J T Mendonça

H Terças

Laser scattering by density fluctuations of ultra-cold atoms in a magneto-optical trap

Keywords:

We study the spectrum of density fluctuations in the ultra-cold gas of neutral atoms, confined in a magneto-optical trap. We determine the corresponding amplitude and spectra of laser light scattered by this medium. We derive an expression for the dynamical structure function, by using a test particle method. We propose to use the collective laser scattering as a diagnostic method for the microscopic properties of the ultra-cold matter. This will also allow us to check on the atomic correlations which are mediated by the collective mean field inside the gas.

I. INTRODUCTION

In recent years, attention has been given to the study of collective oscilations in alkali metal gases, cooled and confined in magneto-optical traps (MOTs) [1][2][3]. Such a cooperative behavior is driven by light and results from the random scattering between the atoms, being in the root of a long-range interaction potential. Surprisingly, this collective interaction is very similar to that observed in Coulomb systems, since it scales as 1/r 2 , which allows one to establish analogies between cold atoms and plasmas.

The evidence of such Coulomb-like forces due the random scattering of photons was first discovered by Walker et al. [4] and Dalibard [5], where the divergence of the effective net force between the atoms was shown to be proportional to the MOT density. As a consequence, it is possible to define an equivalent electric charge for the neutral atoms. The advantage of such a system is that the effective charge depends on the basic parameters of the system, what makes MOTs good candidates to observe plasma physics phenomena with a tunable "electric" charge. A strong manifestation of the plasma character of MOTs was also revealed by the studies of Coulomb explosions of the atomic clouds, performed by Pruvost et al [6].

Recently, we have shown theoretically that waves and oscillations of the plasma type can also exist in the neutral gas [7,8] and have explored the plasma character of magneto-optical traps to the study of parametric instabilities [9].

Here we propose to study the spectrum of density fluctuations in the ultra-cold gas, by using collective laser scattering techniques. In doing this, we explore even further the analogy between the ultra-cold neutral gas confined in a magneto-optical trap and a plasma, by adapting well known plasma physics theoretical techniques to this new problem. First, we determine the scattered fields, and the expected average scattered power. Second, we determine the spectrum of density fluctuations, in the quasi-classical approximation. We use here the test particle method, well known in plasma physics [START_REF] Krall | Principles of Plasma Physics[END_REF]. Finally, we characterize the main properties of the expected scattered signal.

II. SCATTERED LASER POWER

We start by stating the basic equations of our problem. The propagation of a laser pulse along the ultra-cold gas is governed by the wave equation

∇ 2 - 1 c 2 ∂ 2 ∂t 2 E = -µ 0 ∂ 2 P ∂t 2 (1)
where E is the laser electric field and P is the polarization field in the gas, as determined by

P(r, t) = 0 ∞ 0 Π(r, τ ) • E(r, t -τ )dτ, (2)
where Π(r, t) is the atomic susceptibility tensor. Using Fourier transformations of the fields

E(r, t) = E(r, ω) exp(-iωt) dω 2π , (3)
one obtains

P(r, ω) = 0 Π(r, ω) • E(r, ω). (4)
Because we can neglect the anisotropies in the majority of the MOT, the atomic susceptibility tensor Π can be safely replaced by the spectral susceptibility function χ which, for the twolevel atom, is given by

χ(r, ω) = n(r)χ a (ω) , χ a (ω) = Ω 2 3 0 δ + iΓ δ 2 + Γ 2 (5)
Here, n(r) is the number of atoms per unit volume, χ a (ω) is the single atom susceptibility, δ ≡ ω-ω a is the radiation frequency detuning with respect to the atomic transition frequency ω a , Γ is the corresponding line width and Ω represents the Rabi frequency. The local density can fluctuate in time, at frequencies much lower than those of the radiation field frequency ω, thus leading to the replacement of n(r) by n(r, t) in the above expression. The total radiation field E will be determined by the sum of two parts, the incident laser field E 0 , and the scattered field E s . For a real incident laser field, we can use

E(r, t) = 1 2 E 0 exp(ik 0 • r -iω 0 t) + c.c., (6)
where the wave-vector k 0 follows the dispersion relation

k 2 0 = ω 2 0 c 2 [1 + χ(ω 0 )] , χ(ω 0 ) = n 0 χ a (ω 0 ), (7)
with n 0 being the atomic mean density. Such an approximation is valid for MOTs with a moderate number of atoms (typically, N ∼ 10 8 .) On the other hand, the scattered field can be generically written as

E s (r, t) = E s (r, ω) exp(-iωt) dω 2π (8)
and the field components can be determined by solving the corresponding wave equation, which can be written as

∇ 2 + k 2 E s (r, ω) = ω 2 2c 2 E 0 e ik 0 •r n(r, ω ) + c.c., (9)
where n(r, ω ) = n(r, t)e iω t dt [START_REF] Krall | Principles of Plasma Physics[END_REF] and ω = ω -ω 0 is the frequency of density fluctuation. In its turn, the scattered wave number k will be determined by the same dispersion relation as in Eq. ( 7), with k 0 and ω 0 respectively replaced by k and ω. The solution to Eq. ( 9) can therefore be written as

E s (r, ω) = - iω 2 2kc 2 χ a (ω 0 )(e ω • e 0 )E 0 e ik•r dr dk (2π) 3 n(k , ω )e i(k 0 +k -k)•r + c.c., (11)
where we have used the unit polarization vectors for the incident and the scattered fields, e 0 = E 0 /E 0 and e ω = E s (ω)/E s (ω). The integration in volume leads to the appearance of a delta function δ(k 0 + kk), and subsequent integration over k finally leads to

E s (r, ω) = -iA s exp(ik • r) + c.c., (12)
where the amplitude of the scattered field is determined by

A s (ω) = ω 2 2kc 2 χ a (ω 0 )(e ω • e 0 )E 0 n(ω , k ) (13)
with ω = ω 0 + ω and k = k 0 + k . The relative scattered intensity along the direction of k is therefore determined by the dynamical structure factor

S(k, ω) = |E s (k, ω)| 2 |E 0 | 2 = iω 4 4k 2 c 4 |χ a (ω 0 )| 2 (e ω • e 0 ) 2 |n(k , ω )| 2 . ( 14
)
This quantity can easily be related with the density correlation function, by noting that

|n(k , ω )| 2 = dr 1 dt 1 dr 2 dt 2 n(r 1 , t 1 )e -ik •r 1 +iω t 1 n(r 2 , t 2 )e ik •r 2 -iω t 2 . ( 15
)
Performing an average in both space and time, the latter equation reads

< |n(k , ω )| 2 >= lim V,T →∞ 1 V T dr 1 dt 1 dr 2 dt 2 < n(r 1 , t 1 )n(r 2 , t 2 ) > e ik •(r 2 -r 1 ) e -iω (t 2 -t 1 ) (16)
Equation ( 14) establishes the relation between the scattered signal and the fluctuations inside the cloud, which contain the basic features of the laser cooled gas. We should therefore proceed by understanding how to compute such fluctuations by taking into account the microscopic distribution of the atomic states.

III. TEST PARTICLE METHOD

In the quasi-classical approximation, a trapped alkali gas in a MOT can be described by a kinetic equation of the form [7]

∂ ∂t + v • ∇ + F M • ∂ ∂v W = 0, ( 17
)
where W ≡ W (r, v, t) is the atomic distribution function. Here the collective force F can be determined by the Poisson equation

∇ • F = Qn ≡ Q W (r, v, t)dv, ( 18
)
where Q is the atomic effective charge [6,7]

Q = I 0 c σ R (σ R -σ L ). ( 19
)
Here, I 0 = 2I sat Ω 2 /Γ 2 is the total intensity resulting from the six cooling laser beams, I sat is the saturation intensity of the atom, c is the speed of light, σ L represents the optical cross section for absorbing photons of the laser beams and σ R is the optical cross section for absorbing photons that are reradiated from the atoms in the trap. [START_REF] Townsend | [END_REF]. Our procedure will consist in the test particle method [START_REF] Krall | Principles of Plasma Physics[END_REF], by considering a single atom inside the trap moving with speed v as the perturbation source. The presence of such a test particle will lead to a fluctuation in the gas distribution function W , as determined by the linearized kinetic equation

∂ ∂t + v • ∇ W = - δF M • ∂ ∂v W 0 , (20)
where W 0 = W -W is the unperturbed (or the equilibrium) distribution function, and the collective force perturbation δF induced by the test particle in the medium is determined by

∇ • δF = Q W + δ(r -r )δ(v -v ) dv. (21)
The test particle position is assumed to be given by r ≡ r (t) = r 0 + v t. Let us multiply equation ( 21) by exp(-ik • r + iωt) and perfomr integrations over both space and time.

Defining the Fourier components δF ωk and Wωk for the perturbed force and distribution, respectively, we can easily obtain

ik • δF ωk = 2πQδ(ω -k • v ) + Q Wωk (vdv (22)
Similarly, the Fourier transformation of equation ( 20) leads to

Wωk = - i M δF ωk • ∂W 0 /∂v (ω -k • v) (23)
Replacing this in equation ( 22), and noting that the collective force is purely longitudinal, in such a way that δF ωk = kδF ωk /k, we can write

δF ωk = -i 2πQ k 2 δ(ω -k • v ) (ω, k) k, (24)
where we have introduced the dielectric function of the atomic gas

(ω, k) = 1 + χ(ω, k) = 1 + Q M k 2 k • ∂W 0 /∂v (ω -k • v) dv. (25)
Replacing equation (24) in the expression of the perturbed distribution, we then get

Wωk = - 2πQ M k 2 δ(ω -k • v ) (ω, k) k • ∂W 0 /∂v (ω -k • v) . ( 26
)
After inverse Fourier transforming, we can compute the perturbed force due to the test particle

δF(r, t) = -i 2Qk k 2 exp[ik • (r -r 0 -v t)] (k • v , k) dk (2π) 3 (27)
and the associated perturbation to distribution function

W (r, v, t) = - Q M k 2 exp[ik • (r -r 0 -v t)] (k • v , k) k • ∂W 0 /∂v k • (v -v) dk (2π) 3 . ( 28
)
Finally, the density perturbation created at a position r and instant t by a test particle located at position r 0 at t = 0 moving with velocity v , can be now determined by

ñ(r, t) = δ(r -r ) + W (r, v, t)dv. (29)
At this point, it should be notice the power of this method, as all the atoms in the gas can be individually considered as test particles. This means that the total averaged perturbations can be calculated by integrating the relevant quantities defined above over the equilibrium distribution function W 0 (r 0 , v ). In particular, the averaged mean force perturbation can be determined by

< δF(r, t) >= dr 0 dv δF(r, t)W 0 (v). ( 30
)
This quantity is a linear superposition of purely oscillating quantities, and it can easily be found using equation ( 27) that it is identically zero

< δF(r, t) >≡ 0, (31)
while the averaged quadratic mean force < |δF(r, t)| 2 >, on the other hand, generally is not.

