged-particle multiplicity and not on Z bound , which makes the comparison between the two experiments not straightforward. Central collisions in 12 C induced reactions correspond, approximately, to the bin 20-30 in the present experiment. In both cases, α has about half the value observed for peripheral collisions. The present data show that α decreases even further for the more violent collisions initiated with the Sn target.

In the grand-canonical approximation, assuming that the temperature T is about the same, the scaling parameters α and β are proportional to the difference of the neutron and proton chemical potentials for the two systems divided by the temperature, α = ∆µ n /T and β = ∆µ p /T . Of particular interest is their connection with the coefficient γ of the symmetry-energy term E sym = γ(A -2Z) 2 /A, which has been obtained from the statistical interpretation of isoscaling within the SMM [7] and expanding-emitting-source model [10] and confirmed by an analysis of reaction dynamics [12]. The relation is

αT = ∆µ n = µ n,2 -µ n,1 ≈ 4γ Z 2 1 A 2 1 - Z 2 2 A 2 2 = 4γ∆(Z 2 /A 2 ) (7)
where Z 1 , A 1 and Z 2 , A 2 are the charges and mass numbers of the neutron-poor and neutron-rich systems at breakup, respectively. The coefficient γ of the symmetry term can then be obtained from isoscaling knowing the temperature and the isotopic compositions [11]. For this purpose, temperature measurements using isotopic thermometers are currently being investigated with data collected during the S254 experiment [START_REF] Sfienti | Contribution to this proceeding[END_REF]. The difference of the chemical potentials also depends on the isotopic composition at breakup. Although transport models predict that the difference between isotopic compositions for the two systems should not deviate by more than a few percent from the original value [START_REF] Gaitanos | [END_REF], larger deviations would have a significant effect on the deduced γ.

Summary and outlook

Isotopic effects in the projectile fragmentation have been studied with the ALADiN spectrometer at the GSI laboratory. Neutron-poor secondary beams produced at the fragment separator FRS have been used in addition to stable beams in order to cover a larger range of isotopic compositions. Resolved masses have been obtained for light fragments (2≤ Z ≤10) by measuring their charge, their time-of-flight and by reconstructing their trajectory, allowing to distinguish unambiguously each isotope. Isoscaling has been observed for 107,124 Sn+Sn reactions at 600 MeV per nucleon and the relation between the scaling parameter α and the centrality of the collision has been shown. It confirms results obtained earlier with the INDRA multidetector for 12 C+ 112,124 Sn reactions at incident energies 300 and 600 AMeV and demonstrates that, as expected, the value of the scaling parameter α increases with the difference between the isotopic compositions of the two systems. The connection with the symmetry-energy term of the nuclear equation of state has

Figure 1 :

 1 Figure 1: Schematic view of the fragment separator FRS.

Figure 2 :

 2 Figure 2: Event distribution in the plane A/Z vs Z MUSIC for a nominal beam of 124 La.

Figure 3 :

 3 Figure 3: Cross sectional view of the ALADiN spectrometer. The beam enters from the left and is monitored by two beam detectors before reaching the target. Projectile fragments entering into the acceptance of the magnet are tracked and identified in the TP-MUSIC IV detector and in the time of flight (TOF) wall. Fragments and particles emitted in forward directions outside the magnet acceptance and up to θ lab = 16 • are detected in the CsI(Tl) array. Neutrons emitted in directions close to θ lab = 0 • are detected with the Large Area Neutron Detector (LAND). The dashed line indicates the direction of the incident beam. The dash-dotted line represents the trajectory of beam particles after they were deflected by an angle of 7.3 • .

Figure 4 :

 4 Figure 4: Mass spectra obtained by reconstructing fragment trajectories and time-of-flights for 124 Sn+Sn (upper panels) and 107 Sn+Sn (lower panels) at 600 MeV per nucleon for fragments with charge 2≤Z≤10.

Figure 5 :

 5 Figure 5: Yield ratios for He to Ne isotopes from the fragmentation of 124 Sn and 107 Sn projectiles at 600 AMeV as a function of the neutron number N for two different centrality selections. The dashed lines are the results of exponential fits (for elements with 3≤ Z ≤10) according to Eq. (5).

Figure 6 :

 6 Figure 6: Scaled isotopic ratios S(N) for 107,124 Sn+Sn at E=600 AMeV (left panel) and for 12 C+ 112,124 Sn at E=300 AMeV and 600 AMeV obtained with the INDRA multidetector (right panel)[11] for three different centralities. In both cases, the dashed lines are the results of exponential fits according to Eq. (5).

