A Degroot

R Macdonald
email: rob.macdonald@ed.ac.uk

O Richoux

B Gazengel
email: bruno.gazengel@univ-lemans.fr

M Campbell

Suitability of Laser Doppler Velocimetry for the Calibration of Pressure Microphones

Keywords: microphone calibration, LDV, PIV, CRB, uncertainties, pressure estimation PACS: 43.38.Kb, 43.58.Vb, 43.60.Qv

The details of a new approach for absolute calibration of microphones, based on the direct measurement of acoustic particle velocity using Laser Doppler Velocimetry (LDV), are presented and discussed. The calibration technique is carried out inside a tube in which plane waves propagate and closed by a rigid termination. The method developed proposes to estimate the acoustic pressure with two velocity measurements and a physical model. Minimum theoretical uncertainties on the estimated pressure and minimum measurable pressure are calculated from the Cramer Rao Bounds on the estimated acoustic velocity amplitude and phase. These uncertainties and the minimum measurable pressure help to optimize the experimental set up. Acoustic pressure estimations performed with LDV are compared with acoustic pressures obtained with a reference microphone. Measurements lead to a minimum bias of 0.006 dB and a minimum uncertainty of 0.013 dB on the acoustic pressure estimation for frequencies 1360 Hz and 680 Hz.

Measurement microphones are currently used for enclosed and free field applications. The accurate estimation of the measured pressure level requires a precise estimate of the microphone sensitivity. The sensitivity can be obtained in an absolute or in a relative manner. The absolute measurement of condenser microphone sensitivity provides primary calibration in metrology laboratories around the world.

The relative calibration technique is used to estimate the sensitivity of typical microphones used in industrial or research applications.

For relative calibration, the sensitivity of the microphone is deduced from the sensitivity of a reference microphone measuring the same pressure amplitude as the microphone under test. In the case of absolute calibration, the sensitivity of the microphone under test is estimated without using a reference microphone. For both methods the calibration can be performed on pressure and free field microphones. These two types of microphone are fundamentally similar. However, pressure microphones are designed to measure sound pressure in a field where the sound pressure has the same magnitude and phase throughout, whereas free field microphones are designed to measure sound pressure in a field where sound waves propagate freely without obstruction.

Absolute calibration can be performed by implementing the reciprocity technique [START_REF]Measurement microphones-Part2 : Primary method for the pressure calibration of laboratory standard microphones by the reciprocity method[END_REF]. This technique is based on fine modelling of the physical effects involved in the measurement process. With the reciprocity technique three microphones (A,B and C) are necessary. They are pair-wise coupled together (AB, AC, BC) by air (cavity for pressure microphone or free field for free field microphone). One of the two microphones under test emits sound while the second is used as a receiver. The electrical transfer impedance is calculated as the ratio of the receiver output voltage and the transmitter input current. The physical model of the transfer impedance between the input voltage and the output current enables estimation of the product of the two sensitivities. Repeating the process enables the three sensitivities to be deduced. Absolute calibration techniques can be viewed as a type of relative technique, the reference value being estimated by means of a physical model.

The reciprocity technique is commonly applied in enclosed field to estimate the sensitivity of a pressure microphone. This technique uses a small cavity and a good accuracy can be obtained in the sensitivity estimation, typically ±0.05 dB. The reciprocity calibration technique of microphones is approved by the International Electrotechnical Comission (IEC) and detailed in [START_REF]Measurement microphones-Part2 : Primary method for the pressure calibration of laboratory standard microphones by the reciprocity method[END_REF]. Although this method has been standardized, different authors are interested in increasing the measurement accuracy of the technique [START_REF] Guianvarc'h | Improved Formulation of the Acoustic Transfer Admittance of Cylindrical Cavities[END_REF][START_REF] Guianvarc'h | Acoustic transfer admittance of cylindrical cavities[END_REF] by developing more detailed modelling of the transfer impedance.

Free field microphone absolute calibration using the reciprocity technique has been studied by different authors [START_REF] Figueroa | A time-selective technique for free-field reciprocity calibration of condenser microphones[END_REF][START_REF] Figueroa | On the interference between the two microphones in free-field reciprocity calibration[END_REF] and has finally been standardized [START_REF]Measurement microphones-Part3 : Primary method for the free field calibration of laboratory standard microphones by the recsiprocity technique[END_REF]. The absolute calibration of microphones in free field differs from the calibration of pressure microphones. In this case, the acoustic level produced by the emitting microphone is very low and the Signal to Noise Ratio (SNR) is small. This technique also requires that both microphones be considered as point sources located at some effective distance from the membrane (the acoustic centre). The sensitivity measurement needs to estimate the locations of these acoustic centres.

Free field calibration suffers from additional problems. If the microphone distance is sufficiently short, a standing wave can appear between the two membranes. The imperfect performance of the anechoic chamber that is used to provide the free field conditions can also generate reflections which can affect the transfer impedance estimation: it is necessary to use specific signal processing techniques to clean up the measured transfer impedance [START_REF] Figueroa | A time-selective technique for free-field reciprocity calibration of condenser microphones[END_REF][START_REF] Figueroa | On the interference between the two microphones in free-field reciprocity calibration[END_REF]. As a result of these problems, it would be useful to be able to calibrate free field microphones using non-intrusive techniques which would avoid the use of a second microphone as a sound source.

Optical methods such as Laser Doppler Velocimetry (LDV) or Particle Image Velocimetry (PIV) are non-intrusive measurement techniques which enable the measurement of acoustic velocity. LDV has been used for measuring low amplitude velocities since 1976 [START_REF] Taylor | Absolute measurement of acoustic particle velocity[END_REF] while PIV has been used for measuring higher levels [START_REF] Humphreys | Digital piv measurements of acoustic particle displacements in a normal incidence impedance tube[END_REF][START_REF] Campbell | Review of LDA and PIV applied to the measurement of sound and acoustic streaming[END_REF]. LDV provides a local measurement with good time resolution while PIV provides an estimate of the shape of a velocity field in a measuring area defined by the optical system. LDV is more precise than PIV, especially for measuring low velocity amplitudes, typically less than 1 mm/s. The main drawbacks of these two techniques are the complexity of the optical system and signal processing, and the high cost of experimental systems.

Different authors have proposed calibrating a pressure microphone using LDV. The microphone is located at the end of a tube attached to a loudspeaker and a physical model enables the deduction of the acoustic pressure from a single velocity measurement. Taylor [START_REF] Taylor | Absolute calibration of microphone by a laser-doppler technique[END_REF] uses a spectral analysis of the Doppler signal delivered by the LDV system. He shows that it is possible to calibrate a condenser microphone with an accuracy of ±0.03 dB when taking a large sample of measurements, resulting in a long measurement time. MacGillivray et al [START_REF] Macgillivray | The Development of a Microphone Calibration Technique Using Laser Doppler Anemometry[END_REF][START_REF] Macgillivray | The Development of a Microphone Calibration Technique Using Photon Correlation Spectroscopy[END_REF] use the same approach to estimate the acoustic velocity with two methods, frequency analysis and Photon Correlation Spectroscopy. They show that the uncertainty in the pressure estimation is ±0.1 dB when using spectral analysis and is ±0.2 dB when using Photon Correlation Spectroscopy.

The issue of free field microphone calibration is clearly problematic. Both LDV and PIV have been used for characterising the acoustic velocity in a free field. Different authors [START_REF] Mazumder | Directional acoustic measurement by laser doppler velocimeters[END_REF][START_REF] Greated | Measurement of acoustic velocity fields[END_REF] show that the acoustic velocity can be measured with LDV. Gazengel et al. [START_REF] Gazengel | Characterization of a loudspeaker free field radiation by laser doppler velocimetry[END_REF] show that LDV can measure the acoustic velocity profile on the axis of a radiating loudspeaker. PIV has been used by Degroot et al [START_REF] Degroot | Etalonnage de microphones par Vélocimtrie Laser Doppler[END_REF] for characterising the velocity field in the vicinity of the membrane of a microphone placed in a semi free field (Fig. 1). However, these studies only deal with the measurement of acoustic velocity and do not propose to estimate the acoustic pressure. The calibration of microphones using optical non-intrusive techniques such as LDV or PIV requires the construction of a physical model of the acoustic field near the microphone membrane. Fig. [START_REF]Measurement microphones-Part2 : Primary method for the pressure calibration of laboratory standard microphones by the reciprocity method[END_REF] shows that a model with at least two dimensions should be developed for calibrating a free field microphone.

In this paper, as a first step towards being able to calibrate a free field microphone, we develop a new one dimensional physical model of the acoustic field near a microphone membrane. Building on the work of Taylor [START_REF] Taylor | Absolute measurement of acoustic particle velocity[END_REF] and MacGillivray et al [START_REF] Macgillivray | The Development of a Microphone Calibration Technique Using Laser Doppler Anemometry[END_REF][START_REF] Macgillivray | The Development of a Microphone Calibration Technique Using Photon Correlation Spectroscopy[END_REF], where the acoustic pressure was deduced from a single velocity measurement, the new model provides an estimate of the mean acoustic pressure acting on the microphone membrane from velocities measured at two different points located nearby. The new calibration method is tested on a pressure microphone in an enclosed field.

In the next section, the analytical model which yields an estimation of the acoustic pressure in the waveguide using two acoustic velocity measurements is presented. Moreover, the uncertainties in the pressure amplitude and phase are derived using the theoretical minimum uncertainty in the LDV velocity measurement.

In Section 3, the details of the experimental study are presented. First the experi-mental system used for assessing the calibration method is described and then the uncertainty analysis developed in Section 2 is applied to the design of the experiment. Finally, experimental results are presented and discussed.

2 Pressure estimation model

Pressure calculation

Consider an incident plane wave with acoustic particle velocity amplitude V 0 and wavenumber k that experiences viscothermal losses [START_REF] Bruneau | Boundary layer attenuation of higher modes in waveguides[END_REF] as it propagates from left to right along the x-axis in a waveguide having a reflection coefficient R = Re jΦ R (see Fig. 2).

x 0 The mass conservation law gives an expression relating the acoustic pressure p(x, t) and the acoustic particle velocity v(x, t)

x 1 x 2 e x ∆x V 0 e -jkx V 0 Re jkx
∂p(x, t) ∂t = -ρc 2 div( v(x, t)), (1)
where ρ is the air density at rest and c is the speed of sound. In the case of a harmonic plane wave of angular frequency ω propagating along the x axis, acoustic pressure and particle velocity can be written as

v(x, t) = V (x)e jωt e x = V (x)e jΦv(x) e jωt e x , (2)
p(x, t) = P (x)e jωt = P (x)e jΦp(x) e jωt .