It will be rather determined by

< |δF(r, t)| 2 >= Q 2 V dr 0 dv dk 1 (2qπ) 3 k 1 k 2 1 exp[ik 1 • (r -r 0 -v t)] (k 1 • v , k 1 ) (32) × dk 2 (2qπ) 3 k 2 k 2 2 exp[ik 2 • (r -r 0 -v t)] (k 2 • v , k 2 ) .
We next express the fluctuations inside the trap in terms of the statistical average over all test particles in the system.

IV. DENSITY CORRELATIONS

Let us introduce W 0 (v) = n 0 f 0 (v), where the new distribution function f 0 (v) is the normalized distribution function, such that

W 0 (v)dv = n 0 f 0 (v)dv = n 0 . (33)
Using equations ( 28) and ( 29), it is possible to express the atom density fluctuations due to a given test particle initially located at r(t = 0) = r 0 as

n(r, t) = δ(r -r 0 -v t) + W (r, v, t)dv, (34)
which can be more represented in a more suggestive fashion

n(r, t) = dk (2π) 3 1 -ω 2 p exp[ik • (r -r 0 -v t)] (k • v , k) k • ∂W 0 /∂v k • (v -v) . ( 35
)
Here, we have introduced the definition of the equivalent plasma frequency for the neutral gas, ω 2 p = Qn 0 /M [7]. Using the average as in Eq. ( 30), we can then state the density correlations as < n(r 1 , t 1 )n(r 2 , t 2 ) >= n 0 dr 0 dv f 0 (v )n(r 1 , t 1 )n(r 2 , t 2 ).

(36)

In explicit form, this can be written in the following way

< n(r 1 , t 1 )n(r 2 , t 2 ) >= n 0 dr 0 dv f 0 (v ) dk 1 (2π) 3 e iϕ 1 dk 2 (2π) 3 e iϕ 2 g(k 1 , v )g(k 2 , v ), ( 37
)
where we have introduced the new auxiliary quantities

ϕ j = ik j • (r j -r 0 -v t) (38)
and

g(k j , v ) = 1 -ω 2 p k j • ∂f 0 /∂v k 2 j (k j • v , k j )k j • (v -v) . ( 39
)
Integration over the initial position for the generic test particle r 0 leads to the appearance of a delta function δ(k 1 + k 2 ) which, in its turn, allows us to integrate over k 2 . We then replace k 1 by k, in order to simplify the notation. By noting that the velocity v only appears in the parallel direction with respect to the wavemathbftor k, we can write

v = u k k + v ⊥ (40)
and introducing the parallel distribution function

F 0 (u) = f 0 (v)dv ⊥ , (41)
we can finally write

< n(r 1 , t 1 )n(r 2 , t 2 ) >= n 0 du F 0 (u ) dk (2π) 3 e iϕ |I(k, u )| 2 , (42)
where we have used the phase

ϕ = ik • (r 1 -r 2 ) -iku (t 1 -t 2 ) (43)
and new argument

I(k, u ) = 1 + ω 2 p ∂F 0 /∂u k 2 (ku , k)(u -u) du (44)
This is formally very similar to the results obtained for an electron-ion plasma [START_REF] Krall | Principles of Plasma Physics[END_REF], which is due to the Coulomb like interactions between nearby atoms in the ultra-cold neutral gas [7]. The main difference relies on the fact that we only have one particle species here, which suggests that the system can be regarded as a one-component plasma. We can now use these results to determine the structure factor discussed in Sec. II. Inserting Eqs. (42) to (44) in Eq. ( 16), and successively integrating over r 1 , r 2 , t 1 , t 2 , k, and u , we finally obtain

S(k , ω ) = F 0 (ω /k ) k |I(k , ω )| 2 , (45)
where we have used

I(k , ω ) = 1 + ω 2 p (∂F 0 /∂u)du k 2 (k , ω )(u -ω /k ) . (46)
In order to illustrate the collective behavior of the system during the scattering, we assume that the atoms in the trapped approximately follow a Maxwell-Boltzmann distribution

F 0 (v ) = 1 √ πv th e -v 2 /v 2 th , (47)
where v th = 2k B T /m represents the thermal velocity of the atoms, k B is the Boltzmann constant and T is the temperature. Defining the scattering parameter α = k λ D , where λ D = v th /ω P is the Debye length, the dynamical structure factor can be explicitly given by

S(α, ω ) = e -αω /ωp √ πα I(α, ω /ω p ), (48)
where α = k λ D represents the scattering parameter. The latter defines the nature of the scattering processes. Moreover, for α 1, the scattering signal results from a coherent process, as the system is essentially composed of interacting particles. In a plasma language, it means that the Debye length λ D is larger or comparable to the perturbation wavelength 2π/k and therefore the correlations between the atoms play an important role on the scattering signal (unscreened, correlated atoms); on the contrary, if α 1, the scattering is said to be incoherent and the Debye length is assumed to be much smaller than the typical size of the perturbation (screened, uncorrelated atoms). In the figure, we have ploted the normalized structure factor in Eq. ( 48) for three different values of α. We observe a strong resonance near ω = ω p for the case of coherent scattering (α = 0.85 and α = 1.0), while a very broad spectrum is obtained for the case of incoherent scattering (α = 5.0).

The physical reason for such results are related with the interference mechanism during the scattering: the excitation of collective perturbations of the density will result on the constructive interference (and therefore amplification) of the scattered signal around the natural frequency characterizing the long-range order of the interaction, i.e. ω p . On the contrary, if uncorrelated, single-atoms fluctuations are excited in the systems, the interference will be destructive and, therefore, no resonance is expected to be observed in the spectrum S(α, ω ).

Few words are now devoted to discuss the experimental observation of the spectra. The scattering mechanism presented in this work is similar to Rayleigh scattering, with the important difference that long-range order between the atoms is present, which is naturally induced during the laser cooling process. Therefore, this could be experimentally implemented in magneto-optical traps in order to measure the collective excitations of the system,

V. CONCLUSIONS

In this work we have determined the spectrum of density correlations of ultra-cold atoms confined in a magneto-optical trap. We have explored the formal analogies between the physics of the neutral atom gas at that of a plasma medium. The existence of such analogies is related with the repulsive force between two nearby atoms in the ultra-cold gas, associated with the exchange of scattered photons from the laser cooling system. This repulsive interaction can be described by Poisson like equations for the collective force, similar to that describing electrostatic fields in a real plasma medium.

Here we have adapted the test particle approach, well known in plasma physics, to the case of the neutral cold gas. We have determined the spectrum of density correlations in the gas and we have established the corresponding spectra of laser light scattering. We have applied this to a medium in thermal equilibrium and given examples of expected spectra.

This work proposes the use of laser light scattering as a diagnostic technique for probing the internal kinetic properties of a ultra-cold gas, and could be useful for the interpretation of future experiments in this field.

FIG. 1 :

 1 FIG. 1: Dynamical structure factor S(α, ω ) for different values of the scattering parameter α: blue full line (α = 0.85), black dashed line (α = 1.0), and red full line (α = 5.0). Both coherent and incoherent scattering processes are represented.


Chengpu Liu

Karen Z Hatsagortsyan
email: k.hatsagortsyan@mpi-k.de

Wavelength and intensity dependence of multiple forward scattering of electrons at above-threshold ionization in mid-infrared strong laser fields

Wavelength and intensity dependence of multiple forward scattering of electrons at above-threshold ionization in mid-infrared strong laser fields

Chengpu Liu, Karen Z Hatsagortsyan

Introduction

The Coulomb field of the atomic core can play a significant role in the strong-field photoionization process essentially modifying the dynamics of low-energy electrons. It is responsible, in particular, for the appearance of a rich structure in the momentum distribution of photoelectrons near the ionization threshold [1,2,3,4,5,6,7,8], for frustrating the tunneling ionization [9] and for the creation of a low-energy structure (LES) in photoelectron spectra in mid-infrared laser fields [10,11,12,13,14]. The Coulomb field focuses low-energy electrons towards the laser polarization direction which is mostly due to multiple rescattering [15] of ionized electrons by the atomic core at large impact parameters and is termed Coulomb focusing (CF) [16,17,18]. For a theoretical description of Coulomb field effects, different modifications of the strong field approximation [19] have been developed [4,20,21,22,23]. In addition, the classical trajectory Monte Carlo (CTMC) method has been successfully employed, see e.g. [24,25,18,7,11,13], for estimation of the effects which are not intrinsically quantum mechanical.