10 Wed Mar 28 17:28:11 2007

	Masses Z = 2				mass_spectra_Sn124 mass_spectra_Sn124	Masses Z = 3					mass_spectra_Sn124 mass_spectra_Sn124	Masses Z = 4							mass_spectra_Sn124 mass_spectra_Sn124
								Entries 523069 Entries 523069							Entries Entries	95106 95106									Entries Entries	33184 33184
								Mean Mean	3.782 3.782							Mean Mean	6.81 6.81									Mean Mean	8.83 8.83
	60000 70000 80000			He				RMS RMS	0.6297 0.6297	6000 7000	Li					RMS RMS	0.8592 0.8592	1600 1800 2000	Be						RMS RMS	1.337 1.337
	50000									5000								1400
	40000									4000								1000 1200
	30000									3000								800
	20000									2000								600
																		400
	10000									1000								200
	0	1		2	3	4	5	6	7	4 0	5	6	7	8	9	10	11	5 0	6	7	8	9	10	11	12	13	14
	Masses Z = 5				mass_spectra_Sn124 mass_spectra_Sn124	Masses Z = 6					mass_spectra_Sn124 mass_spectra_Sn124	Masses Z = 7							mass_spectra_Sn124 mass_spectra_Sn124
								Entries Entries	31819 31819							Entries Entries	25101 25101									Entries Entries	13980 13980
	3000 3500		B				Mean RMS Mean RMS	10.93 1.055 10.93 1.055	1200 1400	C					Mean RMS Mean RMS	12.66 1.184 12.66 1.184	1000 1200	N							Mean Mean RMS RMS	15.02 15.02 1.15 1.15
	2500								1000
																		800
	2000								800
																		600
	1500								600
	1000								400								400
	500									200								200
	6 0		8	10	12	14	16		8 0	10	12	14		16	18		10 0	12		14		16	18		20
	Wed Mar 28 17:19:27 2007 12 14 16 18 0 50 100 150 200 250 300 350 400 O Masses Z = 8 Masses Z = 2	20	mass_spectra_Sn124 Entries 8058 Mean 17 RMS 1.302 22 mass_spectra_Sn124 Entries 8058 Mean 17 RMS 1.302 Masses Z = mass_spectra_Sn107 mass_spectra_Sn124 Entries 4995 Mean 19.74 RMS 1.252 16 18 20 22 24 26 0 20 40 60 80 100 120 140 160 180 200 mass_spectra_Sn124 Entries 4995 Mean 19.74 RMS 1.252 F Masses Z = 9 16 0 20 40 60 80 100 120 140 160 180 200 Ne 18 mass_spectra_Sn107 mass_spectra_Sn107 mass_spectra_Sn107 Masses Z = 3 Masses Z = 4	20	22		24	26	mass_spectra_Sn124 Entries 4294 Mean 21.62 RMS 1.275 28 mass_spectra_Sn124 Entries 4294 Mean 21.62 RMS 1.275 mass_spectra_Sn107 mass_spectra_Sn107
								Entries 468144 Entries 468144							Entries Entries	61822 61822									Entries Entries	23144 23144
	50000 60000		He				Mean RMS Mean RMS	3.731 0.6447 3.731 0.6447	4000 3000 3500	Li					Mean Mean RMS RMS	6.632 6.632 0.7857 0.7857	1800 2000 2200	Be						Mean Mean RMS RMS	8.165 8.165 1.315 1.315
	40000								2500								1400 1600
	30000								2000								1200
																		1000
	20000								1500								800
										1000								600
	10000								500								200 400
		0	1	2	3	4	5	6	7	4 0	5	6	7	8	9	10	11	5 0	6	7	8	9	10	11	12	13	14
	Masses Z = 5				mass_spectra_Sn107 mass_spectra_Sn107	Masses Z = 6					mass_spectra_Sn107 mass_spectra_Sn107	Masses Z = 7							mass_spectra_Sn107 mass_spectra_Sn107
								Entries Entries	20814 20814							Entries Entries	19167 19167									Entries Entries	8896 8896
	1400 1600 1800	B				Mean RMS Mean RMS	10.69 1.025 10.69 1.025	1000 1200	C					Mean RMS Mean RMS	12.3 1.091 12.3 1.091	500 600	N							Mean RMS Mean RMS	14.74 0.983 14.74 0.983
	1200							800								400
	1000
										600								300
	800
	600								400								200
	400
										200								100
	200
		6 0	8	10	12	14	16		8 0	10	12	14	16	18		10 0	12	14		16	18	20
	Masses Z = 8				mass_spectra_Sn107 mass_spectra_Sn107							mass_spectra_Sn107
								Entries Entries	5277 5277							Entries	2553
								Mean Mean	16.6 16.6							Mean	18.96
	250 300		O				RMS RMS	1.14 1.14							RMS	1.159
	200
	150
	100
	50
		12 0	14	16	18	20	22		0	16	18	20	22		24	26

10 20 30 40 50 60 70 80 90 mass_spectra_Sn107

	Masses Z = 9			Masses Z = 10			mass_spectra_Sn107 mass_spectra_Sn107
		Entries	2553					Entries Entries	2447 2447
		Mean	18.96	120				Mean Mean	20.89 20.89
	F	RMS	1.159	100	Ne			RMS RMS	1.167 1.167
				80
				60
				40
				20
				16 0	18	20	22	24	26	28

been discussed. The temperatures at breakup are currently being investigated using the doubleisotope thermometer in order to quantitatively establish the evolution of the symmetry term [START_REF] Sfienti | Contribution to this proceeding[END_REF].

This work was supported by the European Community under contract No. HPRI-CT-1999-00001.