(

) 3
where V (x), P (x), Φ v (x) and Φ p (x) are respectively the acoustic velocity amplitude, acoustic pressure amplitude, phase of acoustic velocity and phase of acoustic pressure at abscissa x.

Using Eqs. 1, 2 and 3,

jω P (x) = -ρc 2 d V (x) dx . (4)
Knowing that the acoustic velocity is written

V (x) = V 0 e -jkx + Re jkx , (5)
the spatial derivative of the velocity at abscissa x 0 is given by [START_REF] Pascal | Systematic measurement errors with two microphone sound intensity meters[END_REF] d

V dx | x 0 = ∆ V ∆x 1 sinc k∆x 2 , (6)
where

∆ V = V (x 2 ) -V (x 1 ) with x 1 = x 0 -∆x/2 and x 2 = x 0 + ∆x/2 (see Fig. 2).
Using Eqs. 4 and 6, the acoustic pressure at abscissa x 0 is given by

P (x 0 ) = jρc ∆ V 2 sin ( k∆x 2 ) . ( 7
)
2.2 Minimum uncertainty in the pressure estimation

General formulation

This section aims to determine the minimum uncertainty in the pressure modulus and phase using the uncertainties in the acoustic velocity measured by means of LDV and the uncertainties in the physical quantities (ρ, c, ∆x).

The relative uncertainty δP (x 0 ) P (x 0 ) in the estimation of the amplitude pressure at x = x 0 is obtained using the Eq. 7 and is written

δP (x 0 ) P (x 0 ) =   δ∆V ∆V 2 + δ(k∆x) 2|tan(k∆x/2)| 2 + δc c 2 + δρ ρ 2   1/2 , (8)
where ∆V = |∆ V |, δρ/ρ is the relative uncertainty in the density, δc/c = -δρ/2ρ is the relative uncertainty in the speed of sound, assuming that the speed of sound only depends on the density ρ considered as an equivalent density as defined in [START_REF] Gazengel | Measurement of acoustic particle velocities in enclosed sound field: Assessment of two laser doppler velocimetry measuring systems[END_REF]. The uncertainty in k∆x is defined by [START_REF] Gazengel | Measurement of acoustic particle velocities in enclosed sound field: Assessment of two laser doppler velocimetry measuring systems[END_REF]

δ(k∆x) = k∆x   δρ 2ρ 2 + δ∆x ∆x 2   1/2 . ( 9
)
In the same way, the uncertainty in the phase of the pressure can be obtained using Eq. 7 δΦ p = δΦ ∆ V (10) where Φ ∆ V is the phase of ∆ V .

Minimum uncertainty in the velocity difference

The determination of the minimum uncertainty in the acoustic pressure (Eqs. 8 and 10) requires the calculation of the minimum uncertainty in the velocity difference.

Using the notation V 1 = V (x 1 ), V 2 = V (x 2 ), Φ 1 = Φ v (x 1 ) and Φ 2 = Φ v (x 2 ), the relative uncertainty in ∆V is δ∆V ∆V = 1 (∆V ) 2 (δV 2 ) 2 [V 2 -V 1 cos(∆Φ)] 2 + (δV 1 ) 2 [V 1 -V 2 cos(∆Φ)] 2 + [V 1 V 2 sin(∆Φ)] 2 (δΦ 1 ) 2 + (δΦ 2 ) 2 1/2 , ( 11
)
where ∆Φ = Φ 2 -Φ 1 and δV 1 , δV 2 , δΦ 1 and δΦ 2 are respectively the uncertainties in velocity amplitude and phase at abscissa x 1 and x 2 .

The uncertainty in the phase of the velocity difference

Φ ∆ V is δΦ ∆ V = 1 (∆V ) 2 (δV 1 ) 2 V 2 2 sin 2 (∆Φ) + (δΦ 1 ) 2 V 2 1 -V 1 V 2 cos(∆Φ) 2 + (δV 2 ) 2 V 2 1 sin 2 (∆Φ) + (δΦ 2 ) 2 V 2 2 -V 1 V 2 cos(∆Φ) 2 1/2 . ( 12
)
The particle velocity v p (x, t) measured by LDV at abscissa x can be estimated using [START_REF] Albrecht | Laser Doppler and Phase Doppler Measurement Techniques[END_REF]

v p (x, t) = i.IF (x, t), (13)
where i is the interfringe separation of the LDV probe and

IF (x, t) = IF (x). e jφ IF (x) . e jωt (14)
is the complex instantaneous frequency defined by [START_REF] Flandrin | Time-Frequency, Time scale analysis[END_REF] IF (x, t) = 1 2π

dΦ D (x, t) dt , (15)
where Φ D (x, t) is the phase of the LDV probe signal, proportional to the particle displacement x p (t) in the probe volume (Φ D (x, t) = 2π i x p (t)). In the case of sinusoïdal acoustic excitation, IF (x, t) is estimated by specific signal processing ( Short Time Fourier Transform [START_REF] Gazengel | Evaluation of the performance of two acquisition and signal processing systems for measuring acoustic particle velocities in air by means of laser doppler velocimetry[END_REF], Cross Wigner-Ville distribution [START_REF] Valière | Acoustic velocity measurements in the air by means of laser Doppler velocimetry : dynamic and frequency range limitations and signal processing improvements[END_REF][START_REF] Valeau | Instantaneous frequency tracking of a sinusoidally frequency-modulated signal with low modulation index: application to laser measurements in acoustics[END_REF]). The amplitude IF (x) and phase φ IF (x) are estimated with a Least Mean Square Method [START_REF] Simon | Laser doppler velocimetry joint measurements of acoustic and mean flow components : Lms-based algorithm[END_REF]. The uncertainties in the acoustic velocity amplitude V and phase Φ v measured by LDV are given by

δV V = δi i 2 + δIF IF 2 , ( 16
)
δΦ v = δΦ IF , (17)
where δi i is the relative uncertainty in the interfringe separation measurement and δIF IF is the relative uncertainty in the instantaneous frequency amplitude estimation. The minimum uncertainty in the instantaneous frequency is given by the minimum variance in the estimation of the acoustic parameters V (x) and Φ v (x). This minimum variance, depending on the signal, is expressed by the Cramer-Rao Bounds (CRB), estimated using a model of the Doppler signal [START_REF] Duff | A signal processing approach for acoustic velocity measurement[END_REF] . In the case of harmonic excitation at acoustic frequency f and for low mean flow velocity encountered in an enclosed field (typically 0.5 to 2 mm/s due to thermal effects generated by the loudspeaker), Le Duff et al [START_REF] Duff | A signal processing approach for acoustic velocity measurement[END_REF] give the CRB for the acoustic velocity amplitude V (x) and phase Φ v (x)

CRB(V ) = 2 2 π F α 2 N p SNR V 2 , (18)
CRB(Φ v ) = 2 2 π F α 2 N p SNR , (19)
with

N p = 2f d x V f , (20)
F = f F s , (21)
α = V if , (22)
where V f is the mean flow velocity, F s is the sampling frequency and d x is the length of the probe volume along the x axis [START_REF] Duff | A signal processing approach for acoustic velocity measurement[END_REF].

Using Eqs. 11 and 18, the minimum relative uncertainty in the difference in velocity amplitude can be written

δ∆V ∆V min = 2 √ 2Kif ∆V   1 + δi i 2 (V 2 1 -V 1 V 2 cos ∆Φ) 2 + (V 2 2 -V 1 V 2 cos ∆Φ) 2 2∆V 2 (2Kif ) 2   1/2 , ( 23
)
where

K = 2 2 π F N p SNR . ( 24
)
Considering that the acoustic particle velocity is written as the sum of an outgoing and incoming wave (Eq. 5), the minimum relative uncertainty in the difference in velocity amplitude can be obtained using

∆V = 2V 0 sin k∆x 2 |e -jkx 0 -Re jφ R e jkx 0 |, (25)
in Eq. 23. The uncertainty in the phase of the velocity difference is

δΦ ∆ V | min = 2 √ 2Kif ∆V . (26)
Eqs. 23 and 26 show that the uncertainty in the velocity difference (amplitude and phase) is minimized for ∆V large, which occurs when measuring two velocities having the same amplitude and opposite phase.

Total minimum uncertainty in the pressure

The total relative uncertainty in the pressure amplitude estimation is found by substituting Eqs. 23 and 25 into Eq. 8

δP (x 0 ) P (x 0 ) min =       2 √ 2Kif ∆V   1 + δi i 2 (V 2 1 -V 1 V 2 cos ∆Φ) 2 + (V 2 2 -V 1 V 2 cos ∆Φ) 2 2∆V 2 (2Kif ) 2   1/2    2 + δ(k∆x) 2|tan k∆x 2 | 2 + 5 4 δρ ρ 2    1/2 , ( 27
)
with K given in Eq. 24.

The uncertainty in the pressure phase is given by

δΦ p | min = δΦ ∆ V | min , (28)
where δΦ ∆ V | min is given in Eq. 26.

Minimum measurable pressure

The minimum acoustic pressure amplitude that can be estimated using this method is given by Eq. ( 7)

P (x 0 ) min = ρc ∆V min 2 sin( k∆x 2 ) , (29)
where ∆V min is the minimum measurable amplitude of the velocity difference.

3 Experimental study

Experimental system

The experimental study aims at determining the bias and standard deviation of the pressure estimated using two velocity measurements and Eq. [START_REF] Taylor | Absolute measurement of acoustic particle velocity[END_REF]. For this, the acoustic pressure is estimated inside a tube excited with a loudspeaker at one end and closed by a rigid termination at the other end. The estimated pressure is compared with a reference pressure obtained by means of a microphone flush-mounted at the end of the tube.