Recently, the strong field physics in mid-infrared laser fields has attracted a lot of attention in connection with the possibility of improving high-order harmonic generation with mid-infrared driver fields [26]. In mid-infrared laser fields, when the Keldysh parameter is small γ = I p /2U p 1, the electron dynamics after tunneling is mainly classical. This is because the characteristic energies of the process, I p and U p , greatly exceed the photon energy in this regime ω I p U p . Here, I p is the ionization potential, U p = E 2 0 /4ω 2 the ponderomotive energy, E 0 and ω are the laser field amplitude and frequency, respectively (atomic units are used throughout). In this regime, the classical features of the three-step model [15] are conspicuous and not obscured by interference effects. Two recent experiments by Blaga et al. [10] and Quan et al. [11] on the photoionization of atoms and molecules in strong mid-infrared laser fields reveal a characteristic spike-like LES in the energy distribution of electrons emitted along the laser polarization direction. The CF is responsible for the effect [12,13,14]. More concretely, the LES arises due to multiple forward scattering (FS) by Coulomb field [13]. The CF is usually predicted to decrease with increase in the laser intensity and wavelength because the average rescattering velocity and the impact parameter increase in such circumstances. As a consequence, one may expect that the contribution of high-order FS should also decrease. In this context, it was surprising that at a large wavelength of the mid-infrared laser field, the multiple FS plays a decisive role for the creation of the LES.

In this paper, we investigate how the contribution of different components of CF depends on laser intensity and wavelength. Our investigation is limited to the classical interaction regime in mid-infrared laser fields. Separate components of CF are identified which scale differently with laser parameters: CF which happens immediately after ionization -initial CF (ICF); CF due to the electron FS on recollision with atomic core, and asymptotic CF (ACF) when the electron momentum is disturbed by the Coulomb field after the laser pulse is switched off. Special attention is devoted to the contribution of the high-order FS events and to the definition of the effective number of FS events. We use the CTMC method with tunneling and the Coulomb field of the atomic core fully taken into account.

The method

The 3D CTMC method employed in this paper is developed as follows. (1) An ensemble of electrons is formed corresponding to the tunneled electron wave packet according to the PPT model [30]. The electrons are born with the following initial conditions. The electron initial position along the laser polarization direction is derived from the Landau's effective potential theory [START_REF] Landau | Quantum Mechanics[END_REF]. The transverse coordinates of the initial position are zero. The initial longitudinal momentum is zero and the transverse one follows the well-known distribution at infinity [START_REF] Delone | [END_REF] (2) The electron wave-packet propagates in the field of a laser pulse and Coulomb potential via the solution of Newton equations. (3) The positions and momenta of electrons when the laser pulse is switched off are used to calculate the asymptotic momenta at the detector [29]. (4) Each trajectory is weighted by the instantaneous tunneling ionization rate [30] and the initial transverse momentum distribution function [START_REF] Delone | [END_REF]. (5) The shape of the laser pulse is half-trapezoidal: For the first ten cycles, the field has a constant amplitude and is ramped off within the last three cycles. The electrons are launched within the first half cycle since there are no multi-cycle interference effects in the classical calculation. The emitted electrons are collected as along the laser field direction as well as opposite to it, hence the result will not change if electrons are launched on the whole period. The ensemble consists of 10 6 particles and the convergence is checked via double increase of this number. The target atom is neon with ionization potential I p = 21.56 eV which can endure a maximum laser intensity I 0 ≈ 8.66 × 10 14 W/cm 2 [START_REF] Bethe | Quantum Mechanics of Atoms with One and Two Electrons[END_REF]. The process is in the tunneling regime, e.g., γ ≈ 0.2 at I 0 = 7.24 × 10 14 W/cm 2 and wavelength λ = 2µm.

We estimate the contributions of the multiple FS, ICF and ACF to the total CF in the following way: (1) For each trajectory, we monitor the time evolution of the distance r(t) from the core and record its all local minima by comparing numerically r(t) at consecutive time steps. In this way the time of the rescattering event t s is determined. For each rescattering event, the minimal distance from the core r s , the distance from the core in the transverse plane (with respect to the laser polarization direction) ρ s and the electron momentum p s are determined numerically. Then, the transverse momentum change δp ⊥ due to the Coulomb potential V (r) at the s-th forward scattering event is estimated as

δp ⊥ s ≈ ∇ ⊥ V (r(t))dt ∼ -(ρ s /r 3 s )δt s ,
where δt s is the rescattering time duration. When the electron velocity p s in the FS event is large, δt s ∼ 2r s /p s . In the opposite case, δt s ∼ 2 2r s /|E(t s )| is determined by the laser field E(t s ) at the s-th rescattering moment t s . Accordingly,

δp ⊥ s = -2ρ s /(r 2 s p s ), if p 2 s r s |E(t s )| δp ⊥ s = -2 3/2 ρ s / r 5 s |E(t s )|, otherwise. (1)
(2) The transverse momentum change due to ICF is estimated numerically as the deviation of the exact transverse momentum from that neglecting the Coulomb potential, after a half laser period following the ionization moment t i : δp

(I) ⊥ = p ⊥ (t i + T /2) -p (NC) ⊥ (t i + T /2
), where T is the laser period and p (NC) ⊥ is the electron transverse momentum neglecting the Coulomb field. The numerical estimate for δp

(I)
⊥ is slightly larger in absolute value than the analytical one [7]:

δp (I) ⊥ ≈ -2p i⊥ |E(t i )|/(2I p ) 2 , (2)
with the initial transverse momentum p i⊥ . (3) We estimate the ACF contribution via numerical comparison of the asymptotic electron momentum with the one after switching off the laser pulse.

The results

The CF is mainly due to multiple small-angle scattering. It is significant only for low energy photoelectrons, and we will examine the dynamics for such electrons in details. The CF is characterized by the transverse momentum change δp ⊥ induced by the Coulomb field [13] which depends on the ionization phase ϕ i ≡ ωt i . We restrict ourselves to ionization phases and to trajectories which contribute to the low energy part (up to 40 eV) of above-threshold ionization spectrum emitted along the laser polarization direction within an opening angle of ±2.5 o . The electrons, which are emitted out of the laser polarization direction, have experienced large-angle scattering, their CF is interrupted and, consequently, their dynamics is not typical for CF. The laser intensity dependence of the different CF components is shown in Fig. 1 and the wavelength dependence in Fig. 2. For each ϕ i , the transverse momentum change is shown for the electron trajectory which has the maximal probability among the contributing trajectories at this ionization phase. We calculate the total transverse momentum change exactly via the CTMC simulation, see the curves marked as "exact" in Figs. 1 (a1,b1,c1) and 2 (a1,b1,c1). Further in Figs. 1 and2, we show the results of the estimate of δp ⊥ due to the s-th FS (s ≤ 6), ICF and ACF as described in Sec.2. To show the accuracy of our estimations, we sum up all contributions to δp ⊥ and comapare it with the exact result, see the curves marked as "ICF+ACF+FS" in Figs. 1 (a1,b1,c1) and 2 (a1,b1,c1).

From the analysis of Figs. 1 and2, the following conclusions can be drawn. First of all, Figs. 1 (a1,b1,c1) and 2 (a1,b1,c1) show that the contribution of ACF to the total δp ⊥ is generally negligible (the main contribution is at ionization phases near the peak of the laser field within the ionization phase interval of δϕ i ≈ 0.02). It decreases with increasing intensity and does not change with wavelength. The contribution of ICF to the total δp ⊥ increases with increasing intensity and remains almost constant with wavelength which is consistent with the estimate of Eq. ( 2). The contribution of ICF still constitutes a small fraction of the total δp ⊥ (less than 10%) for ionization phases π/2 < ϕ i < ϕ

(1) i (the maximum of the laser field is at ϕ i = π/2), where multiple scattering takes place but competes with the single scattering contribution at ϕ i > ϕ (1) i , especially at high intensities and wavelengths (see the estimate below, Eq. ( 6)). The ionization phase ϕ i ≈ 1.8 at a laser intensity of 1.8 × 10 14 W/cm 2 but decreases slightly with increasing intensity.

The main CF contribution to the total δp ⊥ comes from FS which determines the shape of the curve δp ⊥ versus the ionization phase, shown in Figs. 1 (a1,b1,c1) and 2 (a1,b1,c1). The transverse momentum change δp ⊥ s due to the s-th order FS in the case of different laser intensities and wavelengths are shown in Figs. 1 (a2,b2,c2) and 2 (a2,b2,c2), respectively. δp ⊥ s has a characteristic dependence on the electron ionization phase which is qualitatively the same for each scattering order. The δp ⊥ s increases sharply with decrease in the ionization phase from the threshold value (it is different for different scattering orders), reaches the peak and then decreases slowly down to a flat plateau, the latter having an increasing tail with the further decrease of the ionization phase. Although the contribution of FS decreases on average with increasing order, a higher-order FS can make a larger contribution in some phase intervals than a lowerorder one.

Let us estimate the values of the peaks and plateaux of the transverse momentum change due to high-order FS. The peak in the δp ⊥ s for the s-th order FS arises when the electron trajectory touches the z-axis at a recollision (the coordinate center is chosen at the atomic center, x-axis is in the laser polarization direction and z-axis in the transverse The total transverse momentum change (marked as "exact"), the estimation of ICF and ACF as well as of the total transverse momentum change (marked as "ICF+ACF+FS") as described in Sec.2. (a2,b2,c2) δp ⊥ due to the s-th order FS events (s is indicated in the inset) and due to ICF. (a3,b3,c3) The ratio of the δp ⊥ at the s-th order FS events to the first-order one. The ionization phase ϕ

(1) i corresponding to the threshold of the multiple FS is marked by an arrow in (a1). The peak and the plateau of δp ⊥ for the 2nd FS are marked by arrows in (a2). The maximum of the laser field is at ϕ i = π/2. direction, see Fig. 3). In this case, r s ≈ ρ s , E(t s ) ≈ E 0 , the electron momentum p s is nearly zero, see Fig. 4 (a-d), and δp ⊥ s is determined by the second expression of Eq. (1). The ionization phases corresponding to the peak and the plateau of the s-th order FS are indicated in Fig. 4

by ϕ (p)

is and ϕ (pl) is , respectively. The impact parameter at the peak of the s-th order FS can be estimated as ρ peak s ∼ p i⊥ π(s + 1)/ω, see Fig. 3. Then, using Eq.(1) we have

|δp peak ⊥ s | ∼ 1 √ E 0 2ω πp i⊥ (s + 1) 3/2 . ( 3
)
The plateau in the δp ⊥ s corresponds to the FS case when the electron velocity in the The total transverse momentum change (marked as "exact"), the estimation of ICF and ACF as well as of the total transverse momentum change (marked as "ICF+ACF+FS") as described in Sec.2. (a2,b2,c2) δp ⊥ due to the s-th order FS events (s is indicated in the inset) and due to ICF. (a3,b3,c3) The ratio of the δp ⊥ at the s-th order FS events to the first-order one.