Benoît Beyer

Véronique Feipel

Victor Sholukha

Laurence Chèze

Serge Van Sint

In-vivo analysis of sternal angle, sternal and sternocostal kinematics in supine humans during breathing

Keywords: kinematics, helical axis, thorax, sternocostal, sternal angle joint kinematics, helical axis, thorax, sternocostal, costovertebral, sternum, sternal angle

This paper aims at contributing to the understanding of the combination of in vivo sternum displacement, sternal angle variations and sternocostal joints (SCJ) kinematics of the seven first rib pairs over the inspiratory capacity (IC). Retrospective codified spiral-CT data obtained at total lung capacity (TLC), middle of inspiratory capacity (MIC) and at functional residual capacity (FRC) were used to compute kinematic parameters of the bones and joints of interest in a sample of 12 asymptomatic subjects. 3D models of rib, thoracic vertebra, manubrium and sternum were processed to determine anatomical landmarks (ALs) on each bone. These ALs were used to create local coordinate system and compute spatial transformation of ribs and manubrium relative to sternum, and sternum relative to thoracic vertebra. The rib angular displacements and associated orientation of rotation axes and joint pivot points (JPP), the sternal angle variations and the associated displacement of the sternum relative to vertebra were computed between each breathing pose at the three lung volumes.

Results can be summarized as following: 1) sternum cephalic displacement ranged between 17.8 and 19.2 mm over the IC; 2) the sternal angle showed a mean variation of 4.4° ± 2.7° over the IC; 3) ranges of rib rotation relative to sternum decreased gradually with increasing rib level; 4) axes of rotation were similarly oriented at each SCJ; 5) JPP spatial displacements showed less variations at first SCJ compared to levels underneath; 6) linear relation was demonstrated between SCJ ROMs and sternum cephalic displacement over the IC.

Introduction

The sternum was demonstrated to participate to rib cage stability [START_REF] Watkins | Stability provided by the sternum and rib cage in the thoracic spine[END_REF] and to be related to rib motion during breathing [START_REF] De Troyer | Mechanical coupling between the ribs and sternum in the dog[END_REF][START_REF] De Troyer | Sternum dependence of rib displacement during breathing[END_REF]. Sternocostal junctions (SCJ) include two joint components, i.e., the costo-chondral joint and the chondro-sternal joint, that are involved into thorax shape alterations and motion transmission from ribs towards the sternum. The 3D geometry of the ribs, their decreasing ranges-of-motion (ROMs) at costovertebral joints with increasing rib number [START_REF] Beyer | In vivo thorax 3D modelling from costovertebral joint complex kinematics[END_REF][START_REF] Beyer | Effect of anatomical landmark perturbation on mean helical axis parameters of in vivo upper costovertebral joints[END_REF][START_REF] Wilson | Geometry and respiratory displacement of human ribs[END_REF][START_REF] Wilson | Respiratory effects of the external and internal intercostal muscles in humans[END_REF], and the shape and size differences in costal cartilages seem to have an influence on the coupling between the ribs and sternum during breathing. Thus, the nature of each joint is specific to different regions of the thorax. Indeed, all chondro-sternal joints, but the first one, are synovial joints. The first chondro-sternal joint and all costo-chondral joints show an anatomical and functional continuity between bone and cartilage (i.e., so called synchondrosis joints) [START_REF] Osmond | Functionnal anatomy of the chest wall[END_REF].

Furthermore, the manubrio-sternal joint (MSJ) is recognized to allow slight variations of the sternal angle (or angle of Louis) as a secondary cartilaginous pliable hinge joint, enabling thorax deformation during deep breathing [START_REF] Kaneko | Breathing Movements of the Chest and Abdominal Wall in Healthy Subjects[END_REF][START_REF] Osmond | Functionnal anatomy of the chest wall[END_REF].

Previous works have analyzed the mechanical coupling between the ribs and sternum in dog [START_REF] De Troyer | Mechanical coupling between the ribs and sternum in the dog[END_REF][START_REF] De Troyer | Sternum dependence of rib displacement during breathing[END_REF], and concluded that the upper rib cage is tightly linked to the sternum [START_REF] De Troyer | Mechanical coupling between the ribs and sternum in the dog[END_REF][START_REF] De Troyer | Sternum dependence of rib displacement during breathing[END_REF]. Similar relation was then observed in 2 high tetraplegic patients [START_REF] De Troyer | Rib cage motion and muscle use in high tetraplegics[END_REF]. While the relationships between sternum and rib motions are widely recognized, no quantitative data are available in literature, neither on asymptomatic human subjects nor in pathological conditions. Therefore, the aim of the present study was to obtain quantitative analysis of sternal angle variations and the relation between the "true ribs" rotation (i.e., ribs 1 to 7 articulating anteriorly with the sternum) and sternum displacements as a function of lung volume over the inspiratory capacity.

The following hypotheses were tested: 1) the sternal angle changes during breathing motion ; 2) the rib rotation relative to sternum decreases with increasing rib number following costo-vertebral joints pattern (rib rotation relative to vertebrae was previously reported to decrease inversely with rib number [START_REF] Beyer | In vivo thorax 3D modelling from costovertebral joint complex kinematics[END_REF][START_REF] Beyer | Effect of anatomical landmark perturbation on mean helical axis parameters of in vivo upper costovertebral joints[END_REF][START_REF] Wilson | Respiratory effects of the external and internal intercostal muscles in humans[END_REF]; 3) the position and orientation of the axes of rib rotation relative to sternum differ between rib levels.