Acoustic system

The acoustic set-up consists of a square cross-section duct (0.1 × 0.1 m 2 ) made of Perspex of thickness 10 mm. The cut-off frequency associated with the first transverse acoustic mode is 1720 Hz. The tube is 0.5 m long. A loudspeaker (GUO GUANG 450100) is mounted at one end of the waveguide and the other end is closed by a rigid termination (see Fig. 3). The acoustic pressure is measured at the rigid end of the tube by means of a 1/2 inch microphone (B&K 4192) connected to a preamplifier (B&K 2619) and a conditioning amplifier (B&K 2609).

LDV system

The LDV apparatus used in this study is a dual beam system operating in the differential Doppler mode. Only one velocity component is measured. The laser source, producing light of 514.5 nm wavelength in air, is installed in a separate room with the beams delivered to the lab using fibre optics. In order to get enough light intensity the forward scattering configuration is used. The laser power is 20 mW at the location of the probe volume. The focal distance of the emitting optics is 1000 mm. The angle between the two incident beams is set to about 28 deg. The probe volume length d x ≃ 0.1mm and the interference pattern contains about 100 fringes. The emitting and receiving optics are supported by a traverse system which enables to measure the velocity at different locations. The velocity sign is determined using a Bragg cell introduced in the path of one of the incident beams. The Bragg cell operates here in the -1 mode, which decreases the frequency value of the beam that is frequency shifted. The cell is driven at f B = 40 MHz. The seeding is SAFEX Super Fog Fluid, injected inside the tube.

The optical signal is converted into an electrical signal by means of a photomultiplier (PM) using a 1200 V supply. The signal is converted into two signals in quadrature and analysed using the Phase Derivative Based Estimator [START_REF] Duff | A signal processing approach for acoustic velocity measurement[END_REF] in order to estimate the instantaneous frequency. The parameters of the acoustic velocity (V , Φ v ) are calculated using a Least Mean Square Method [START_REF] Simon | Laser doppler velocimetry joint measurements of acoustic and mean flow components : Lms-based algorithm[END_REF] applied to the instantaneous frequency defined in section 2.2.2.

The acquisition of Doppler signals was performed using F s = 1 MHz and F s = 500 kHz. The velocities measured at abscissa x 1 and x 2 were estimated using 10 acquisitions, with each signal comprising of about 10 bursts. This enables 10 values of the acoustic parameters V and Φ v to be estimated. The mean of these 10 gives the estimation of acoustic velocity and the standard deviations σ V and σ Φv . The uncertainties are then δ V = 2σ V √ 10 and δ Φv = 2σ Φv √ 10 .

Experiment design

The aim of this section is to define an experimental configuration which minimizes the uncertainty in the pressure estimation. By assuming that the termination is rigid ( R = -1), the minimum measurable pressure is calculated (see Eq. 33). Then, in section 3.2.2, the uncertainties in the pressure estimated with LDV and with the reference microphone are studied. We use parameters encountered in the usual experimental configuration as given in table 1.

δρ ρ δi i δL i F s SNR V f d x
0.05% 0.1% 0.1 mm 1µm 1 MHz 15 dB 5 mm/s 0.1 mm Table 1 Values of parameters corresponding to usual experimental configuration in enclosed field.

Eqs. 27 and 28, which give the uncertainty in the amplitude and phase of the pressure estimated with LDV, are made up of three terms and one term respectively. The last term of Eq. 27 is a constant value describing the uncertainty in the air density due to the seeding. The second term of Eq. 27 shows the effect of the microphone probe spacing (term in k∆x). The first term of Eq. 27 shows the uncertainty in the acoustic velocity estimation due to the LDV signal processing (term in Kif ) and to the interfringe measurement (term in δi). Eq. 28 shows that the uncertainty in the phase depends only on the signal processing (term in Kif ). For R = -1, the uncertainty in the velocity estimation is minimized using kx 0 = mπ (m ∈ N), which means that the pressure is best estimated at one of its antinodes. This configuration is used in the experiment. Assuming that the velocity is measured at

x 1 = x 0 + ∆x 2 and
(30)

x 2 = x 0 - ∆x 2 , (31)
V1 = -V2 if ∆x is chosen correctly, which leads to V 1 = V 2 and ∆φ = π. These assumptions enable the deduction of the uncertainties in the amplitude and phase of the pressure estimated with LDV.

Minimum measurable pressure

Using the assumption V1 = -V2 , the minimum measurable amplitude of the velocity difference is written ∆V min = δV 1 + δV 2 . Using Eq. 16, Eq. 18 and Eq. 22, ∆V min is given by

∆V min = 2Kif       1 + (δi/i) 2 2Kif V 1 2    1/2 +   1 + (δi/i) 2 2Kif V 2 2    1/2     . ( 32
)
The minimum measurable pressure is given by Eq. ( 29) and takes the following form

P (x 0 ) min = ρc 2Kif | sin k∆x 2 |   1 + δi i 2 V 0 sin ∆x 2 Kif 2   1/2 . ( 33
)
Considering the acoustic field in a resonant tube and using the conservation of mass law P (x 0 ) = 2ρcV 0 | cos kx 0 |, the minimum pressure is

P (x 0 ) min = 2ρcKif | sin k∆x 2 | 1 1 -δi i 2 . ( 34
)
Fig. 4 shows the minimum pressure amplitude that can be estimated using two LDV measured velocities as a function of frequency for different spacings ∆x and using parameters given in table 1.

Uncertainty in the pressure estimation

LDV estimated pressure Eq. 30 and the condition kx 0 = π combined with Eq. 25 lead to

∆V = 4V 0 sin k∆x 2 . (35)
Eq. 30, Eq. 31 and the condition kx 0 = π combined with Eq. 5 lead to

V 1 V 2 = 2V 2 0 |1 -cos k∆x| . (36)
The total minimum relative uncertainty in the pressure amplitude estimation is

δP (x 0 ) P (x 0 ) min =   √ 2Kif 2V 0 | sin k∆x 2 | 2   1 + δi i 2 V 2 0 |1 -cos k∆x| (2Kif ) 2   + δ(k∆x) 2|tan( k∆x 2 |) 2 + 5 4 δρ ρ 2   1/2 , (37)
and the total minimum uncertainty in the pressure phase estimation is

δΦ p | min = √ 2Kif 2V 0 | sin k∆x 2 | . (38)
In order to minimize the uncertainties given in Eqs. ( 37) and (38), the probe spacing ∆x should satisfy k∆x 2 = (2n + 1) π 2 (n ∈ N), which corresponds to ∆x = (2n + 1)λ/2, λ being the acoustic wavelength. However this spacing can be very large for low frequencies and such configurations can be unusable. For this reason, different values of ∆x are used in the experiment. Eqs. 37, 38 show that the uncertainty is minimized if the velocity amplitude is large. Excitation of the tube at the resonance frequency is therefore favourable. The uncertainties in the pressure amplitude and the pressure phase, estimated with LDV, are shown in Fig. 5 and6 respectively for an acoustic frequency of 680 Hz and a spacing ∆x = 6.25 cm .

Microphone reference pressure

The reference pressure Pref (x) is obtained using the pressure Pe measured by a microphone mounted flush at the end of the tube Pref (x) = Pe cos (kx).

The relative uncertainty in the reference pressure amplitude at x 0 is given by

δP ref (x 0 ) P ref (x 0 ) =   δP e P e 2 + (δ(kx 0 ) tan kx 0 ) 2   1/2 , (40)
with

δP e P e =   δU c U c 2 + δU e U e 2 + δU f U f 2   1/2 , (41)
where δU c /U c is the relative uncertainty due to the microphone calibrator, δU e is the uncertainty in the measured voltage of the reference microphone due to variation of the air density during the measurement duration and δU f is the uncertainty in the calibration voltage (δU f = U res /3 with U res the resolution of the sinusoidal voltage signal). The relative uncertainty δP ref (x 0 )/P ref (x 0 ) equals δP e /P e using the condition kx 0 = π.

Considering that the excitation frequency is a resonant frequency of the tube (680 Hz), we choose values of ∆x which minimize the uncertainty in the pressure amplitude for an acoustic level of 90 dB SPL (see table 2). For frequency f = 680 Hz and a probe spacing ∆x = 6.25 cm, Fig. 5 and Fig. 6 show the uncertainty in the pressure amplitude and phase estimation as a function of the acoustic level measured at the rigid end of the tube for different Doppler Signal to Noise Ratio. These figures show that for a SNR of 15 dB, which is commonly encountered in LDV measurement, the minimum relative uncertainty in the pres-sure amplitude is less than 0.06 dB if the acoustic level is greater than 90 dB SPL . The minimum uncertainty in the pressure phase is less than 2.6 degrees if the acoustic level is greater than 90 dB SPL . These uncertainties are mainly due to the signal processing (first term in Eq. 37) especially when the acoustic level is low (90 dB SPL : 3.5.10 -4 dB and 49 dB SPL : 3.52 dB for a SNR= 15 dB). The uncertainty associated with the second term of Eq. 37 does not depend on the acoustic level and is about 2.10 -5 dB.

Results

Experimental results have been obtained using the conditions given in Table 2. In this experiment, the reference microphone was calibrated using a B&K 4231 calibrator with accuracy ±0.2 dB SPL . 2 Values of parameters used for making the experiment in enclosed field.

Initially, the velocity pattern in the tube was measured at f = 680 Hz and at an acoustic level of 120 dB using LDV and compared with the velocity Vref (x) = j sin kx ρc Pe (42) estimated using pressure Pe measured at the end of the tube. Fig. 7 shows that LDV provides an estimate of the velocity pattern which is in good agreement with the reference velocity. However, a bias of 1.8 mm/s (2.6 % corresponding to 0.22 dB SPL ) can be seen between the two curves.

Secondly, the pressure at x 0 = λ/2 was estimated with LDV and compared with the reference pressure as shown in Fig. 8. For these experiments, the acoustic velocity was measured using a single LDV probe, moving between the two measurement points x 1 and x 2 with the traverse system (section 3.1.2). The measurement was repeated 10 times after the seeding was introduced into the tube. In this configuration, the acoustic pressure amplitude changes during the experiment because the air density varies with the seeding density. These variations serve to maximise the uncertainties in the reference and estimated pressures due to the finite time for the displacement of the traverse system between the two measurements. These uncertainties would be smaller with two simultaneous LDV measurements.