FS point is the largest, see Fig. 4 (c). The latter is determined by the amplitude of the velocity oscillation in the laser field: v s ≈ β s E 0 /ω, with β s ≈ 0.8 at even s and β s ≈ 1 at odd s, according to the numerical results. The impact parameter in this case is estimated as ρ plateau s ∼ p i⊥ πs/ω, which yields

|δp plateau ⊥ s | ∼ 2ω 2 πp i⊥ E 0 β s s . ( 4
)
The estimates of Eqs. ( 3) and ( 4), which are in agreement with the numerical calculations presented in Figs. 1 and2, show that the peaks for the higher order FS ((s + 1)-th order) can exceed the plateaux of the lower-order FS (s-th order). In fact, this ratio is which is between 1.1 and 1.2 for s = 2 -6 at 1.81 × 10 14 W/cm 2 . Especially, the peaks of the even order FS (2nd, 4th,...) are larger than the corresponding odd FS plateaux (1st, 3rd,...). The plateaux of the even order (2nd, 4th,...) FS are comparable with that of the corresponding odd FS (1st, 3rd,...). These are because the velocity at even FS events is smaller than that at odd FS. Eq. ( 5) shows a remarkable feature that the peakto-plateau ratio increases with increasing intensity and wavelength. In particular, due to a larger contribution of the 6th order FS peak with respect to the plateau of the 5th order FS at intensity 7.24 × 10 14 W/cm 2 , see Fig. 1 (c2), an additional oscillation in the δp ⊥ dependence on the ionization phase arises, at ϕ i ≈ 1.64 in Fig. 5 (b), which induces an additional lower energy peak (at about 9 eV) in the energy distribution within the LES, see Fig. 5 (a).

|δp peak ⊥ s+1 |/|δp plateau ⊥ s | ≈ 2E 0 πp i⊥ ω sβ s (s + 2) 3/2 , (5)
ρ s ϕ i 3 (p) ϕ i 2 (p) (a) 1 2 3 4 5 ϕ i 4 (p) r s (b)
p s ϕ i ϕ i 3 (pl ) ϕ i 2 (pl ) (c)
ϕ i 4 (pl ) ϕ i E(t s ) (d)
Using Eqs. ( 2) and (4), we calculate the ratio of ICF to the plateau of the first-order FS:

δp (I) ⊥ δp plateau ⊥ 1 = π p i⊥ 2I p E 0 ω 2 . ( 6
)
The latter confirms the above statement that ICF can compete with the single scattering contribution to CF at high intensities and wavelengths. For instance, at typical parameters p i⊥ = 0.1 a.u., I p = 0.79 a.u., I = 7 × 10 14 W/cm 2 and λ = 2µm the ratio in Eq. ( 6) amounts to δp

(I) ⊥ /δp plateau ⊥ 1
≈ 0.4. The contribution of the FS (as well as the total CF effect) decreases with increasing intensity and wavelength because of the increased scattering velocity and the impact parameter, see Eqs. ( 3) and (4). For the same reason the curves in the phase space move down with higher intensities and wavelengths in Figs. 5 (b) and 5 (d). However, the ratio of δp ⊥ of different scattering orders does not significantly variate with variation of laser intensity and wavelength. Thus, the peak of the transverse momentum change due to the s-th FS scaled with that of the first FS can be estimated

|δp peak ⊥ s |/|δp plateau ⊥ 1 | ≈ 2E 0 πp i⊥ ω 1 (s + 1) 3/2 . ( 7
)
It shows that the relative role of the s-th FS even incerases slowly with increasing laser intensity and wavelength. This can also be seen from Figs. 1 (a3,b3,c3) and 2 (a3,b3,c3).

The mentioned feature can be interpreted as a slow variation of the effective number of scattering.

The effective number of scattering

The effective number of scattering N ef f can be defined employing Eqs. ( 3) and ( 4). We define N ef f as follows. First of all, we choose a small parameter 1 to determine the accuracy in which the contributions of the high-order FS to the total δp ⊥ can be neglected with respect to that of the first FS δp ⊥1 . The effective number of FS N ef f is defined to determine the highest order of FS which makes nonnegligible contribution to the total δp ⊥ . Namely, at a given ,

δp peak ⊥ s /δp plateau ⊥1 > , if s < N ef f , δp peak ⊥ s /δp plateau ⊥1 < , if s > N ef f . (8)
The latter definition yields the following expression for the effective number of FS

N ef f ≈ 1 2/3 2 π E 0 ωp i⊥ 1/3 -1. (9)
For the intensity range shown in Fig. 1, our criterion gives for N ef f a number between 5 and 6 (for the concreteness = 0.1 is assumed). The number of scattering according to Eq.( 9) increases slowly with increase in the laser intensity and wavelength. Generally, the total CF effect decreases with intensity and wavelength because the main contribution in CF comes from the multiple forward scattering which, in total, decreases as expected, see Fig. 5 (b) and(d), where the curves in the phase space move down, generally, with increasing laser intensity and wavelength. The exception is the tail at ϕ i > ϕ

(1) i in Fig. 5 (b) which is due to the competition of the first FS with the initial CF as mentioned above. The most important property is that the ratio of the transverse momentum changes due to FS of different orders are almost constant with increasing laser intensity and wavelength, see Figs. 1 (a3,b3,c3) and 2 (a3,b3,c3). Therefore, the shape of the phase space distribution (dependence of δp ⊥ on the ionization phase) remains similar, see Fig. 5 (b) and (d). Note that the consecutive slope changes of the phase space distribution are responsible for the creation of LES and are determined by the contributions of the second, third and forth FS [13].

We point out some features which distinguish the wavelength dependence of CF from the intensity dependence, see Fig. 2. The FS contribution to the total δp ⊥ decreases more strongly with increasing wavelength as Eqs. ( 3) and ( 4) indicate. Due to the latter, the knee of the phase space distribution becomes less prominent at higher wavelengths. The relative contribution of ICF to the total δp ⊥ with respect to FS increases with increasing wavelength but to a lesser extent than in the case of the intensity dependence. This is because of the p i⊥ factor in Eq. ( 6) which decreases with increase in the wavelengths.

Conclusion

At above-threshold ionization in the realm of intensities and wavelengths corresponding to the classical regime ω I p and γ 1, multiple forward scattering of an ionized electron has a nonperturbative contribution to Coulomb focusing. In some regions of ionization phase (photoelectron energy), the contribution of the higher-order forward scattering to the total Coulomb focusing can dominate the lower-order one which creates local peaks in the photoelectron spectra. The effective number of scattering does not depend significantly on laser intensity and wavelength.

  of the multiple FS, see the indication of ϕ

Figure 1 .

 1 Figure 1. (color online) The transverse momentum change δp ⊥ versus the ionization phase ϕ i = ωt i . The CTMC simulation for a neon atom in a mid-infrared laser field with a wavelength λ = 2µm for the following laser intensities: (a1-a3) I = 1.81 × 10 14 W/cm 2 , (b1-b3) I = 3.62×10 14 W/cm 2 and (c1-c3) I = 7.24×10 14 W/cm 2 . (a1,b1,c1)The total transverse momentum change (marked as "exact"), the estimation of ICF and ACF as well as of the total transverse momentum change (marked as "ICF+ACF+FS") as described in Sec.2. (a2,b2,c2) δp ⊥ due to the s-th order FS events (s is indicated in the inset) and due to ICF. (a3,b3,c3) The ratio of the δp ⊥ at the s-th order FS events to the first-order one. The ionization phase ϕ

Figure 2 .

 2 Figure 2. (color online)The transverse momentum change δp ⊥ versus the ionization phase ϕ i . The CTMC simulation for a neon atom in a mid-infrared laser field with an intensity of I = 1.81×10 14 W/cm 2 for the following wavelengths: (a1-a3) λ = 2 µm, (b1-b3) λ = 2.828 µm and (c1-c3) λ = 4 µm. (a1,b1,c1) The total transverse momentum change (marked as "exact"), the estimation of ICF and ACF as well as of the total transverse momentum change (marked as "ICF+ACF+FS") as described in Sec.2. (a2,b2,c2) δp ⊥ due to the s-th order FS events (s is indicated in the inset) and due to ICF. (a3,b3,c3) The ratio of the δp ⊥ at the s-th order FS events to the first-order one.

Figure 3 .

 3 Figure 3. The electron trajectories at ϕ i = 1.75 (thick line) and ϕ i = 1.64 (thin line). The x-coordinate along the laser polarization direction is scaled by E 0 /ω 2 and the transverse z-coordinate by p i⊥ /ω. The position A corresponds to the plateau and B to the peak of the transverse momentum change at the second forward scattering.

Figure 4 .Figure 5 .

 45 Figure 4. (color online) The parameters of the s-th order FS (s is indicated in the inset): (a) ρ s the distance from the atomic core in the transverse plane, (b) r s the distance from the core, (c) p s the momentum, (d) E(t s ) the field at the scattering moment. ϕ (p) i s and ϕ (pl)i s are the ionization phases corresponding to the peak and plateau for the s-th order FS, respectively, which are indicated with dashed lines. The CTMC simulation for a neon atom in a laser field with I = 1.81 × 10 14 W/cm 2 and λ = 2 µm.

Acknowledgments

The fruitful discussions with C. H. Keitel are acknowledged.