Materials and method

2.1.Sample and data collection

The protocol included processing and analysis of retrospective codified medical imaging datasets obtained from the Department of Radiology of the Erasme Academic Hospital. Spiral computed tomography (Siemens SOMATOM, helical mode, slice thickness = 0.5 mm, inter-slice spacing = 1 mm, Voxel size: 0.65*0.65*0.5 mm³, image data format: DICOM 3.0) performed at 3 lung volumes: total lung capacity (TLC), functional residual capacity (FRC) and middle of inspiratory capacity (MIC) which corresponds to FRC + 50% of the inspiratory capacity [START_REF] Cassart | Effect of chronic hyperinflation on diaphragm length and surface area[END_REF][START_REF] Pettiaux | Three-dimensional reconstruction of human diaphragm with the use of spiral computed tomography[END_REF]. CT images were sequentially performed while the subjects were connected to a spirometer and instructed to maintain inflation at each lung volume of interest while relaxing their respiratory muscle against closed airway [START_REF] Cassart | Effect of chronic hyperinflation on diaphragm length and surface area[END_REF]. A sample of 12 datasets from asymptomatic adults (mean age 31± 6 years old) was analysed. Details of anthropometric characteristics of the subjects are given in Annex 1.

Bone 3D models, anatomical landmarks and local coordinate systems

From the available CT data, 3D models of ribs, vertebrae, manubrium and sternal body with xiphoid process were obtained using a dedicated data segmentation software (Amira 4.0, San Diego, CA, USA) as previously detailed [START_REF] Beyer | In vivo thorax 3D modelling from costovertebral joint complex kinematics[END_REF]. Models were then imported within a custom-made software called lhpFusionBox [START_REF] Van Sint Jan | A technological platform for cerebral palsy -The ICT4Rehab project[END_REF] to obtain the spatial coordinates of anatomical landmarks (ALs) located at the surface of the models following previously validated methods for ribs, vertebrae and sternum [START_REF] Beyer | In vivo thorax 3D modelling from costovertebral joint complex kinematics[END_REF][START_REF] Van Sint | Color atlas of skeletal landmark definitions: guidelines for reproducible manual and virtual palpations[END_REF]. Note that all details concerning the ALs are given in Figure 1A.

ALs were then virtually grouped into so-called "AL clouds" that were subsequently used to build anatomical frames (AFs) on each bone of interest. Ribs and vertebrae coordinate systems were obtained as explained in previous analysis of costovertebral joints [START_REF] Beyer | In vivo thorax 3D modelling from costovertebral joint complex kinematics[END_REF][START_REF] Beyer | Effect of anatomical landmark perturbation on mean helical axis parameters of in vivo upper costovertebral joints[END_REF]. Manubrium and sternum AFs are detailed in Figure 1B.

2.3.3D kinematic parameters computation

Note that all rib landmarks clouds were registered in Th7 coordinate system at FRC position chosen as reference position. The displacement of the sternum was computed in the Th7 coordinate system using change in the position vector of the sternum body relative to the origin of the vertebra coordinate system of interest (i.e. at the midpoint between V1 and V2 in Figure 1). In addition, the sternal angle (also called angle of Louis) is usually described at MSJ level as the angle in the anatomical sagittal plane between the manubrium and the sternal body [START_REF] Kaneko | Breathing Movements of the Chest and Abdominal Wall in Healthy Subjects[END_REF][START_REF] Osmond | Functionnal anatomy of the chest wall[END_REF]. Therefore, this sternal angle was computed as the angle between the y-axes of the manubrium and sternum coordinate systems (see Figure 1B) at each breathing pose.

The kinematics of ribs AL clouds relative to sternum were computed using rigid body transformation [START_REF] Söderkvist | Determining the movements of the skeleton using wellconfigured markers[END_REF] and determination of finite helical axis (FHA) including joint pivot point (JPP) [START_REF] Beyer | In vivo thorax 3D modelling from costovertebral joint complex kinematics[END_REF][START_REF] Beyer | Effect of anatomical landmark perturbation on mean helical axis parameters of in vivo upper costovertebral joints[END_REF][START_REF] De Lange | Effects of data smoothing on the reconstruction of helical axis parameters in human joint kinematics[END_REF][START_REF] Ehrig | A survey of formal methods for determining functional joint axes[END_REF]. The rotation around FHA was used to express rib rotation relative to sternum as a single rotation component. Dispersion of FHA orientations and positions was also computed following previous recommendations [START_REF] Beyer | Effect of anatomical landmark perturbation on mean helical axis parameters of in vivo upper costovertebral joints[END_REF]. FHA positions dispersion was determined from the JPP displacements as following. First, a rectangular parallelepiped that contains (bounds) all of the JPPs was defined, aligned with the ribcage coordinate system.

Then, the length of the diagonal of this parallelepiped was calculated to define the dispersion of the JPP as a scalar value.