The observed bias values (mean of the difference between reference and estimated

Φ v Φ v,ref (b)

Conclusion

This work deals with the estimation of acoustic pressure using acoustic velocity measured with LDV. A physical model of plane wave propagation in a waveguide is developed to calculate the pressure from two velocity measurements. This model is based on the mass conservation law. It can be seen as the equivalent of the model used for acoustic intensity measurement in the case of a 1D propagation model.

The theoretical minimum uncertainty in the LDV measured velocity given by the Cramer Rao Bounds is used in order to deduce the uncertainty in the pressure amplitude and phase. Moreover, this provides knowledge of the minimum measurable pressure level which is about 50 dB SPL for usual conditions encountered inside a waveguide (with small mean flow velocity).

The estimation technique is assessed experimentally using a tube excited by a loudspeaker. The uncertainty analysis is incorporated into the design of the experiment.

To define the maximum admissible uncertainty, the optimal position for estimating the pressure, the optimal spacing between the two velocity measurements, the optimal frequency and the minimum acoustic level are determined.

The LDV estimated pressure is compared with reference pressure obtained from a microphone located at the end of the tube. Results show a bias in the interval [-0.36; 1.07] dB and a relative uncertainty in the pressure estimated by LDV of [0.013; 0.11] dB. Bias and uncertainty values remain small (minimum bias of 0.006 dB and minimum relative uncertainty of 0.013 dB) in some cases and show that it is possible to estimate the pressure with two velocity measurement in a waveguide excited with a plane wave. Large values of bias can be explained by errors that can occur when calibrating either the microphone or the LDV probe. Uncertainties observed experimentally show values broadly in agreement with the theoretical approach using the Cramer-Rao Bounds. For example, an acoustic level of 90 dB SPL leads to theoretical relative uncertainties under 0.06 dB and experimental relative uncertainties between [0.03; 0.1] dB. As the acoustic level becomes higher, theoretical uncertainties in the pressure estimated by LDV diminish (level > 120 dB SPL , uncertainties < 0.015 dB).

The absolute calibration of microphones can be performed with LDV measurements if the acoustic level is high enough, typically 120 dB SPL . In these conditions, experimental uncertainties are in the interval [0.013; 0.055] dB. This spread of values can be explained mainly by the fact that the two velocity measurements are not performed simultaneously and that the physical state of the system changes over the measurement duration. The uncertainty in the pressure estimation could therefore be lowered by using a system with two LDV probes measuring the two velocities at the same time.

Figure 1 .

 1 Figure 1. View of the velocity field in front a one inch microphone membrane measured with PIV [16].

Figure 2 .

 2 Figure 2. Schematic view of the problem

Figure 3 .

 3 Figure 3. View of the acoustic system.

Figure 4 .

 4 Figure 4. Minimum measurable pressure level with LDV as a function of the acoustic frequency f for different probe spacings ∆x (-25 cm, -• -12.5 cm and --6.25 cm)

Figure 5 .

 5 Figure 5. Uncertainty in the pressure amplitude estimated with LDV as a function of the acoustic level for an acoustic frequency of 680 Hz and a spacing ∆x = 6.25 cm (-SNR= 5 dB, --SNR= 10 dB, -• -SNR= 15 dB and • • • SNR= 20 dB).

Figure 6 .

 6 Figure 6. Uncertainty in the pressure phase estimated with LDV as a function of the acoustic level for an acoustic frequency of 680 Hz and a spacing ∆x = 6.25 cm (-SNR= 5 dB, --SNR= 10 dB, -• -SNR= 15 dB and • • • SNR= 5 dB).

  f (Hz) x 0 (kx 0 = π) (cm) Level (dB SPL )∆x(cm) (4) 6.25 (5) 12.5 (6) Table

Figure 7 . 5 PPFigure 8 .

 758 Figure 7. Velocity profile in the tube for an acoustic level of 120 dB SPL and an acoustic frequency of 680 Hz.

  complex amplitude IF e jφ IF of the instantaneous frequency of the Doppler signal IF (x) amplitude of the instantaneous frequency of the Doppler signal Φ IF phase of the instantaneous frequency of the Doppler signal

	Notations SNR 1 Introduction Doppler Signal to Noise Ratio
	CRB	Cramer Rao Bounds for Doppler signal model
	F s	Sampling frequency
	Acoustics
	General
	k	wavenumber
	ρ	air density at rest
	c f ω x j = v p (x, t) √ -1	speed of sound at rest acoustic frequency acoustic angular frequency is a complex value particle velocity
	v(x, t) V f	acoustic particle velocity mean flow velocity amplitude
	V (x)	acoustic particle velocity amplitude
	Φ v	acoustic particle velocity phase
	p(x, t) P (x)	acoustic pressure complex acoustic pressure amplitude
	P (x)	acoustic pressure amplitude
	Φ p R	acoustic pressure phase acoustic reflection coefficient in velocity
	R	acoustic reflection coefficient amplitude
	Φ R Pe (x) Pref (x)	acoustic reflection coefficient phase complex pressure amplitude at the rigid termination reference pressure
	Optics
	i	interfringe separation
	d x	probe volume length
	IF (x)
	Geometry
	x 1	position of measurement 1
	x 2	position of measurement 2
	∆x = x 2 -x 1
	Signal processing

  pressure) are in the interval [-0.36; 1.07] dB with an absolute minimum of 0.006 dB.The largest biases could be due to large uncertainties in the estimated pressure but for both cases (92.7 and 120 dB ), the different results show a low variance. For this reason, we explain the largest biases by the errors made when calibrating the reference microphone at the end of the tube. Results show relative uncertainties in the reference pressure of around 0.2 dB. The relative estimated pressure uncertainties are in the interval [0.15; 1.27] % corresponding to [0.013; 0.11] dB for the acoustic level between [90; 124] dB SPL . Concerning the estimated phase, the uncertainties are in the interval [0.34; 1.77] deg.Results show a relatively good correlation between experimental uncertainties on the estimated pressure (amplitude, phase) and theoretical uncertainties obtained with the CRB. CRB give, for all the configurations tested, relative uncertainties on the amplitude of under 0.06 dB for an acoustic level greater than about 90 dB SPL . For the phase, theoretical uncertainties are under 2.6 deg for an acoustic level greater than 90 dB SPL . Even if uncertainties obtained in the pressure estimated with LDV (amplitude [0.013; 0.11] dB and phase [0.34; 1.77] deg) reach higher values for the amplitude than the theoretical uncertainties, the experimental and theoretical ranges are of the same order of magnitude.


Anastasia Nyman Iliadou
email: anastasia.iliadou@ki.se

Ilona Koupil

Eduardo Villamor

Daniel Altman

Christina Hultman

Niklas Langstrom

Sven Cnattingius

Iliadou An

Långström

Familial factors confound the association between maternal smoking

Keywords: smoking, body mass index, siblings

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

We also investigated the association within siblings, controlling for common genes and shared environment.

Results:

In the cohort analyses, the risk of overweight was increased in sons of smoking mothers compared to sons of non-smokers: adjusted odds ratios(OR) 1.42, 95% confidence interval (CI) 1.35 to 1.49, and 1.56, 95% CI 1.46 to 1.66, for 1-9 cigarettes per day, and more than 10 cigarettes per day, respectively. Stratifying for maternal smoking habits across two subsequent male pregnancies, there was an increased risk of overweight for the second son only if the mother was smoking in both male pregnancies. The effect of smoking during pregnancy on the offspring's body mass index (BMI) was not present when the association was evaluated within full and half sibling pairs.

Conclusion:

The association between maternal smoking during pregnancy and offspring's risk of overweight appears to be confounded by familial factors.

INTRODUCTION

Maternal smoking during pregnancy is causally associated with fetal growth restriction 1 . It has also been associated with increased risks of adverse outcomes in the long term, including obesity 2 , which is considered an "epidemic" of our time. An association between maternal smoking during pregnancy and childhood obesity has been found in several recent studies, although the mechanism by which prenatal smoking exposure influences offspring's risk of overweight remains uncertain [2][3][4][5][6][7] .

Although high birth weight for gestational age is associated with increased risk of obesity in the offspring 8 , it has also been suggested that a reduction in fetal growth may "program" the newborn child to later develop obesity [9][10][11] . Whether the association between maternal smoking during pregnancy and obesity is mediated through fetal growth restriction per se remains unclear.

However, a recent meta-analysis of 14 studies showed an association between maternal smoking during pregnancy and child overweight independent of birth weight 2 .

Recently, novel approaches have been used in observational studies to elucidate the etiology behind the association between maternal smoking during pregnancy and a range of outcomes.

For example, by examining changes in maternal smoking behavior from one pregnancy to another, we can partially control for unmeasured familial confounding such as common genes and shared environment 12 . D' Onofrio et al. found that the association between smoking during pregnancy and externalizing behavior problems was due to unmeasured environmental factors when comparing offspring with their own siblings 13 . Similarly, in a large study of children from the Collaborative Perinatal Project, the associations of maternal smoking during pregnancy and several outcomes related to cognitive and physical development of the offspring (including intelligence, academic achievement, Apgar score, conduct problems and asthma) were entirely explained by measured or unmeasured familial confounders 14 .

In the present study of young Swedish males who underwent military conscription, we aim to investigate the association between maternal smoking during pregnancy and obesity in early adulthood, controlling for measured (such as parental socioeconomic status, education level, and maternal pregnancy characteristics) and unmeasured familial confounders (such as common genes and shared childhood and early adolescent environment).

METHODS

Study Sample

There were 305 896 Swedish males born between 1983 and 1988 and recorded in the Swedish Medical Birth Register. We excluded multiple births (N= 6000), infants with congenital malformations (N= 14 736), and males born to non-Scandinavian mothers (N= 18 793) to increase the homogeneity of the study population. After also excluding 2028 males who died before 18 years of age and 4588 that emigrated, the sample consisted of 259 751 males, of whom 201 896 went through military conscription up until 2006. BMI at conscription, calculated from measured weight and height as kg/m 2 , was available for 132 838 individuals. Information on maternal smoking during pregnancy was available in 124 203 of them, and this constituted the final sample. It is not known why some males who underwent conscription have missing information on height and/or weight. However, we noted that their mothers were significantly younger, shorter, smoked more during pregnancy, more often did not live with the father of the child, and that both parents had on average lower socioeconomic status and educational level. The offspring were significantly older at conscription, were born with lower birth weight, birth length, and head circumference, and were less often the first born son.