Markus Luengen
email: markus.luengen@uk-koeln.de

Martin § Siegel

Karl W Lauterbach

Markus § Lungen

German Parliament

universal coverage for all citizens?

Could inequality in health be cured by universal

coverage for all citizens?

The well documented social gradient in health in the developed world will not just disappear on its own. Tackling health inequalities by introducing a universal coverage healthcare system recently became an important notion in the U.S. Using cross-sectional data from Germany which has maintained its compulsory egalitarian healthcare system for more than fifty years now, we apply logistic and negative binomial regression to uncover utilization behavior patterns under universal coverage. We find that lower education and unemployment raise the risks for all diseases under consideration. Unemployment increases the chance of contacting a physician, while income and education do apparently not affect the healthcare utilization behavior. Those diseases concentrated among unemployed and less educated, however, are associated with intensified healthcare utilization. We conclude that universal coverage may make access to healthcare easier for those facing the worst health; the unemployed and lower educated. Universal coverage is widely understood as a compulsory health insurance or national health system providing access to a core bundle of healthcare services for all people in a state, regardless of their social, economic, or health status [START_REF] Emanuel | Health Care Vouchers -A Proposal for Universal Coverage[END_REF]. While the egalitarian approach is common in most European countries [START_REF] Walgate | European health systems face scrutiny in US debate[END_REF], introducing universal coverage to tackle health inequities recently became an important notion in the United States [START_REF] Porter | A Strategy for Health Care Reform -Toward a Value-Based System[END_REF]. Besides the political and ethical debate, economic arguments include the statement that poor population health contributes to social and economic instability [START_REF] Garrett | All for universal health coverage[END_REF].

It is widely agreed that health inequality will not just disappear from the developed world on its own. [START_REF] Mackenbach | Health Inequalities: Europe in Profile[END_REF] compares low and high socioeconomic status groups in several developed countries over the last decades and finds growing health inequalities. He argues that the growing gap may partly result from the fact that privileged groups gained health benefits and healthy life years considerably faster than the deprived [START_REF] Mackenbach | Health Inequalities: Europe in Profile[END_REF]. Analyzing panel data from the UK, [START_REF] Balia | Mortality, lifestyle and socio-economic status[END_REF] find that the concentration of adverse health behaviors among the deprived contributes substantially to the observed inequalities in morbidity and mortality to the detriment of the poor [START_REF] Balia | Mortality, lifestyle and socio-economic status[END_REF].

The present paper aims to uncover the patterns of healthcare utilization under universal coverage. For this purpose, we use German cross-sectional survey data because Germany has maintained its compulsory health insurance system, including free choice of and access to general and specialist practitioners (at least until 2004, when a fee of 10 € per three month for access to a physician was introduced), low copayments and an egalitarian supply of health services, for more than fifty years now. We use logistic regression models to describe the distribution of risks for obesity, chronic cardiovascular and lung diseases, and diabetes mellitus. Using a two-part model, we then analyze the utilization behavior in terms of general and specialized physician consultations. We focus on the issue of whether inequalities persist in the German egalitarian system and thereby contribute to the ongoing discussion of whether universal coverage may be a promising step toward an equitable distribution of health.

Data and Methods

We use cross-sectional data from the 2002 sample of the Health Care Access Panel (HCAP), a voluntary mail survey conducted by TNS Infratest Health Care. Excluding people younger than 25 (to obtain reliable socioeconomic information) and dropping individuals with missing information leaves us 39,553 observations. We fit logistic and negative binomial count models using maximum-likelihood estimation techniques and compute heteroscedasticityconsistent standard errors.

The impact of education and income on health

We evaluate the impact of socio-economic aspects on health to identify possible reasons for persisting health inequalities outside the healthcare system. Table 1 presents the results from the logistic regression (to economize on space, we refrain from presenting the results for age and sex as demographic controls in both tables; these are available from the authors on request). Adjusted Wald tests demonstrate that education has a statistically significant influence on the risks for obesity and diabetes mellitus, while income influences the risks for obesity as well as chronic cardiovascular and lung diseases. We find that lower education and unemployment seem to raise the risks for all diseases under consideration. Unemployed individuals have the highest risk for obesity while having estimated risks comparable to the retired for cardiovascular conditions, diabetes mellitus, and lung diseases. As the healthiest groups are the lowest and highest income quintiles, we cannot support the notion of an One may consider a lower socioeconomic status coinciding with less consumption of resources at a given health status as a possible explanation for the persistence of health inequalities. We hence draw our attention to the utilization of resources in the healthcare system. Table 2 presents the estimation results for healthcare utilization. The table contains both stages of the two-part model for both general and specialized practitioner visits. From an insignificant estimate for the odds ratio of obesity in terms of general practitioner visits, for instance, one may conclude that the shares of individuals contacting a general physician do not differ between the obese and non-obese. The incidence ratios (IRR) provide information about the influence of certain characteristics on the predicted number of doctor visits. For example, considering the result for the unemployed in terms of general practitioner visits, one may expect the unemployed to see their physician approximately one and a half times more often than employed people after the first contact was made.

The chance for making first contact with a general practitioner does not differ significantly between the educational levels, and according to the performed Wald F-test, the set of dummies is not jointly significant. While no difference between house workers and the employed can be observed, the unemployed exhibit an almost 30 percent increased chance of contacting a general practitioner. Although income is statistically significant, we do not observe a clear gradient. All diseases under consideration increase the odds for contacting a general practitioner; however, obesity does not. These results change somewhat when we consider the number of doctor visits as the intensity of utilization. Higher education significantly decreases the estimated number of doctor visits. The unemployed use the healthcare system 50 percent more than the employed and even more than the retired. Although significant, income yields no obvious gradient. Obesity and chronic conditions apparently increase the need for doctor consultations. The privately insured do not show different utilization intensity compared with people who have compulsory health insurance.

We find that people with lower educational status are less likely to contact a specialized practitioner. Again, while houseworkers appear to have no different odds for a first visit, we estimate significantly increased odds for unemployed and retired. Income exhibits no unique gradient. While the first, fourth, and fifth quintiles are not (statistically) different, the second and third quintiles have lower chances of making first contact with a specialized practitioner.

Whether one be privately insured or under the compulsory health insurance system seems to make no difference for the probability of contacting a specialized practitioner. Obesity does not significantly change the odds for contacting a specialized practitioner; however, the considered diseases do.

The results for the numbers of visits do not differ much from those for the chances of contacting a specialized physician. The major difference is that income does not have a significant influence on the number of visits. Obesity increases the predicted number of visits significantly once a first contact is made.

Concluding remarks

Analyzing health distribution and healthcare utilization behavior, we find persisting health and healthcare inequalities in Germany despite the fact that its healthcare system has a longestablished universal coverage. With unemployment remaining a substantive risk factor, one may consider getting people into jobs to be the essential approach toward a reduction of health inequalities. Considering education as a substantive factor for the risk of unemployment, the educational system may be seen as a second major determinant for the distribution of health and longevity within a society. One may conclude that important parts of inequalities in societies stems from factors outside the health care system. Relieving One may, however, expect that substantial differences related to unemployment and education will remain. Effective preventive action should therefore include both, labor market and educational interventions.

It is important to mention that universal coverage apparently raises the utilization among those groups that may benefit most: the ill and unemployed. Those facing the worst health are able to seize healthcare services as required. However, receiving the full number of visits involves some limitations. Our data provide no evidence on the quality of care, the physicians' skills, or the treatment outcomes. It may be that people with higher income are able to choose better-performing health services.

It is well documented in the literature that education influences lifestyle and health behavior considerably. The influence of education on health found in our data may therefore be transmitted through the so-called lifestyle factors (see [START_REF] Balia | Mortality, lifestyle and socio-economic status[END_REF]).

Although the concept of universal coverage may not be perfectly able to relieve the consequences of illness, we conclude that it should be considered an important step toward health equity or at least toward an equitable access to healthcare.

Author Contributions

ML concept and design, drafting, and critical revision MS data analysis and interpretation, statistics, and critical revision.

KL critical revision, approval of the article

No conflict of interests.

  [START_REF] Mackenbach | Health Inequalities: Europe in Profile[END_REF] Deleted: in the developed world Deleted: In 2004 low copayments of 10 € per three month were introduced for visits to physician offices.

  gradient. The estimated risks for the considered diseases do not differ between the compulsory and privately insured; an exception is obesity, where the privately insured have a significantly lower risk.

Deleted:

  The four income dummies are jointly significant; however,

  to care and thereby increasing utilization may reduce health disparities.

Table 1 :

 1 Comparing the risk for diseases over socioeconomic subgroups socioeconomic risk for certain conditions

				chronic
				cardiovascular
		obesity		conditions	lung diseases	diabetes
	factor	OR	p-Value OR	p-Value OR	p-Value OR	p-Value
	lower educational level	1.340 0.000	1.038 0.462	1.038 0.615	1.315 0.015
	medium educational level	reference category
	higher educational level	0.811 0.000	0.954 0.402	0.948 0.494	1.089 0.524
	employed	reference category
	unemployed	1.485 0.000	1.417 0.000	1.352 0.002	2.324 0.000
	retired	1.186 0.049	1.470 0.000	1.550 0.000	2.003 0.000
	house worker	1.188 0.006	1.193 0.010	1.082 0.421	1.256 0.110
	1st income quintile	reference category
	2nd income quintile	1.235 0.001	1.294 0.000	1.327 0.002	1.225 0.140
	3rd income quintile	1.143 0.022	1.115 0.091	1.133 0.158	1.198 0.191
	4th income quintile	1.043 0.489	1.060 0.382	1.001 0.990	0.945 0.704
	5th income quintile	0.861 0.019	0.961 0.555	0.960 0.657	0.923 0.593
	private health insurance	0.762 0.000	0.893 0.082	0.983 0.866	0.961 0.816

Table 1 :