Finally, the mean helical axis (MHA) at each rib level was computed as the optimal direction vector with the smallest angle between FHA [START_REF] Stokdijk | Determination of the optimal elbow axis for evaluation of placement of prostheses[END_REF][START_REF] Woltring | Biomechanics of Human Movement[END_REF]. Details of the procedure to define spatial position and orientation of MHA in local coordinate systems were previously published [START_REF] Beyer | In vivo thorax 3D modelling from costovertebral joint complex kinematics[END_REF][START_REF] Beyer | Effect of anatomical landmark perturbation on mean helical axis parameters of in vivo upper costovertebral joints[END_REF]. MHA direction cosines in sternum coordinate system were then used to report axes orientation. The location of the mean rotation center (i.e. the mean pivot point (MPP), see [START_REF] Beyer | Effect of anatomical landmark perturbation on mean helical axis parameters of in vivo upper costovertebral joints[END_REF][START_REF] Woltring | Finite centroid and helical axis estimation from noisy landmark measurements in the study of human joint kinematics[END_REF]) was also determined in the sternum coordinate system.

2.4.Statistical analysis

Normal distribution of variables was verified using Kolmogorov-Smirnov test. No gender difference in ROM was found (independent t-test). Analysis of variance (ANOVA) for repeated measurements was used to evaluate the influence of the side, rib level and breathing pose on rib kinematics. A one-way ANOVA test was used to analyse the influence of breathing pose on sternal angle. The relation between rib kinematics and sternal displacements was tested using Pearson correlation coefficient (r). Values of p<0.05 were considered statistically significant. When ANOVA indicated significant difference for specific factor, Bonferroni post-hoc tests were used to determine the significant comparisons at p<0.05. A linear regression was conducted to elucidate the relation between sternum axial displacement and SCJ ROMs. Statistical analysis was performed using Statistica software (Statistica 8.0© StatSoft. Inc., Tulsa, USA).

Results

All results are given as mean ± standard errors.

3.1.Sternum displacement in thoracic vertebra coordinate system

The mean displacement of the sternum relative to vertebra Th1 was 9.6 mm ± 7.1, 17.8 mm ± 5.9 and 0.8 mm ± 2.3 along x-, y-and z-axis respectively (see figure 2). The displacement occurred mainly in cephalic (y-axis) and, to a lesser extent, anterior (x-axis) directions.

FIGURE 2

3.2.Sternal angle variations

The mean sternal angle was significantly decreasing from 16.7° ± 5.5° at TLC to 14.9° ± 5.2° at MIC (p=0.016) and to 12.4° ± 4.9° (p=0.0011) at FRC. The average ROM of the sternal angle was 4.4° ± 2.7° similarly distributed above and below MIC with respectively 1.9° ± 1.2° and 2.5° ± 2.1°.

FIGURE 3

3.3.Rib angular displacement relative to sternum

Rib1 to Rib7 angular displacements were then all expressed in sternum coordinate system to facilitate comparison and interpretation (see Figure 4). ROMs were significantly influenced by lung volume (p<0.001) and rib level (p<0.001). The interaction between the lung volume and the rib level also had a significant influence (p<0.001) on ROMs. The total ROMs gradually decreased from 15.5° ± 1.7° at Rib1 to 7.6° ± 0.8° at Rib7. Note that Bonferroni post hoc tests demonstrated no significant differences between two to four adjacent rib levels.

Above MIC, the ROMs ranged from 4.7° ± 0.9° at Rib1 to 3.9° ± 0.7° at Rib7 without any significant difference between rib levels. Below MIC, ROMs were gradually decreasing from 10.9° ± 1.8° at Rib1 to 3.7° ± 0.9° at Rib7. Note that as between TLC and FRC, no significant ROMs difference was demonstrated between adjacent rib levels (similarly as below MIC). Furthermore, from Rib1 to Rib3, ROMs significantly differed between above and below MIC while other lower rib levels (i.e. Rib4 to Rib7) were not altered by lung volume above or below MIC.

Dispersion of the FHAs and joint pivot points (JPP)

Results are presented in figure 5. The dispersion angle between FHAs was not altered by rib level (p>0.05) and ranged between 14.7° ± 1.3° and 18.5° ± 1.5°. The displacement of the JPP increased significantly with increasing rib number (p<0.001). Note that significant difference (p<0.01) was observed for all rib levels but the first one when compared to the one at Rib2.

The mean dispersion of JPP ranged between 28.9 mm ± 3.8 at Rib2 to 151.3 mm ± 10.6 at Rib7. Supplementary material 1 gives opportunity to visualize the displacement of each FHA.

Mean helical axes orientation and centers of rotation

All direction cosines for the left bones were mirrored and expressed as right sided to enable comparison between sides. The side had no significant influence on the orientation of MHAs (p=0.864) (see Figure 6).

MHA mean direction cosines ranged between -0.52 and -0.31 on x-axis; between 0.49 and 0.53 on y-axis and between 0.35 and 0.56 on z-axis. In other words, the axes were oriented obliquely caudally, ventrally and medially at all rib levels considered (i.e. Rib1 to Rib7). No significant difference were observed between rib levels (p=0.587). The interaction between rib level and x,y,z component did not show any significant influence (p=0.06), confirming that MHA orientation did not change between rib levels. An example of the 3D visualization obtained is presented in Figure 8 where the left sides MHAs are pointing obliquely caudally, ventrally and medially at each rib level.