Data Sources

The cohort was set up through linkages of national registers: the Medical Birth Register, the Military Service Conscription Register, the Multigeneration Register, the Population and Housing Census in 1990, and the Register of Education in 2000. The linkage was possible through the unique National Registration Number assigned to each Swedish resident at birth. Information about maternal smoking during pregnancy has been routinely included in the Swedish Medical Birth Register since 1983 15 . Self-reported information about smoking habits is collected and recorded by the midwives at the first antenatal visit (usually at 8 to 12 gestational weeks), and is categorized as non-smoker, smoking 1-9 cigarettes per day, and smoking at least 10 cigarettes per day. Information on maternal pre-pregnancy weight and height, pregnancy weight gain, mode of delivery, age at delivery, living with the father of the child, Apgar score at 5 minutes, birth order (in the present study first born child who is also a son or not), infant's birth weight, birth length, head circumference, and gestational age were retrieved from the Medical Birth Register. Birth weight, birth length, and head circumference were standardized according to Swedish reference standards for weight, length, and head circumference at birth for given

Statistical Analysis

We used generalized estimating equation models to estimate odds ratios and 95% CI for overweight in early adulthood in relation to maternal smoking during pregnancy, birth characteristics, and other parental and adult characteristics. An exchangeable correlation matrix was specified in order to control for the correlations between siblings (PROC GENMOD, SAS Institute, Inc, Cary, NC). Associations between birth and parental characteristics with offspring's risk of overweight were estimated using both univariable and multivariable analyses. Risks of overweight associated with smoking during pregnancy were presented in two multivariable models. In the first model we adjusted for parental characteristics and in the second model we additionally adjusted for birth characteristics. The models only included variables that influenced the risk of obesity.

To examine whether a possible effect of maternal smoking on overweight in male offspring in early adulthood was influenced by unmeasured familial factors, we proceeded in two ways. First, we estimated the risks of overweight in first and second-born sons, stratified by maternal smoking habits across the first and second male pregnancies. Risks of overweight by changes in maternal smoking habits in two subsequent male pregnancies were estimated in both first-and second born male siblings separately by using logistic regression models. Second, to further elucidate the importance of common genes and/or shared childhood environment (familial confounding), we estimated the effects of maternal smoking during pregnancy on continuous 18 . Full and half siblings share, on average, 50% and 25% of their segregating genes, respectively, while all of them share childhood environment to a large extent. Maternal smoking during pregnancy is decomposed into a within-family effect. The within-family effect estimates the expected change in offspring BMI by a one unit change in maternal smoking behavior between male pregnancies. A within-family score is assigned to each son, defined as the difference between smoking status at the index pregnancy and the mean value of maternal smoking status across the two pregnancies 18 . For example, if a mother smoked in one pregnancy but not the other, the exposed sibling would have a within-score of 0.5 and the unexposed would have a within-score of -0.5. This within score compares exposure to maternal smoking during pregnancy relative to their sibling's exposure. If familial factors are of importance they would tend to make family members more alike. Hence we would expect the within-family estimates to be smaller than the effects shown in the cohort. We carried out these analyses separately among full and half sibling pairs. Further, by investigating the within-family association according to two different degrees of kinship (full or half siblings), and relating it to the results from the cohort analysis, we can elucidate whether or not common genes are likely to confound the association. If the size of the within effect of maternal smoking during pregnancy and offspring BMI is weaker in half compared to full siblings, the association is likely to be confounded by common genetic factors. In order to test whether the magnitude of the within family component was different according to kinship, an interaction between a kinship index (coded 1for full siblings, 0 for half siblings) and the within family component was tested.

Analyses were done with PROC MIXED in SAS v 9.2. 1 presents parental and birth characteristics with respect to prevalences and crude odds ratios of overweight in the cohort of young males. Prevalences of overweight in offspring increased monotonically with maternal BMI and reached up to 47.6 % in mothers with a BMI above 30. Compared with sons of mothers with normal BMI (18.5-24.9), sons of overweight and obese mothers experienced a 2.6-fold (95% CI, 2.49 to 2.71) and a 4-fold (95% CI, 3.73 to 4.52) increased risk of overweight, respectively. The risks of overweight were also increased in sons born to younger or shorter mothers, mothers who experienced very large pregnancy weight gains (≥17 kg), mothers and fathers of lower socioeconomic status and educational level, in large-forgestational age boys (defined as larger than 2 standard deviation scores), in sons who were older at the time of conscription, and in offspring living in rural areas.

RESULTS

F

Rates of maternal smoking during pregnancy increased with decreasing maternal age and height, with decreasing maternal and paternal socio-economic position and education, and were higher among mothers with either very low or high BMI and mothers not living with the father of the child. Offspring with lower birth weight, birth length and head circumference showed higher rates of maternal smoking. Shorter gestational ages were also related to higher rates of maternal smoking during the 1 st trimester (data not shown).

Compared with the offspring of non-smokers, there was a 51% (95 % CI, 46% to 57%) and a 72% (95% CI, 65% to 80% ) increase in risk of overweight in the sons of mothers who smoked 1-9 cigarettes /day and more than 10 cigarettes /day, respectively (Table 2). In the analyses, a correlation matrix was specified in order to control for the correlations between siblings in the cohort. These associations were slightly attenuated when adjusting for parental characteristics 2). Finally, birth characteristics, such as birth weight, may be considered to be in the causal pathway between maternal smoking during pregnancy and offspring risk of overweight. Therefore we adjusted for these in the last model (fully adjusted). Although, large for gestational age boys were at increased risk of overweight in early adulthood (Table 1), adjusting for birth characteristics did not change the associations between maternal smoking during pregnancy and offspring overweight risk (Table 2). Due to missing measurements in various confounders, a complete case analyses was also done showing essentially the same results (Table 2). Complete case analyses was carried out with the restricted sample of subjects (N=68 248), without missing information on any of the co-variates, across all three regression models. Since there seemed to be a linear trend in the risk of overweight with maternal smoking habits the analyses were also done considering offspring's BMI as a continuous outcome and maternal smoking during pregnancy dichotomized as yes or no. The regression coefficients after full adjustment showed an increase of 0.69 (95% CI, 0.62 to 0.75) BMI units if the mother smoked (Table 2).

We did not find any interactions between maternal smoking during pregnancy and any of the confounding variables we adjusted for.

The results from comparing the risk of overweight in first and second born sons in relation to the mothers' smoking habits across pregnancies are shown in Table 3. In the crude analyses, sons of mothers who smoked in both pregnancies were at increased risk of overweight; this association was still evident after adjustments for birth and parental characteristics (adjusted OR 1.65, 95% CI 1.35 to 2.01 for the first son and adjusted odds ratio 1.71, 95% CI 1.39 to 2.09 for the second ). If mothers smoked only during their first male pregnancy or only in their second male pregnancy, the adjusted risk estimates of overweight in both first and second born sons were smaller.

Finally, to investigate the importance of familial factors, we studied the effect of maternal smoking during pregnancy on BMI among full-and half-siblings (Figure). In the half-sibling subset, there was no within-family effect of maternal smoking during pregnancy (adjusted within family component: 0.07, 95% CI, -4.32 to 4.45). Although the full sibling effect of 0.39 (95% CI, -0.01 to 0.78) was higher than the half sibling effect the interaction between kinship and the within family component, indicated no difference in the magnitude of the effect of maternal smoking during pregnancy between full and half siblings (p-value 0.79). Given that the withinfamily associations were much smaller compared to the cohort effect, it is likely that the effect of maternal smoking during pregnancy on the offspring's BMI is partly confounded by familial factors.

DISCUSSION

We found that the association between maternal smoking during pregnancy and risk for overweight in young adult male offspring can be explained partly by parental socioeconomic status and education, but also by unmeasured familial factors.

In the cohort analyses we found an association of maternal smoking during pregnancy and risk of overweight in male offspring. This association has been shown in previous studies 2, 5-7, 19, 20 .

Recently, a systematic review and meta-analysis on the subject showed a significant increase in

F o r R e v i e w O n l y
13 child overweight with maternal smoking during pregnancy 2,4 . Moreover, animal studies have also shown that prenatal nicotine exposure resulted in metabolic changes in the offspring that were consistent with obesity and type 2 diabetes [21][22][23] . However, it is difficult to extrapolate the results of animal studies to humans. Smoking behaviors vary a lot, since not all smokers inhale cigarette smoke the same way and some individuals may be more or less affected, or metabolize toxins in smoke differently, compared to the controlled environments of animal studies 24 .

The adverse effects of smoking during pregnancy on fetal development are well known 1,25 . In the current study, smoking-related birth outcomes such as birth weight and gestational age did not mediate the association between smoking during pregnancy and overweight in the offspring.

This indicates that any effect of prenatal smoking exposure on offspring risk for overweight may be independent of fetal growth or gestational age.

In the current study we were able to adjust for a range of covariates that have been shown to be important predictors of adult obesity 26,27 , including maternal pre-pregnancy BMI and gestational weight gain, as well as parental socioeconomic status and educational level. However, it is almost impossible to control for all potential confounders. A study of 1 110 mother-child pairs showed that a combination of four modifiable pre-and postnatal determinants, including prenatal smoking, large gestational weight gain, absence or short duration of breastfeeding, and short duration of infant sleep, were associated with higher risks of childhood overweight than each factor individually 19 . A Japanese study of 1 417 mother-child pairs showed that maternal lifestyle habits along with smoking during pregnancy were important risk factors for childhood obesity 20 . Although we have not adjusted for breastfeeding, and other maternal and adult important predictors of adult obesity, but concluded also that residual confounding in these associations could not be excluded. However, studies have also shown that paternal smoking is almost equally important for childhood obesity 6,28 , indicating that parental smoking is more likely to be a surrogate for social factors associated with obesity 29 .