 1 Healthcare Utilization; chance of first contact and numbers of visits

		healthcare utilization
			general practitioners	specialized practitioners
		chance for first	number of	chance for first	number of
		contact	visits	contact	visits
	factor	OR	p-Value IRR	p-Value OR	p-Value IRR	p-Value
	lower educational level	0.926	0.164 1.072	0.001 0.901	0.005 1.051	0.065
	medium educational level				reference category
	higher educational level	0.951	0.316 0.940	0.002 1.044	0.233 0.924	0.003

Acknowledgements: We thank Claus Wendt for his helpful comments Page 7 of 10 International Journal of Clinical Practice International Journal of Clinical Practice


Manel Mata-Cases

Cristina De Prado-Lacueva

Virginia Salido-Valencia

Ester Fernández-Bertolín

José Casermeiro-Cortés

Manuel García-Durán

Susana Jabalera-López

Maria Isabel Fernández-Sanmartín

INCIDENCE OF COMPLICATIONS AND MORTALITY IN A TYPE 2 DIABETES PATIENT COHORT STUDY FOLLOWED FROM DIAGNOSIS IN A PRIMARY HEALTHCARE CENTER

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Type 2 diabetes mellitus (T2DM) is associated with microvascular and macrovascular complications [START_REF] Goday | Epidemiología de la diabetes y sus complicaciones no coronarias[END_REF][START_REF] Deshpande | Epidemiology of diabetes and diabetesrelated complications[END_REF]. Moreover, T2DM is an independent risk factor for cardiovascular disease [START_REF] Selvin | Meta-analysis: glycosylated hemoglobin and cardiovascular disease in diabetes mellitus[END_REF] and is frequently associated with other cardiovascular risk factors (CVRF) such as hypertension, dyslipidemia and obesity. The levels of glucose and Glycosylated Hemoglobin (HbA1c) are directly related to the increased risk of microvascular and macrovascular complications [START_REF] Selvin | Meta-analysis: glycosylated hemoglobin and cardiovascular disease in diabetes mellitus[END_REF][START_REF] Gall | Prevalence of micro-and macroalbuminuria, arterial hypertension, retinopathy and large vessel disease in European type 2 (non-insulin-dependent) diabetic patients[END_REF]. There are cohort follow up studies based on crosssectional studies [START_REF] Gimeno-Orna | Microalbuminuria presents the same vascular risk as overt CVD in type 2 diabetes[END_REF][START_REF] Gimeno-Orna | Ability of retinopathy to predict cardiovascular disease in patients with type 2 diabetes mellitus[END_REF][START_REF] Costa | en representación del Grupo de Investigación ITG. La escala de Framingham sobrevalora el riesgo cerebrovascular de la diabetes y el síndrome metabólico en la población española[END_REF][START_REF] Riu | A prospective study of cardiovascular disease in patients with Type 2 diabetes. 6.3 years of followup[END_REF][START_REF] Elley | Glycated haemoglobin and cardiovascular outcomes in people with Type 2 diabetes: a large prospective cohort study[END_REF] or population-based computer records [START_REF] Mcalpine | The annual incidence of diabetic complications in a population of patients with Type 1 and Type 2 diabetes[END_REF][START_REF] Brocco | Monitoring the occurrence of diabetes mellitus and its major complications: the combined use of different administrative databases[END_REF][START_REF] Ringborg | Prevalence and incidence of Type 2 diabetes and its complications 1996-2003--estimates from a Swedish population-based study[END_REF] with the aim of establishing the incidence or prevalence of complications or mortality [START_REF] Mulnier | Mortality in people with type 2 diabetes in the UK[END_REF][START_REF] Standl | Predictors of 10-year macrovascular and overall mortality in patients with NIDDM: the Munich general practitioner project[END_REF][START_REF] Brun | Verona Diabetes Study. Diabetes duration and cause-specific mortality in the Verona Diabetes Study[END_REF][START_REF] Fox | The significant effect of diabetes duration on coronary heart disease mortality: the Framingham Heart Study[END_REF][START_REF] Lutgers | Life expectancy in a large cohort of type 2 diabetes patients treated in primary care (ZODIAC-10)[END_REF]. On the other hand, studies on the incidence of complications in patient cohorts followed from the moment of T2DM diagnosis [START_REF] Hanefeld | Risk factors for myocardial infarction and death in newly detected NIDDM: the diabetes intervention study, 11-year follow-up[END_REF][START_REF] Smith | New-onset diabetes and risk of all-cause and cardiovascular mortality: the Cardiovascular Health Study[END_REF][START_REF] Guzder | Early mortality from the time of diagnosis of Type 2 diabetes: a 5-year prospective cohort study with a local age-and sex-matched comparison cohort[END_REF][START_REF] Guzder | Impact of metabolic syndrome criteria on cardiovascular disease risk in people with newly diagnosed type 2 diabetes[END_REF][START_REF] Hillier | Complications in young adults with early-onset type 2 diabetes: losing the relative protection of youth[END_REF][START_REF] Mollet | Variabilidad en el calculo del riesgo coronario en la diabetes mellitus tipo 2[END_REF][START_REF] Valdés | Riesgo de mortalidad en diabetes diagnosticada, diabetes no diagnosticada y prediabetes en población adulta española. Estudio Asturias 1998-2004[END_REF][START_REF] Hu | Gender difference in all-cause and cardiovascular mortality related to hyperglycaemia and newly-diagnosed diabetes[END_REF][START_REF] Hansen | 16-year excess all-cause mortality of newly diagnosed type 2 diabetic patients: a cohort study[END_REF][START_REF] Saydah | GHb level and subsequent mortality among adults in the U[END_REF][START_REF] Harris | Onset of NIDDM occurs at least 4-7 yr before clinical diagnosis[END_REF] are more interesting, although the majority only explore macrovascular disease [START_REF] Hanefeld | Risk factors for myocardial infarction and death in newly detected NIDDM: the diabetes intervention study, 11-year follow-up[END_REF][START_REF] Guzder | Early mortality from the time of diagnosis of Type 2 diabetes: a 5-year prospective cohort study with a local age-and sex-matched comparison cohort[END_REF][START_REF] Guzder | Impact of metabolic syndrome criteria on cardiovascular disease risk in people with newly diagnosed type 2 diabetes[END_REF] or mortality [START_REF] Hanefeld | Risk factors for myocardial infarction and death in newly detected NIDDM: the diabetes intervention study, 11-year follow-up[END_REF][START_REF] Smith | New-onset diabetes and risk of all-cause and cardiovascular mortality: the Cardiovascular Health Study[END_REF][START_REF] Guzder | Early mortality from the time of diagnosis of Type 2 diabetes: a 5-year prospective cohort study with a local age-and sex-matched comparison cohort[END_REF][START_REF] Mollet | Variabilidad en el calculo del riesgo coronario en la diabetes mellitus tipo 2[END_REF][START_REF] Valdés | Riesgo de mortalidad en diabetes diagnosticada, diabetes no diagnosticada y prediabetes en población adulta española. Estudio Asturias 1998-2004[END_REF][START_REF] Hu | Gender difference in all-cause and cardiovascular mortality related to hyperglycaemia and newly-diagnosed diabetes[END_REF][START_REF] Hansen | 16-year excess all-cause mortality of newly diagnosed type 2 diabetic patients: a cohort study[END_REF][START_REF] Saydah | GHb level and subsequent mortality among adults in the U[END_REF]. However, the main limitation of those studies is that it is difficult to determine the start of the illness, which may be several years before clinical diagnosis [START_REF] Harris | Onset of NIDDM occurs at least 4-7 yr before clinical diagnosis[END_REF], when blood glucose levels prior to diagnosis are not available. The most well-known source of information is the United Kingdom Prospective Diabetes Study (UKPDS), a clinical trial carried out in the United Kingdom between 1978 and 1998. The observational epidemiological analysis of the entire patient cohort, independently of the type of treatment to which they were assigned, constitutes a source of data so as to calculate the T2DM complications incidence rates relative to the mean HbA1c values during the follow up [30] as well as the coronary and cerebrovascular risk prediction equation [START_REF] Stevens | UKPDS 56. The UKPDS risk engine: a model for the risk of coronary heart disease in type 2 diabetes[END_REF].

Several follow up studies of those recently diagnosed have been done in order to validate different coronary risk tables [START_REF] Mollet | Variabilidad en el calculo del riesgo coronario en la diabetes mellitus tipo 2[END_REF] or to learn the causes of mortality in our The aim of the present study is to determine the microvascular and macrovascular complications incidence and death rates in a recently-diagnosed T2DM patient cohort.

They were diagnosed between 1991 and 2000 and followed until the end of 2006 in a primary healthcare center. As secondary objectives, the aims were to identify the factors associated with the incidence of complications and mortality and the time-period between T2DM diagnosis and the appearance of complications.

MATERIALS AND METHODS

A retrospective longitudinal observational study was designed that included T2DM cases diagnosed between 1991 and 2000 in a primary healthcare center. The center is the main healthcare resource in the area. It is a poor area in the mainly Caucasian neighborhood of La Mina de Sant Adrià de Besòs (Barcelona, Spain) in which the Romani ethnic group makes up some 20% of the total population.

A detailed description of the methodology as well as the characteristics of the patients and the presence of cardiovascular disease at the time of diagnosis has been previously published [START_REF] Mata-Cases | Incidencia de diabetes tipo 2 y análisis del proceso diagnóstico en un centro de atención primaria durante la década de los 90[END_REF][START_REF] Mata-Cases | Prevalencia de enfermedad cardiovascular en personas recién diagnosticadas de diabetes tipo 2[END_REF].

Of the total diabetes cases, 598 patients, 118 were excluded for not having blood glucose measurements below the threshold for diabetes diagnosis in the 3 years prior to diagnosis.