FIGURE 6

The side had no influence on the position of the mean pivot point (p=0.701) while significant differences were observed between rib levels (p<0.001). The position of the MPP was close to 0 mm on dorso-ventral axis (x-axis), in other words close to the sternum frontal plane, laterally to the sternal body and gradually caudally regarding each rib level. See Figure 7.

Relation between rib and sternum displacement

The range of cephalo-caudal displacement of the sternum was related to the ROMs at SCJ 1 (r=0.92, p<0.001) and SCJ7 (r=0.74, p =0.006). Linear regressions were determined at these 2 levels of interest (see Figure 9). In addition, ROMs obtained in previous study at costovertebral joints [START_REF] Beyer | Effect of anatomical landmark perturbation on mean helical axis parameters of in vivo upper costovertebral joints[END_REF] were used to test the correlation and linear regression between costovertebral kinematics and cephalic displacement of the sternum. A significant correlation was demonstrated between costovertebral ranges of motion and sternum displacement at rib1 (r=0.95, p<0.001) and rib7 (r=0.81, p<0.01).

Discussion

The present study describes the sternal displacement, sternal angle variation and sternocostal kinematics between different positions obtained at three different lung volumes on a sample of 12 supine human adults. To the author's best knowledge, this is the first study reporting detailed in-vivo quantification of these specific joints of the human thorax in breathing conditions. The functional role of costal cartilages was previously analyzed in dogs using experimental approach [START_REF] Fick | Handbuch der Anatomie und Mechanik der Gelenke T[END_REF] and during in-vitro experimentation [START_REF] De Troyer | Mechanical coupling between the ribs and sternum in the dog[END_REF][START_REF] De Troyer | Sternum dependence of rib displacement during breathing[END_REF]. The linkage between sternal displacement and ribs was also described in two tetraplegic patients [START_REF] De Troyer | Rib cage motion and muscle use in high tetraplegics[END_REF]. Mechanical properties of the costal cartilages and the influence of growth on cartilage geometry were reported in the literature [START_REF] Andriacchi | A model for studies of mechanical interactions between the human spine and rib cage[END_REF][START_REF] Sandoz | Quantitative geometric analysis of rib, costal cartilage and sternum from childhood to teenagehood[END_REF]. However, the present study enabled for the first time to describe quantitative in-vivo human data related to rib and sternum kinematic behavior (i.e. ROM and axes of rotation).

The first major finding concerns averaged variation of 4.4° observed at the sternal angle. Since the sternal angle increases between each lung volume (see Figure 3), MSJ could act as a torsion spring able to store energy during lung inflation and restore it to facilitate thoracic cage deflation. This is supported by the fact that exhalation is recognized to be a mainly passive mechanism resulting from elastic recoil of mainly the lungs (i.e. pulmonary alveoli) with contribution of chest wall above 75% of the TLC (Agostoni et al., 1965a;[START_REF] Agostoni | Static Behavior of the Respiratory System[END_REF][START_REF] Osmond | Functionnal anatomy of the chest wall[END_REF]. Note that aging seems to be responsible of altering the torsion elastic modulus of cartilaginous joint leading to a decrease in rib cage compliance [START_REF] Estenne | Rib cage and diaphragm-abdomen compliance in humans: effects of age and posture[END_REF][START_REF] Sharma | Effect of aging on respiratory system physiology and immunology[END_REF]. The increase in sternal angle with increasing lung volume could have been related to the differences in rib length. Indeed, during cephalic displacement of the sternum, the shortest ribs (i.e. rib1 and 2) should lead to a backward shift of the cephalic extremity of the sternum (i.e. manubrium), and by consequence to an increase of the sternal angle.

Another result obtained in this study concerns the gradual decrease of sternocostal ROMs occurring inversely to the analyzed rib level (i.e., the larger the rib level, the smaller the related ROM). As previously underlined [START_REF] De Troyer | Mechanical coupling between the ribs and sternum in the dog[END_REF], if the rib cage behaved as a rigid entity, all ribs should display equal motions relative to the sternum. However, it was not the case in dogs for which the upper portion of the rib cage was demonstrated to behave more as a unit than the lower ribs [START_REF] De Troyer | Mechanical coupling between the ribs and sternum in the dog[END_REF][START_REF] De Troyer | Sternum dependence of rib displacement during breathing[END_REF]. The present study seems to indicate similar behavior in human, and that the rib cage does not move as a rigid entity.

The mechanical linkage between ribs and sternum is highlighted by the variability of both FHAs orientation and position of JPP during breathing motion. From a mechanical aspect, when a joint mechanism is more constrained, the dispersion of FHAs orientation and of JPP position should be smaller. The present result showed that the dispersion of FHAs orientation was similar at all SCJ levels; however, the dispersion of JPP position increased significantly and gradually from Rib1 to Rib7. This finding indicates that the constraint is probably higher at Rib1 and decreases gradually at the rib levels underneath. The supplementary material 1 enables to visualize this finding. [START_REF] De Troyer | Mechanical coupling between the ribs and sternum in the dog[END_REF] obtained in dogs largely apply to humans. Note that the decrease in sternocostal ROMs is similar to costovertebral joint motion behavior in breathing [START_REF] Beyer | In vivo thorax 3D modelling from costovertebral joint complex kinematics[END_REF][START_REF] Beyer | Effect of anatomical landmark perturbation on mean helical axis parameters of in vivo upper costovertebral joints[END_REF][START_REF] Wilson | Geometry and respiratory displacement of human ribs[END_REF] . Furthermore, the sample used in the present analysis was the same as in previously reported costovertebral joint (CVJ) analysis [START_REF] Beyer | In vivo thorax 3D modelling from costovertebral joint complex kinematics[END_REF][START_REF] Beyer | Effect of anatomical landmark perturbation on mean helical axis parameters of in vivo upper costovertebral joints[END_REF]. Comparing the CVJ and SCJ ROMs, it appears that ROMs were systematically smaller at SCJ than at CVJ levels. This difference in ROMs could be attributed to the difference in MHA orientation at CVJ and SCJ (i.e. which are not parallel) and moreover the small rotation obtained at each intervertebral joint [START_REF] Beyer | In vivo thorax 3D modelling from costovertebral joint complex kinematics[END_REF].