One way of elucidating the importance of unmeasured confounders common to both exposure and outcome is by investigating the effects of changing smoking patterns in subsequent pregnancies and within families 12 . In the analyses of subsequent male births we could only observe an effect of maternal smoking during pregnancy on the first and second male pregnancies as long as the mother smoked during the first trimester in both pregnancies. This could either indicate that smoking reaches harmful levels only if it is persistent and/or reaches a specific threshold level. It could also indicate that the timing of smoking during pregnancy is important for fetal development, since some studies have indicated that the effect of intrauterine tobacco exposure on childhood obesity may depend largely on cigarette smoking during the first trimester 5,7 . Lastly it could indicate residual confounding that we have not accounted for, since smoking was only known for the first trimester.

The within-sibling analyses indicated that familial factors shared within a family may account for the association between maternal smoking during pregnancy and risk of overweight in early adulthood. To our knowledge this is the first study to investigate whether there is a direct effect of maternal smoking during pregnancy on offspring overweight or whether the association is due to unmeasured familial confounding. In the current study, the association diminished in both full

F o r R e v i e w O n l y
15 and half siblings, indicating that regardless of how many genes siblings have in common, it is the shared environment that accounts for the association and that direct effects of maternal smoking during pregnancy on offspring overweight may be small. Shared environment could include lifestyle factors that are common in mothers and their offspring such as dietary habits established during early childhood, or other lifestyle behaviors such as attitudes towards physical activity 30 .

However, due to a limited number of half siblings the results should be interpreted with caution, since the lack of association among half siblings could be due to random error. Further, the point estimate for full siblings showed that there could still be a small effect of maternal smoking during pregnancy, which compared to half siblings would perhaps indicate the importance of common genetic factors shared within family members to the studied association.

The main strengths of this study are its size, the prospective design, and the range of covariates gathered from population-based registries that we could adjust for. However, limitations include self-reported data on maternal smoking during pregnancy which was collected at the first prenatal care visit, and hence is limited to the duration of smoking during the first trimester. The proportion of women who stop smoking during pregnancy has been reported to be around 30% in previous Swedish studies. However, in Sweden during the 1980's, 11% of smokers at time for registration to prenatal care stopped smoking later during pregnancy 31 . Women with a higher level of education and a higher age at the initiation of smoking were more likely to stop smoking when pregnant, while women not living with the father of the child, heavy smokers, and women exposed to daily passive smoking at home were more likely to continue smoking throughout the pregnancy 32,33 . We therefore adjusted for parental socioeconomic status, age and whether the mother was living with the father of child. Further, previous studies on smoking patterns and

F o r R e v i e w O n l y
16 risks in successive pregnancies from the Swedish Medical Birth Register have found that women who smoke in the first but not in the second pregnancy reduce their risks of preterm birth 34 , stillbirth 35 and placental abruption 36 in the second pregnancy, outcomes all likely to be causally associated with prenatal smoking. In contrast, when studying prenatal smoking and offspring school grades 12 , we find, similar to the present results, that the association disappeared when we account for familial effects. However, misclassification of smoking exposure between pregnancies or residual confounding may have influenced the risk estimates obtained. Finally, most pregnant smokers continue to smoke after pregnancy, and we cannot distinguish between the effects of prenatal and postnatal smoking exposure. Also, information on BMI was only available in males and we could not explore potential gender differences in the effect of maternal smoking during pregnancy. The conscripts with missing BMI data (about 34%) were born to mothers who smoked more during pregnancy than the males included for analyses; thus there might be some room for selection bias.

Maternal smoking during pregnancy is from a preventive view recognized in many countries as the most important risk factor for adverse pregnancy outcomes 31 • The association is partly confounded by familial factors.

• Specific familial factors common to both maternal smoking during pregnancy and offspring overweight need to be identified.

F

F o r R e v i e w

O n l y We also investigated the association within siblings, controlling for common genes and shared environment.

Results:

In the cohort analyses, the risk of overweight was increased in sons of smoking mothers compared to sons of non-smokers: adjusted odds ratios(OR) 1.42, 95% confidence interval (CI)

1.35 to 1.49, and 1.56, 95% CI 1.46 to 1.66, for 1-9 cigarettes per day, and more than 10 cigarettes per day, respectively. Stratifying for maternal smoking habits across two subsequent male pregnancies, there was an increased risk of overweight for the second son only if the mother was smoking in both male pregnancies. The effect of smoking during pregnancy on the offspring's body mass index (BMI) was not present when the association was evaluated within full and half sibling pairs.

Conclusion:

The association between maternal smoking during pregnancy and offspring's risk of overweight appears to be confounded by familial factors. Although high birth weight for gestational age is associated with increased risk of obesity in the offspring 8 , it has also been suggested that a reduction in fetal growth may "program" the newborn child to later develop obesity [9][10][11] . Whether the association between maternal smoking during pregnancy and obesity is mediated through fetal growth restriction per se remains unclear.

However, a recent meta-analysis of 14 studies showed an association between maternal smoking during pregnancy and child overweight independent of birth weight 2 .

Recently, novel approaches have been used in observational studies to elucidate the etiology behind the association between maternal smoking during pregnancy and a range of outcomes.

For example, by examining changes in maternal smoking behavior from one pregnancy to another, we can partially control for unmeasured familial confounding such as common genes and shared environment 12 . D'Onofrio et al. found that the association between smoking during pregnancy and externalizing behavior problems was due to unmeasured environmental factors when comparing offspring with their own siblings 13 . Similarly, in a large study of children from the Collaborative Perinatal Project, the associations of maternal smoking during pregnancy and In the present study of young Swedish males who underwent military conscription, we aim to investigate the association between maternal smoking during pregnancy and obesity in early adulthood, controlling for measured (such as parental socioeconomic status, education level, and maternal pregnancy characteristics) and unmeasured familial confounders (such as common genes and shared childhood and early adolescent environment).

METHODS

Study Sample

There It is not known why some males who underwent conscription have missing information on height and/or weight. However, we noted that their mothers were significantly younger, shorter, smoked more during pregnancy, more often did not live with the father of the child, and that both parents had on average lower socioeconomic status and educational level. The offspring were significantly older at conscription, were born with lower birth weight, birth length, and head circumference, and were less often the first born son.

Data Sources

The cohort was set up through linkages of national registers: the Medical Birth Register, the

Statistical Analysis

We used generalized estimating equation models to estimate odds ratios and 95% CI for overweight in early adulthood in relation to maternal smoking during pregnancy, birth characteristics, and other parental and adult characteristics. An exchangeable correlation matrix was specified in order to control for the correlations between siblings (PROC GENMOD, SAS Institute, Inc, Cary, NC). Associations between birth and parental characteristics with offspring's risk of overweight were estimated using both univariable and multivariable analyses. Risks of overweight associated with smoking during pregnancy were presented in two multivariable models. In the first model we adjusted for parental characteristics and in the second model we additionally adjusted for birth characteristics. The models only included variables that influenced the risk of obesity.

To examine whether a possible effect of maternal smoking on overweight in male offspring in early adulthood was influenced by unmeasured familial factors, we proceeded in two ways. First, we estimated the risks of overweight in first and second-born sons, stratified by maternal smoking habits across the first and second male pregnancies. Risks of overweight by changes in maternal smoking habits in two subsequent male pregnancies were estimated in both first-and second born male siblings separately by using logistic regression models. Second, to further elucidate the importance of common genes and/or shared childhood environment (familial confounding), we estimated the effects of maternal smoking during pregnancy on continuous BMI within full and half sibling pairs 18 . Full and half siblings share, on average, 50% and 25% of their segregating genes, respectively, while all of them share childhood environment to a large extent. Maternal smoking during pregnancy is decomposed into a within-family effect. The within-family effect estimates the expected change in offspring BMI by a one unit change in maternal smoking behavior between male pregnancies. A within-family score is assigned to each son, defined as the difference between smoking status at the index pregnancy and the mean value of maternal smoking status across the two pregnancies 18 . For example, if a mother smoked in one pregnancy but not the other, the exposed sibling would have a within-score of 0.5 and the unexposed would have a within-score of -0.5. This within score compares exposure to maternal smoking during pregnancy relative to their sibling's exposure. If familial factors are of importance they would tend to make family members more alike. Hence we would expect the within-family estimates to be smaller than the effects shown in the cohort. We carried out these analyses separately among full and half sibling pairs. Further, by investigating the within-family association according to two different degrees of kinship (full or half siblings), and relating it to the results from the cohort analysis, we can elucidate whether or not common genes are likely to confound the association. If the size of the within effect of maternal smoking during pregnancy and offspring BMI is weaker in half compared to full siblings, the association is likely to be confounded by common genetic factors. In order to test whether the magnitude of the within family component was different according to kinship, an interaction between a kinship index (coded 1for full siblings, 0 for half siblings) and the within family component was tested.

Analyses were done with PROC MIXED in SAS v 9.2. increased risk of overweight, respectively. The risks of overweight were also increased in sons born to younger or shorter mothers, mothers who experienced very large pregnancy weight gains (≥17 kg), mothers and fathers of lower socioeconomic status and educational level, in large-forgestational age boys (defined as larger than 2 standard deviation scores), in sons who were older at the time of conscription, and in offspring living in rural areas.

RESULTS

F

Table 1 here

Rates of maternal smoking during pregnancy increased with decreasing maternal age and height, with decreasing maternal and paternal socio-economic position and education, and were higher among mothers with either very low or high BMI and mothers not living with the father of the child. Offspring with lower birth weight, birth length and head circumference showed higher rates of maternal smoking. Shorter gestational ages were also related to higher rates of maternal smoking during the 1 st trimester (data not shown).