Another four patients were excluded for having been followed for a period of less than a year and another 7 became diabetes-free during the follow up period. In the end, 469 were included. The standing criteria for the diagnosis of T2DM were applied at each instance: those of the World Health Organization (WHO) up until July of 1997 [START_REF] Standl | Predictors of 10-year macrovascular and overall mortality in patients with NIDDM: the Munich general practitioner project[END_REF]; from July 1997, the fasting glycaemia ≥126 mg/dl following the criteria of the American Diabetes Association [START_REF] Brun | Verona Diabetes Study. Diabetes duration and cause-specific mortality in the Verona Diabetes Study[END_REF] that was also accepted by WHO [START_REF] Fox | The significant effect of diabetes duration on coronary heart disease mortality: the Framingham Heart Study[END_REF].

The clinical records of all the patients were reviewed in order to register variables related to the follow up on T2DM and to detect the complications that arose up to December of 2006.

Study variables.

The clinical characteristics registered upon diabetes diagnosis were: age, gender, diagnostic glucose values, HbA1c, blood pressure, total cholesterol, High-density lipoprotein (HDL) and Low-density lipoprotein (LDL) cholesterol, weight and height. The following CVRF were also registered: hypertension (blood pressure ≥140/90 mm Hg), hypercholesterolemia (total cholesterol ≥250mg/dl), hypertriglyceridemia (triglycerides ≥150mg/dl), obesity (body mass index ≥30 kg/m 2 ) and current or ex-smoker. The measurement of HbA1c was instituted in mid-1992. The mean HbA1c was calculated during the follow up period based on the annual average of the values annotated in the clinical history.

The macrovascular variables were: coronary heart disease (acute myocardial infarction -AMI-, angina pectoris -in the absence of AMI-and silent AMI based on electrocardiographic criteria), cerebrovascular disease (stroke or transitory ischemic accident), peripheral arteriopathy and a combined variable of all of them. As far as microvascular complications go: nephropathy (macroalbuminuria: Albuminuria ≥ 300 mg / 24h or albumin/Creatinine ratio ≥ 300 mg/mmol), autonomic or peripheral diabetic neuropathy and diabetic retinopathy (background or proliferative and/or maculopathy) and a combined variable of some of them. In those cases in which a funduscopy was not performed over the 3 years prior to the appearance of retinopathy, the midpoint of the period was considered as the start date.

The diabetic foot variable (ulcers or amputations) was not included in the microvascular or macrovascular combined variables.

The follow up period for the microvascular variables was taken from the diagnosis up to the date of the last screening. In the case in which any data was not available, the value was considered missing. For macrovascular variables and mortality, the follow up period was until the appearance of the event or the date of the last visit.

In the case of deceased patients, the cause of death was investigated in the clinical records and the center's death registry. The data was requested from the National Institute of Statistics in those cases in which it was not given or there were doubts as to the cause or date.

For the calculation of the annual incidence rate and the analysis of survival, the first event for each complication and the date of appearance were recorded. The events recorded in the paper or computerized clinical records were checked against hospital reports (i.e. admittance for AMI, stroke…), reports from specialists, diagnostic test results (i.e. The incidence rate per 1000 patients/year for macro and microvascular events and mortality, excluding those patients that already presented the complication at the start of the follow up or during the 3 month after diagnosis, were calculated.

The confidence intervals at 95% (CI 95%) were estimated assuming a Poisson distribution.

The survival curves were calculated separately for males and females with the Kaplan-Meier method for the microvascular and macrovascular variables and mortality. The comparison between the survival curves according to independent variables was done with the Log-Rank test.

In order to evaluate the relationship between variables and the appearance of events, adjusting for the follow up time, the Cox proportional models were estimated separately for males and females. Those variables that turned out to be marginally significant with a p<0.20, those considered clinically relevant (like the basal HbA1c and the mean during the follow up) and all the major interactions were included for each model (macrovascular, microvascular and mortality). Previously, linearity and proportionality criteria for each covariable were assessed. The model was adjusted by excluding: first, the non-significant interactions; second, those variables that were not significant and whose exclusion did not change the beta coefficients of the other variables by more than 20%. Each final model is presented with the estimate of the hazard ratio (HR) and the 95% CI. The validation of the model was carried out by the Hosmer and Lemeshow calibration test [START_REF] Agostino | Evaluation of the performance of survival analysis models: Discrimination and calibration measures[END_REF], and the area under the curve (AUC). For its calculation, the Somer's D correlation ranges index was used for the analysis of the data [START_REF] Newson | Confidence intervals for rank statistics: Somers'D and extensions[END_REF].

RESULTS

Of the 469 cases included, 253 were women (53.9%). The mean age at diagnosis was 60.4 (SD 10.7) years [in women 61.7 (SD 10.9) years and in men 58.9 (SD 10.2) years; p=0,006]. Of those studied, 96.4% of the patients presented some of the CVRF studied.

The most prevalent in the diagnosis were (Table 1): hypertension (72.3%), obesity (60.6%), hypercholesterolemia (50.5%) and current or former smoking (40.8%; 23.7% smokers and 17.1% ex-smokers) with statistically significant differences depending on gender and age groups. There were significantly more smokers and ex-smokers among males (42.1% and 32.9%, respectively in males and 7.9% and 3.6% in females; p<0.001).

Women presented obesity (p<0.001) and hypertension (p=0.002) more frequently. Patients younger than 65 years of age had greater mean diastolic blood pressure (DBP) values (p=0.006), first HbA1c and follow up HbA1c means (p<0.001 and p=0.031, respectively) and lower HDL cholesterol values (p=0.015); a higher tobacco habit prevalence (p=0.001) and less hypertension prevalence (p=0.033). Cardiovascular disease was present more frequently at diagnosis in ex-smokers (28.7%) than in smokers (18%) or non-smokers (11.2%) (p<0.001).

During the follow up period (8.81 yrs., SD 3.21), forty-seven patients (10%) moved to another center and there were 80 deaths (17%); 44 males and 36 females. The cause of death was tumoral in 31 cases (38.75%), macrovascular in 24 cases (30%), other causes in 22 cases (27.5%) and unknown in 3 cases (3.75).There were no significant differences between genders except for mortality due to tumors which was more frequent in men (52.3%) than women (22.2%) (p=0.008).

The frequency of complications prior to diagnosis and the annual incidence rate for macrovascular complications (24.10), microvascular complications (29.11) (23.52 versus 15.72) were also greater in men. However, none of them reached statistically significant levels. Those over 65 years of age had a higher incidence of macrovascular complications (p=0.049) and, specifically, cerebrovascular disease (p<0.001). The time of survival up to the appearance of macrovascular complications was not related to the HbA1c values. The survival time period for microvascular complications was less when the first HbA1c was greater than 7% (p<0,001) and when the mean follow up HbA1c was greater than 7% (p=0,001) in both sexes (Figure 1). The variables related to the greater probability of having a macrovascular complication in the follow up were different between men and women (Table 3). In women, the risk is increased with greater first HbA1c values (HR 1.31; CI 95%: 1.03-1.66), HbA1c in the follow up (HR 5.26; CI 95%: 1.61-17. [START_REF] Hanefeld | Risk factors for myocardial infarction and death in newly detected NIDDM: the diabetes intervention study, 11-year follow-up[END_REF]) and with age (HR 1.30; CI 95%: 1.10-1.53).

The relationship between the HbA1c and the appearance of macrovascular complications behaves differently depending on the age of the woman. The strength of the association diminishes when the age increases. In males, the variables associated with a greater risk of complications are age (HR 1.05; CI 95%: 1.01-1.09) and the total cholesterol level even though the magnitude of the association is weak (HR 1.01; CI 95%: 1.00-1.02).

Microvascular complications in women are related to the initial HbA1c value (HR 1.40; CI 95%: 1.20-1.63) and the HDL cholesterol (HR 0.95; CI 95%: 0.91-0.99). In males, the variables associated with microvascular complications are HDL cholesterol (HR 0.97; CI 95%: 0.94-1.00) and, above all, hypertension (HR 2.92; CI 95%: 1.28-6.69). On the In terms of mortality in women, the probability of dying is greater the lower the HDL (HR 0.92; CI 95%: 0.88-0.96) and the DBP (HR 0.71; ICI 95%: 0.54-0.94) are and whether a smoker or non-smoker (HR 3.67; CI 95%: 1.16-11.56). Age interacts slightly in the relationship between DPB and mortality. The most relevant factor in males in relation to mortality is age (HR 1.07; CI 95%: 1.04-1.11) and smoking. Then again, this association is not statistically significant (HR 1.91; CI 95%: 0.85-4.32).

The differences between the expected and the observed mortality rates were statistically significant according to the Hosmer and Lemeshow calibration test. It showed a low adjustment of this model. The other models (micro and macrovascular complications) had an acceptable adjustment and a high predictive capacity (AUC >65).

DISCUSSION

This study gives the complications and mortality incidence rates in patients recently diagnosed with T2DM identified during a 10 year period in a primary care center and followed an average of almost 9 years. The annual rates for death and complications in this Mediterranean population were lower than those published in anglo-saxon countries [19-23, 26-27,30] except for the mortality rates observed in the UKPDS epidemiological study in which patients were younger (53 yrs.) than those in our study (60 yrs.) [30].

Studies of recently diagnosed patients are rare in the international literature [START_REF] Hanefeld | Risk factors for myocardial infarction and death in newly detected NIDDM: the diabetes intervention study, 11-year follow-up[END_REF][START_REF] Smith | New-onset diabetes and risk of all-cause and cardiovascular mortality: the Cardiovascular Health Study[END_REF][START_REF] Guzder | Early mortality from the time of diagnosis of Type 2 diabetes: a 5-year prospective cohort study with a local age-and sex-matched comparison cohort[END_REF][START_REF] Guzder | Impact of metabolic syndrome criteria on cardiovascular disease risk in people with newly diagnosed type 2 diabetes[END_REF][START_REF] Hillier | Complications in young adults with early-onset type 2 diabetes: losing the relative protection of youth[END_REF][START_REF] Mollet | Variabilidad en el calculo del riesgo coronario en la diabetes mellitus tipo 2[END_REF][START_REF] Valdés | Riesgo de mortalidad en diabetes diagnosticada, diabetes no diagnosticada y prediabetes en población adulta española. Estudio Asturias 1998-2004[END_REF][START_REF] Hu | Gender difference in all-cause and cardiovascular mortality related to hyperglycaemia and newly-diagnosed diabetes[END_REF][START_REF] Hansen | 16-year excess all-cause mortality of newly diagnosed type 2 diabetic patients: a cohort study[END_REF][START_REF] Saydah | GHb level and subsequent mortality among adults in the U[END_REF]. In our country only two follow up studies of recently diagnosed patients with the aim of validating different coronary risk tables relative to their comparison with the accumulated incidence observed [START_REF] Mollet | Variabilidad en el calculo del riesgo coronario en la diabetes mellitus tipo 2[END_REF] or to find out the rates and causes of mortality [START_REF] Valdés | Riesgo de mortalidad en diabetes diagnosticada, diabetes no diagnosticada y prediabetes en población adulta española. Estudio Asturias 1998-2004[END_REF] have been In terms of the observed annual incidence rates, it is worthy to note that they are greater in males for all complications except for cerebrovascular disease as well as for mortality.