Results of the present study indicates that the conclusion of De

In addition, the significant influence of lung volume and rib level on SCJ ROMs amplitude is a behavior that was already observed at CVJ levels [START_REF] Beyer | Relationship between costovertebral joint kinematics and lung volume in supine humans[END_REF]. Similar to CVJs, SCJ ROMs decreased above MIC. Besides, this observation was not true for all rib levels. Indeed, only Rib1 to Rib3 showed larger SCJ ROMs below MIC, while Rib4 to Rib7 showed similar ROM above or below MIC. Previous CVJ analysis [START_REF] Beyer | Effect of anatomical landmark perturbation on mean helical axis parameters of in vivo upper costovertebral joints[END_REF] reported similar ROM decrease above MIC at rib level 1 to 7. These observations are in agreement with the change in rib cage compliance with increasing lung volume [START_REF] Agostoni | Static Behavior of the Respiratory System[END_REF].

Finally, to the author's knowledge, the orientation of SCJ axes of rotation (i.e., MHAs) was never previously described. MHAs observed in the present study were orientated obliquely, ventrally, downward and inward, and were not influenced by rib level. The computation of rib transformation relative to manubrium gives insight about the cartilages structures in-between.

The costal cartilages were positioned close to the sternal frontal plane and gradually oriented downward from the second to the seventh level [START_REF] Osmond | Functionnal anatomy of the chest wall[END_REF]. The orientation of the first costal cartilage was almost parallel to the 3D oblique orientation of the first MHA. At lower rib levels (Rib2 to Rib7) the MHAs were clearly intersecting the plane of the costal cartilage.

Note that the position of the MPP followed the position of the costal cartilage, (see figure 7 along y-axis). Mechanically, MHA orientation variations indicate different costal cartilage behavior during breathing. From a mechanical point of view, when the axis of rotation is following the natural longitudinal axis of a costal cartilage (like for the first costal cartilage), one might assume that such costal cartilage is working as a one degree of freedom torsion bar (or spring) with a torque generated perpendicular to the axis of the bar. However, for lower rib levels (i.e., with MHAs intersecting the cartilage) the torque generated during inflation should be considered around multiple degrees of freedom. These considerations are in agreement with the fact that the first rib is more rigidly attached to the first costal cartilage and to the sternum, but also with the complex morphology of the lower costal cartilages. Thus, it could be considered that the first SCJ is driving the rib cage displacement, and is not able to deform as much as the SCJ underneath. Some other limitations of the study merit discussion. Results obtained in the present work were determined from an in-vivo sample of young adults (average age 30 yrs) and should not be generalized to elderly or infants for various reasons. Indeed, previous studies reported that ageing tends to modify both thoracic shape [START_REF] Gayzik | Quantification of age-related shape change of the human rib cage through geometric morphometrics[END_REF][START_REF] Joshua | Variations in Dimensions and Shape of Thoracic Cage with Aging: An Anatomical Review[END_REF][START_REF] Kent | Structural and material changes in the aging thorax and their role in crash protection for older occupants[END_REF] and material properties of costal cartilages [START_REF] Forman | The effect of calcification on the structural mechanics of the costal cartilage[END_REF][START_REF] Guo | Age and gender related changes in biomechanical properties of healthy human costal cartilage[END_REF][START_REF] Lau | Indentation stiffness of aging human costal cartilage[END_REF]. Indeed, costal cartilages often undergo progressive calcification with age [START_REF] Semine | Costochondral Ossification and Aging in Five Populations[END_REF] resulting in an increase of cartilage stiffness [START_REF] Forman | The effect of calcification on the structural mechanics of the costal cartilage[END_REF][START_REF] Lau | Indentation stiffness of aging human costal cartilage[END_REF] and a decrease in rib cage compliance [START_REF] Estenne | Rib cage and diaphragm-abdomen compliance in humans: effects of age and posture[END_REF][START_REF] Sharma | Effect of aging on respiratory system physiology and immunology[END_REF]. Following the present interpretation of considering costal cartilage as a torsion spring, it is relevant to expect that the change in costal cartilage stiffness with ageing will be translated in a decrease of SCJ ROMs.