Compared with the offspring of non-smokers, there was a 51% (95 % CI, 46% to 57%) and a 72% (95% CI, 65% to 80% ) increase in risk of overweight in the sons of mothers who smoked 1-9 cigarettes /day and more than 10 cigarettes /day, respectively (Table 2). In the analyses, a correlation matrix was specified in order to control for the correlations between siblings in the

F o r R e v i e w O n l y 12
cohort. These associations were slightly attenuated when adjusting for parental characteristics and for parental socioeconomic characteristics in particular (Table 2). Finally, birth characteristics, such as birth weight, may be considered to be in the causal pathway between maternal smoking during pregnancy and offspring risk of overweight. Therefore we adjusted for these in the last model (fully adjusted). Although, large for gestational age boys were at increased risk of overweight in early adulthood (Table 1), adjusting for birth characteristics did not change the associations between maternal smoking during pregnancy and offspring overweight risk (Table 2). Due to missing measurements in various confounders, a complete case analyses was also done showing essentially the same results (Table 2). Complete case analyses was carried out with the restricted sample of subjects (N=68 248), without missing information on any of the co-variates, across all three regression models. Since there seemed to be a linear trend in the risk of overweight with maternal smoking habits the analyses were also done considering offspring's BMI as a continuous outcome and maternal smoking during pregnancy dichotomized as yes or no. The regression coefficients after full adjustment showed an increase of 0.69 (95% CI, 0.62 to 0.75) BMI units if the mother smoked (Table 2).

Table 2 here

We did not find any interactions between maternal smoking during pregnancy and any of the confounding variables we adjusted for.

The results from comparing the risk of overweight in first and second born sons in relation to the mothers' smoking habits across pregnancies are shown in Table 3. In the crude analyses, sons of mothers who smoked in both pregnancies were at increased risk of overweight; this association

F o r R e v i e w O n l y
13 was still evident after adjustments for birth and parental characteristics (adjusted OR 1.65, 95% CI 1.35 to 2.01 for the first son and adjusted odds ratio 1.71, 95% CI 1.39 to 2.09 for the second son). If mothers smoked only during their first male pregnancy or only in their second male pregnancy, the adjusted risk estimates of overweight in both first and second born sons were smaller.

Table 3 here Finally, to investigate the importance of familial factors, we studied the effect of maternal smoking during pregnancy on BMI among full-and half-siblings (Figure). In the half-sibling subset, there was no within-family effect of maternal smoking during pregnancy (adjusted within family component: 0.07, 95% CI, -4.32 to 4.45). Although the full sibling effect of 0.39 (95% CI, -0.01 to 0.78) was higher than the half sibling effect the interaction between kinship and the within family component, indicated no difference in the magnitude of the effect of maternal smoking during pregnancy between full and half siblings (p-value 0.79). Given that the withinfamily associations were much smaller compared to the cohort effect, it is likely that the effect of maternal smoking during pregnancy on the offspring's BMI is partly confounded by familial factors.

Figure here

DISCUSSION

We found that the association between maternal smoking during pregnancy and risk for overweight in young adult male offspring can be explained partly by parental socioeconomic status and education, but also by unmeasured familial factors. In the cohort analyses we found an association of maternal smoking during pregnancy and risk of overweight in male offspring. This association has been shown in previous studies 2, 5-7, 19, 20 .

Recently, a systematic review and meta-analysis on the subject showed a significant increase in child overweight with maternal smoking during pregnancy 2,4 . Moreover, animal studies have also shown that prenatal nicotine exposure resulted in metabolic changes in the offspring that were consistent with obesity and type 2 diabetes [21][22][23] . However, it is difficult to extrapolate the results of animal studies to humans. Smoking behaviors vary a lot, since not all smokers inhale cigarette smoke the same way and some individuals may be more or less affected, or metabolize toxins in smoke differently, compared to the controlled environments of animal studies 24 .

The adverse effects of smoking during pregnancy on fetal development are well known 1,25 . In the current study, smoking-related birth outcomes such as birth weight and gestational age did not mediate the association between smoking during pregnancy and overweight in the offspring.

This indicates that any effect of prenatal smoking exposure on offspring risk for overweight may be independent of fetal growth or gestational age.

In the current study we were able to adjust for a range of covariates that have been shown to be important predictors of adult obesity 26,27 , including maternal pre-pregnancy BMI and gestational weight gain, as well as parental socioeconomic status and educational level. However, it is almost impossible to control for all potential confounders. A study of 1 110 mother-child pairs showed that a combination of four modifiable pre-and postnatal determinants, including prenatal smoking, large gestational weight gain, absence or short duration of breastfeeding, and short 15 duration of infant sleep, were associated with higher risks of childhood overweight than each factor individually 19 . A Japanese study of 1 417 mother-child pairs showed that maternal lifestyle habits along with smoking during pregnancy were important risk factors for childhood obesity 20 . Although we have not adjusted for breastfeeding, and other maternal and adult offspring life style factors, studies that have examined these factors have shown that they are important predictors of adult obesity, but concluded also that residual confounding in these associations could not be excluded. However, studies have also shown that paternal smoking is almost equally important for childhood obesity 6,28 , indicating that parental smoking is more likely to be a surrogate for social factors associated with obesity 29 .

One way of elucidating the importance of unmeasured confounders common to both exposure and outcome is by investigating the effects of changing smoking patterns in subsequent pregnancies and within families 12 . In the analyses of subsequent male births we could only observe an effect of maternal smoking during pregnancy on the first and second male pregnancies as long as the mother smoked during the first trimester in both pregnancies. This could either indicate that smoking reaches harmful levels only if it is persistent and/or reaches a specific threshold level. It could also indicate that the timing of smoking during pregnancy is important for fetal development, since some studies have indicated that the effect of intrauterine tobacco exposure on childhood obesity may depend largely on cigarette smoking during the first trimester 5,7 . Lastly it could indicate residual confounding that we have not accounted for, since smoking was only known for the first trimester. The within-sibling analyses indicated that familial factors shared within a family may account for the association between maternal smoking during pregnancy and risk of overweight in early adulthood. To our knowledge this is the first study to investigate whether there is a direct effect of maternal smoking during pregnancy on offspring overweight or whether the association is due to unmeasured familial confounding. In the current study, the association diminished in both full and half siblings, indicating that regardless of how many genes siblings have in common, it is the shared environment that accounts for the association and that direct effects of maternal smoking during pregnancy on offspring overweight may be small. Shared environment could include lifestyle factors that are common in mothers and their offspring such as dietary habits established during early childhood, or other lifestyle behaviors such as attitudes towards physical activity 30 .

However, due to a limited number of half siblings the results should be interpreted with caution, since the lack of association among half siblings could be due to random error. Further, the point estimate for full siblings showed that there could still be a small effect of maternal smoking during pregnancy, which compared to half siblings would perhaps indicate the importance of common genetic factors shared within family members to the studied association.

The main strengths of this study are its size, the prospective design, and the range of covariates gathered from population-based registries that we could adjust for. However, limitations include self-reported data on maternal smoking during pregnancy which was collected at the first prenatal care visit, and hence is limited to the duration of smoking during the first trimester. The proportion of women who stop smoking during pregnancy has been reported to be around 30% in previous Swedish studies. However, in Sweden during the 1980's, 11% of smokers at time for registration to prenatal care stopped smoking later during pregnancy 31 . Women with a higher 17 level of education and a higher age at the initiation of smoking were more likely to stop smoking when pregnant, while women not living with the father of the child, heavy smokers, and women exposed to daily passive smoking at home were more likely to continue smoking throughout the pregnancy 32,33 . We therefore adjusted for parental socioeconomic status, age and whether the mother was living with the father of child. Further, previous studies on smoking patterns and risks in successive pregnancies from the Swedish Medical Birth Register have found that women who smoke in the first but not in the second pregnancy reduce their risks of preterm birth 34 , stillbirth 35 and placental abruption 36 in the second pregnancy, outcomes all likely to be causally associated with prenatal smoking. In contrast, when studying prenatal smoking and offspring school grades 12 , we find, similar to the present results, that the association disappeared when we account for familial effects. However, misclassification of smoking exposure between pregnancies or residual confounding may have influenced the risk estimates obtained. Finally, most pregnant smokers continue to smoke after pregnancy, and we cannot distinguish between the effects of prenatal and postnatal smoking exposure. Also, information on BMI was only available in males and we could not explore potential gender differences in the effect of maternal smoking during pregnancy. The conscripts with missing BMI data (about 34%) were born to mothers who smoked more during pregnancy than the males included for analyses; thus there might be some room for selection bias.

Maternal smoking during pregnancy is from a preventive view recognized in many countries as the most important risk factor for adverse pregnancy outcomes 31

  Smoking during pregnancy has been shown to an increase the risks of several adverse birth outcomes. Associations with overweight and/or obesity in the offspring have also been suggested. We aim to investigate whether familial factors confound the association between maternal smoking during pregnancy and overweight in early adulthood in young Swedish males born 1983-1988. Methods: In a population-based Swedish cohort comprising 124 203 singleton males born to Nordic mothers between 1983 and 1988, we examined the association between maternal smoking during pregnancy and the risk of overweight in the offspring at around age 18 years.

  28 and 42 weeks of gestation16 . Four hundred and twenty three observations with less than 28 or more than 42 weeks of gestation were put to missing.Conscription was mandatory and enforced by law in Sweden up to 2007. Most men were conscripted at 17-24 years of age, except for those with severe handicaps, congenital malformations or chronic diseases. Information from the Military Service Conscription Register was used to define age and BMI, calculated from measured weight and height at conscription.Males were defined as overweight if they had a BMI of 25 or more according to the World Health Organization (WHO) criteria17 .Maternal and paternal socioeconomic status, classified according to recommendations set forth by Statistics Sweden (see table 1 for categories), and area of living (urban or rural) was obtained from the Population and Housing census of 1990. Maternal and paternal educational levels were retrieved from the Register of Education of 2000.Within this cohort, we identified 8441 sibling pairs by using information included in the Multigeneration Register. The sibling subset included 8250 full siblings and 182 half siblings (on the maternal side) and 9 pairs with unknown father. The first two sons born subsequently with data on maternal smoking during pregnancy and BMI were selected from each family (N=8 250 full and 182 half sibling pairs).The study was approved by the research ethics committee of Karolinska Institutet (No 2007/546-31, 2008/1737-32 and 2009/266-32). All authors had full access to all of the data (including tables) in the study and can take responsibility for the integrity of the data and the accuracy of the data analysis.