However, the differences are not significant due to the low number of cases.

With regards to the causes of mortality, the main cause in our study was not cardiovascular but tumoral. This is different from the majority of cohort follow up epidemiological studies based on cross sectional studies [1,2,14-18], as well as in those of the recently diagnosed [START_REF] Hanefeld | Risk factors for myocardial infarction and death in newly detected NIDDM: the diabetes intervention study, 11-year follow-up[END_REF][START_REF] Smith | New-onset diabetes and risk of all-cause and cardiovascular mortality: the Cardiovascular Health Study[END_REF][START_REF] Guzder | Early mortality from the time of diagnosis of Type 2 diabetes: a 5-year prospective cohort study with a local age-and sex-matched comparison cohort[END_REF][START_REF] Hu | Gender difference in all-cause and cardiovascular mortality related to hyperglycaemia and newly-diagnosed diabetes[END_REF][START_REF] Hansen | 16-year excess all-cause mortality of newly diagnosed type 2 diabetic patients: a cohort study[END_REF]30]. On the other hand, the causes of mortality were quite similar to ours in the only study in our country carried out in Asturias [START_REF] Valdés | Riesgo de mortalidad en diabetes diagnosticada, diabetes no diagnosticada y prediabetes en población adulta española. Estudio Asturias 1998-2004[END_REF].

The survival curves show how the initial and the mean HbA1c in the follow up greater than 7% are significantly related to the microvascular complications but not to the macrovascular complications. Then again, an inverse relationship in the survival curves was observed in our study with mortality greater in those that had a mean HbA1c <7% during the follow up. This significance disappeared upon separating by gender as much in terms of the survival curves as in the Cox regression after adjusting for other variables.

The Cox regression analysis reveals that the variables related to a greater probability of having a cardiovascular event in the follow up were different for men and women. These relationships probably have something to do with the difference of the prevalence of risk factors between the sexes. One might emphasize that in spite of the great difference in smoking habits in men as opposed to women (75% vs 11.5%) the rate of coronary heart disease was not substantially different (15.10 vs 11.39). This fact is perhaps related to the greater prevalence of obesity and Hypertension in women. It is surprising that significant predictors of cardiovascular disease. It is probably due to the low incidence of complications related to the bias of survival as those patients that already had cardiovascular disease have been excluded. In these excluded patients, the association was significant (previously published data), but it was only for smoking [START_REF] Mata-Cases | Prevalencia de enfermedad cardiovascular en personas recién diagnosticadas de diabetes tipo 2[END_REF]. A more extended follow up with a greater number of events would have conferred significance to the differences. On the other hand, it is true that smoking is positively related to mortality, although it is only significant in women.

With respect to the relationship between the HbA1c and the complications, the results are dissimilar in the analysis by sexes. Thus, the macrovascular complications are associated with the initial and the follow up HbA1c in a significant way in females but not in males. In terms of microvascular complications, the HbA1c again behaves differently by gender: it is the initial HbA1c in women while it is the mean in the follow up in men although it was not confirmed in the Cox regression. With respect to mortality, no relationship to the HbA1c was observed in either men or women. With respect to the relationship of DBP to death in women, it agrees with that observed in other studies in which a relationship was seen between lower blood pressure values and a greater probability of death in people of advanced age [START_REF] Ungar | Low diastolic ambulatory blood pressure is associated with greater allcause mortality in older patients with hypertension[END_REF].

The main limitations of our study are due to its retrospective observational design. The variables and the complications were obtained from the clinical records and some of them might have been missed. For some variables like smoking, the length of the followup permitted the retrieval of this data retrospectively in those cases without information annotated at the moment of diagnosis. In the case of retinopathy and/or nephropathy, a significant number of patients did not have annual screening. The exclusion of the patients that did not have a screening or with a short follow up (up to the last screening), might explain why the microvascular rates were greater than the macrovascular rates.

We excluded 118 patients without any glycaemia measurement before diagnosis so as to be sure that they were at the onset of the disease. Excluded patients were less obese, hypertensive and hypercholesterolemic (previously published data) [START_REF] Mata-Cases | Prevalencia de enfermedad cardiovascular en personas recién diagnosticadas de diabetes tipo 2[END_REF]. In fact, in our cohort, the main reason for diabetes diagnosis was the monitoring of blood samples in the follow up of hypertension and hypercholesterolemia [START_REF] Mata-Cases | Incidencia de diabetes tipo 2 y análisis del proceso diagnóstico en un centro de atención primaria durante la década de los 90[END_REF]. However, there was the same sex distribution, mean age and HbA1c and smoking prevalence at diagnosis for excluded and included patients [START_REF] Mata-Cases | Prevalencia de enfermedad cardiovascular en personas recién diagnosticadas de diabetes tipo 2[END_REF].

As a routine clinical practice study, diagnosis was usually made with fasting plasma glucose values but 87 patients (18%) where diagnosed based on an OGTT. These patients were mainly diagnosed before 1997. After that year, in which the ADA proposed abandoning the use of OGTT for clinical purposes, it was rarely performed in our center.

Finally, the low socioeconomic level and the ethnic composition of our community can impede the generalization of the results to other populations.

CONCLUSIONS

Our study provides the annual death and complications rates in a patient cohort followed from diagnosis with the findings being that they are greater for microvascular complications than for macrovascular complications. The annual rates for death and complications in this Mediterranean population were lower than those published in anglo-saxon countries. In terms of mortality, unlike in other studies, only a third of the deaths were for cardiovascular causes. Except for cerebrovascular disease, males had greater death and complication rates. Multi-center studies carried out in primary care centers that include a greater number of participants and events are needed. They would make it possible to confirm these results and allow for greater accuracy in the analysis of the observed differences by age and gender.

  ]. Then again, none relative to the incidence of microvascular complications have been published.

  coronarography, electromyogram, retinal fluorescein angiography, etc.) or clinical anamnesis or examination in the absence of the aforementioned (i.e. intermittent claudication, diabetic foot ulcers or amputations).

  the HbA1c does not reach a statistically significant level (HR 1.2; CI 95%: 0.94-1.54).

  like smoking, hypertension and LDL-cholesterol are not

  (19.23) during the follow up are shown in Table 2. Males had more macrovascular complications (29.28 versus 20.48 in females) except for cerebrovascular disease (10.36 versus 11.55). The annual rate of microvascular complications (34.51 versus 24.30) and mortality

	F o
	r
	P
	e e r
	R e v i e w
	O n
	l y
	, and mortality
	7

Table 1 . Basal characteristics of the patients. by sex and age groups.

 1

	SD: standard deviation; SBP: sistolic blood pressure; DBP: diastolic blood pressure; BMI: body-mass index; CVRF: cardiovascular risk factors; HbA1c:
	glycosilated haemoglobin; HDL-cholesterol: high density lipoprotein-cholesterol .
	* Number of patients are shown only when available data are less than the total population (N=469)
	† p<0.05

Table 2 . Incidence rates per 1000 patients/year and 95% confidence intervals for micro and macrovascular complications and mortality

 2

	IRx1000: incidence rate per 1000 patients/year ; CHD: coronary heart disease; AMI: acute myocardial infarction; CVD: cerebrovascular disease; PA:
	peripheral arteriopathy.
	* macroalbuminuria(>300mg/dL)

Page 18 of 22 International Journal of Clinical Practice International Journal of Clinical Practice

		AUC: 0.85 (95%CI: 0.79-0.91)			H-L test: p<0.001
	Men	Adj_HR	95%CI Adj_HR	p	Crude_HR	95%CI Crude_HR	p
	Age at diagnosis	1.07	1.04	1.11	<0.001	1.07	1.04	1.11	<0.001
	Smoking	1.91	0.85	4.32	0.119	1.67	0.74	3.78	0.216
		F o r P e e r R e v i e w AUC: 0.71 (95%CI: 0.64-0.78)	O n l y H-L test: p=0.052
									4

Table 3 .

 3 Factors associated with the appearence of events. Cox proportional regression models

Page 19 of 22 International Journal of Clinical Practice International Journal of Clinical Practice

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

Figure 1. Survival curves for macrovascular and microvascular complications and mortality by first HbA1c and mean follow up HbA1c. Comparisons between patients with HbA1c ≥7% or HbA1c <7%.

International Journal of Clinical PracticeInternational Journal of Clinical Practice

Acknowledgements:

All the professionals, doctors and nurses, at the Centro de Salud La Mina (la Mina Healthcare Center), without whose day-to-day work it would not have been possible to carry out this study, Joan Vila, researcher from the Institut Municipal d'Investigacions Mèdiques de l'Ajuntament de Barcelona (Barcelona Municipal Medical Investigations Institute), for his help and collaboration in the statistical analysis and Eric L. Goode for assisting in the translation.

International Journal of Clinical Practice International Journal of Clinical Practice International Journal of Clinical Practice International Journal of Clinical Practice

A. FIRST MACROVASCULAR COMPLICATION Mean follow-up HbA1c