Finally, changes in posture have been demonstrated to alter rib cage compliance [START_REF] Estenne | Rib cage and diaphragm-abdomen compliance in humans: effects of age and posture[END_REF] and supine position was shown to increase rib cage circumference (Agostoni et al., 1965b) by changing the slope of the rib orientation [START_REF] Sharp | The rib cage in normal and emphysematous subjects: a roentgenographic approach[END_REF]. As previously reported [START_REF] Sharp | The rib cage in normal and emphysematous subjects: a roentgenographic approach[END_REF](Sharp et al., , p. 1986), these modifications could be adequately explained by the change in orientation of the gravity vector that induce a change in orientation of the gravitational pull exerted on the ribs and their attached structures (i.e. muscles and fascia).

Conclusion

To the authors' best knowledge, the present study is the first to describe sternocostal joint behavior quantitatively in breathing humans. Reported results are of interest to improve our current understanding related to normal thorax joints physiology and present data should be useful for modelling of respiratory mechanics. Moreover, 3D representation of results enables both qualitative and quantitative kinematics visualization that can be used for pedagogical purposes. Further research will focus on the effect of pathological conditions or treatments on MSJ and SJC kinematics.

FIGURE 1

 1 FIGURE 1

FIGURE 4

 4 FIGURE 4

FIGURE 5

 5 FIGURE 5

  FIGURE 7

FIGURE 9

 9 FIGURE 9

Figure 1 :Figure 2 :

 12 Figure 1: A: Anatomical landmarks (ALs) located on vertebrae, ribs, manubrium and sternum. For ribs and vertebrae: see Beyer et al, 2015, 2016; For manubrium: M1: uppermost point of the right clavicular surface, M2: uppermost point of the left clavicular surface, M3: central point of the jugular notch, M4: at the center of manubriosternal edge on the manubrium, For sternum body: S1: on the right top of the 2 nd chondro-sternal surface, S2: on the left top of the 2 nd chondro-sternal surface, S3: at the center of manubriosternal edge on the sternum (mirror of M4), S4: at the center of the lowermost extremity of the sternum at xyphisternal joint.

Figure 3 :

 3 Figure 3: Sternal angle variations between each available lung volume in degree (°). Black stars represent significant difference (p<0.05) between lung volumes. Vertical bars denote +/-standard errors.

Figure 4 :

 4 Figure 4: Rib1 to Rib7 ROMs between each available lung volume. Results are presented in degree (°) in the sternum coordinate system. Vertical bars denote +/standard errors.

Figure 5 :

 5 Figure 5: A: Dispersion of FHAs in degree at each rib level regardless of the side. Results are expressed in degree (°), vertical bars denote +/-standard errors. B: Displacement of JPP. Results correspond to the norm of the vector that represents the "bounding box" in millimeter. Vertical bars denote +/-standard errors.

Figure 6 :

 6 Figure 6: A: MHA direction cosines according sternal coordinate system. Note that direction cosines of left ribs were mirrored and expressed as right ribs. Results are presented as mean direction cosines; vertical bars denote +/-standard errors.

Figure 7 :

 7 Figure 7: Position of the mean pivot point in sternum coordinate system. Data are presented in millimeter +/-0.95 confidence intervals along each axis of the sternal frame. Note that left sided rotation centers were mirrored to right side to allow comparison.

Figure 8 :

 8 Figure 8: 3D representation of mean helical axes (MHAs), anatomical frames and bones of interest observed in this study. Because they were not clearly visible in the original CT datasets used for this study, costal cartilages were approximated as straight lines between the anterior extremity of the rib and the insertion site on the sternum body or manubrium. The mean pivot point is displayed as a ball on each MHA. A: Frontal plane B: Sagittal plane. 3D visualization of finite helical axes during breathing motion is available in supplementary material 2.

Figure 9 :

 9 Figure 9: Rib angular as a function of cephalo-caudal displacement of the sternum at costovertebral joint (A) and sternocostal joint (B). Results are given for each of the 12 subjects, at uppermost rib1 and lowermost rib7. Ranges of motions are expressed in degree and sternum displacement in millimeter.

  FIGURE 1

Anthropometric and functional characteristics of the subjects. Values are means ± SD. All lung volumes were measured seated during functional pulmonary tests. Thoracic height was computed as distance between V3 landmark of Th1 and Th7 at functional residual capacity. Thoracic indices were measured in sagittal plane at Th1 and Th7 at FRC following Bellemare et al, 2001, as follows: (Anteroposterior / Lateral diameter)*100.

	Age, yr	30	±	6
	Sex, M/F	7 /5
	Height, cm	171	±	8
	Weight, kg	63	±	13
	TLC, l	6.25	±	1.1
	MIC, l	4.86	±	0.7
	FRC, l	3.44	±	0.43
	IC, l	2.82	±	0.87
	FEV 1	3.70	±	0.84
	Thoracic index at Th3	28.1	±	3.7
	Thoracic index at Th7	41.0	±	6.1
	Th1-Th7 height, cm	12.9	±	0.7
	Annex 1:

Acknowledgement

The authors thank the Radiology department of Erasme Academic Hospital and Dr Dufresne.

The authors are most grateful to Pr. De Troyer for helpful discussions. The authors also thank Mr. L. Campestrini for his contribution during his Master thesis related to the present paper.

Conflict of interest statement

I declare that all authors that have participated to the study and to the redaction of this manuscript have no financial and personal relationships with other people or organizations that could inappropriately influence this work.