9 BMI

 9 within full and half sibling pairs

  socioeconomic characteristics in particular (Table

  factors, studies that have examined these factors have shown that they are

  . Less is known about maternal smoking during pregnancy and possible long-term effects in offspring. Our results support the importance of familial factors for the association between maternal smoking during pregnancy and overweight in young adult males. Further research will have to identify specific familial factors common to both maternal smoking during pregnancy and offspring overweight, and address specific mechanisms that link features of familial environment with overweight in children and adolescents.

•

  Maternal smoking during pregnancy is associated with offspring risk for overweight in young adulthood.

FIGURE 1 LEGENDFigure 1 .

 11 FIGURE 1 LEGEND Figure 1. Crude and adjusted estimates of the expected change in offspring BMI (kg/m 2 ) according to one-unit change in maternal smoking

INTRODUCTION

  Maternal smoking during pregnancy is causally associated with fetal growth restriction 1 . It has also been associated with increased risks of adverse outcomes in the long term, including obesity 2 , which is considered an "epidemic" of our time. An association between maternal smoking during pregnancy and childhood obesity has been found in several recent studies, although the mechanism by which prenatal smoking exposure influences offspring's risk of overweight remains uncertain[2][3][4][5][6][7] .

  to cognitive and physical development of the offspring (including intelligence, academic achievement, Apgar score, conduct problems and asthma) were entirely explained by measured or unmeasured familial confounders14 .

FIGURE 1 LEGENDFigure 1 .

 11 FIGURE 1 LEGEND Figure 1. Crude and adjusted estimates of the expected change in offspring BMI (kg/m 2 ) according to a one-unit change in maternal smoking

Table

	o
	r
	R e v i e w
	O n
	l y
	10

Table 1 .

 1 Maternal and birth characteristics and the risk of overweight (BMI ≥ 25 kg/m 2 ) in 124 203 Swedish male offspring born 1983-1988.

	o
	r
	R e v i e w
	O n
	l y

Table 2 .

 2 Maternal smoking during pregnancy and the risk of overweight (BMI ≥25) in the offspring in early adulthood in a cohort of young Swedish males born1983-1988.

	Adjusted for
	Parental
	Characteristics †

* Reference category. † Adjusted for maternal age, height, BMI and pregnancy weight gain, maternal and paternal socioeconomic category and education, and offspring urban living. ‡ Adjusted for characteristics as above and also birth weight, head circumference, gestational age, and age at conscription.

Table 3 .

 3 Maternal Smoking in first and second born son and the risk of overweight in siblings based on 8441 women with subsequent male births between 1983-1988. Adjusted for , maternal age, height, BMI and pregnancy weight gain, maternal and paternal socioeconomic category and education, and offspring birth weight, head circumference, gestational age, urban living and age at conscription

	Maternal smoking during	First Son

* Reference category. †

  were 305 896 Swedish males born between 1983 and 1988 and recorded in the Swedish

	F o
	r
	Medical Birth Register. We excluded multiple births (N= 6000), infants with congenital R e v i e w
	malformations (N= 14 736), and males born to non-Scandinavian mothers (N= 18 793) to increase the homogeneity of the study population. After also excluding 2028 males who died O n
	before 18 years of age and 4588 that emigrated, the sample consisted of 259 751 males, of whom 201 896 went through military conscription up until 2006. BMI at conscription, calculated from l y
	measured weight and height as kg/m 2 , was available for 132 838 individuals. Information on
	maternal smoking during pregnancy was available in 124 203 of them, and this constituted the
	final sample.
	7

  28 and 42 weeks of gestation16 . Four hundred and twenty three observations with less than 28 or more than 42 weeks of gestation were put to missing.Conscription was mandatory and enforced by law in Sweden up to 2007. Most men were conscripted at 17-24 years of age, except for those with severe handicaps, congenital malformations or chronic diseases. Information from the Military Service Conscription Register was used to define age and BMI, calculated from measured weight and height at conscription. Males were defined as overweight if they had a BMI of 25 or more according to the World Health Organization (WHO) criteria17 . tables) in the study and can take responsibility for the integrity of the data and the accuracy of the data analysis.

	Information about maternal smoking during pregnancy has been routinely included in the Swedish Medical Birth Register since 1983 15 . Self-reported information about smoking habits is collected and recorded by the midwives at the first antenatal visit (usually at 8 to 12 gestational F o r R e v i e w O n F o r R e v i e w O n gestational age between Within this cohort, we identified 8441 sibling pairs by using information included in the statistical reports and
	weeks), and is categorized as non-smoker, smoking 1-9 cigarettes per day, and smoking at least 10 cigarettes per day. Information on maternal pre-pregnancy weight and height, pregnancy l y Multigeneration Register. The sibling subset included 8250 full siblings and 182 half siblings (on the maternal side) and 9 pairs with unknown father. The first two sons born subsequently with l y
	weight gain, mode of delivery, age at delivery, living with the father of the child, Apgar score at data on maternal smoking during pregnancy and BMI were selected from each family (N=8 250
	5 minutes, birth order (in the present study first born child who is also a son or not), infant's birth full and 182 half sibling pairs).
	weight, birth length, head circumference, and gestational age were retrieved from the Medical
	Birth Register. Birth weight, birth length, and head circumference were standardized according The study was approved by the research ethics committee of Karolinska Institutet (No 2007/546-
	to Swedish reference standards for weight, length, and head circumference at birth for given 31, 2008/1737-32 and 2009/266-32). All authors had full access to all of the data (including
	8 9

Military Service Conscription Register, the Multigeneration Register, the Population and Housing Census in 1990, and the Register of Education in 2000. The linkage was possible through the unique National Registration Number assigned to each Swedish resident at birth. Maternal and paternal socioeconomic status, classified according to recommendations set forth by Statistics Sweden (see table 1 for categories), and area of living (urban or rural) was obtained from the Population and Housing census of 1990. Maternal and paternal educational levels were retrieved from the Register of Education of 2000.

Table 1

 1 presents parental and birth characteristics with respect to prevalences and crude odds ratios of overweight in the cohort of young males. Prevalences of overweight in offspring increased monotonically with maternal BMI and reached up to 47.6 % in mothers with a BMI

	above 30. Compared with sons of mothers with normal BMI (18.5-24.9), sons of overweight and
	obese mothers experienced a 2.6-fold (95% CI, 2.49 to 2.71) and a 4-fold (95% CI, 3.73 to 4.52)
	o
	r
	R e v i e w
	O n
	l y
	11

Table 1 .

 1 Maternal and birth characteristics and the risk of overweight (BMI ≥ 25 kg/m 2 ) in 124 203 Swedish male offspring born 1983-1988.

	. Less is known about maternal

with the father of the child

	-2 to 2 17,5 -18,5		117 562 23 732 20.2 106 374 21 138 19.9	1 1
	>2 >18,5		3086 16 648	885 28.7 3915 23.5	1.58 (1.46-1.71) 1.24 (1.19-1.29)
	Missing Urban living		1010
	Birth length for gestational age no	26 256	5936 22.6	1
	(standard deviation score) yes	97 622 19 300 19.8	0.84 (0.82-0.87)
	<-2 missing		2337 325	469 20.1	0.99 (0.90-1.10)
	-2 to 2		117 573 23 852 20.3	1
	>2 Missing	F o r F o r	3103 1190	698 22.5	1.14 (1.05-1.24)
	R e v i e w Head circumference for gestational age (standard deviation score) <-2 4697 -2 to 2 113 949 23 101 20.3 894 19.0 >2 3238 809 25.0 R e v i e w	0.92 (0.86-0.99) 1 1.30 (1.20-1.41)
	Missing Gestational age (weeks)	O n 2319 O n
	Yes 28-31 32-36		116 785 23 679 20.3 l y 318 49 15.4 4367 891 20.4 l y	1 0.70 (0.52-0.96) 1.01 (0.94-1.09)
	No 37-41		5422 103 030 20 872 20.3 1222 22.5	1.14 (1.07-1.22) 1
	Missing 42-		1996 16 155	3396 21.0	1.05 (1.00-1.09)
	Birth weight for gestational age Missing	333
	(standard deviation score) Age at conscription (years)
	<-2 <17,5		2545 1181	450 17.7 242 20.5	0.85 (0.77-0.94) 1.04 (0.90-1.20)
					26 27

Table 2 .

 2 Maternal Smoking During Pregnancy and the risk of overweight (BMI ≥25) in the offspring in early adulthood in a cohort of young Swedish males born 1983-1988. Adjusted for maternal age, height, BMI and pregnancy weight gain, maternal and paternal socioeconomic category and education, and offspring urban living. ‡ Adjusted for characteristics as above and also birth weight, head circumference, gestational age, and age at conscription.

					Adjusted for
				Crude	Parental	Fully Adjusted ‡
	Mother's smoking				Characteristics †
		Total	Overweight
				OR (95% CI)	OR (95% CI)	OR (95% CI)
	(Number of cigarettes per day)	n	n
	0 *	90 621	16 507	1.00	1.00	1.00
	1-9	21 090	5320	1.51 (1.46-1.56)	1.40 (1.33-1.48)	1.41 (1.34-1.49)
	10 or more	12 492	3468	1.72 (1.65-1.80)	1.55 (1.45-1.65)	1.56 (1.46-1.66)
	Total n			124 203	69 692	68 248
	Effect of maternal smoking
	(yes/no) on continuous BMI
	regression coefficient b (95% CI) :	124 203	25 295	0.81 (0.77-0.86)	0.67 (0.60-0.73)	0.69 (0.62-0.75)

* Reference category. †

Table 3 .

 3 Maternal Smoking in first and second born son and the risk of overweight in siblings based on 8441 women with subsequent male births between 1983-1988.

	First Son

* Reference category.

FUNDING

This work was supported by grants from the Swedish Research Council (project number K2007-70X-20510-01-4 to A.N.I) and SIMSAM (project number 839-2008-7483). IK is currently funded by the Swedish Council for Working Life and Social Research. FUNDING This work was supported by grants from the Swedish Research Council (project number K2007-70X-20510-01-4 to A.N.I) and SIMSAM (project number 839-2008-7483). IK is currently funded by the Swedish Council for Working Life and Social Research.

CONFLICT OF INTEREST

None declared.

CONFLICT OF INTEREST

None declared.