Anissa Eddhahak-Ouni

Ingrid Masson

Eric Allaire

Professor Mustapha Zidi
email: zidi@univ-paris12.fr

Stochastic approach to estimate the arterial pressure

Keywords: Stochastic, Arterial pressure, Hyperelastic material, Maximum entropy principle

The aim of this paper is to illustrate the application of a stochastic approach to estimate the human common carotid arterial pressure. The analysis took into account the possible random uncertainties of the problem inputs such as geometric information and mechanical model parameters so that it is called a probabilistic parametric approach. Based on the only available information reported in literature, entropy maximum principle was used to develop probabilistic density functions for every random variable. In addition, in vivo human experimental data were considered for the determination of the so-called mean or deterministic model. Furthermore, numerical simulations of Monte Carlo were carried out involving the dispersion of all the uncertain parameters. Results showed that uncertainty of 5% led to error up to 20% in the arterial pressure estimation. Convergence was proved and a region with a confidence probability of 95% was constructed to allow the prediction of the random response of the arterial pressure. Eventually, we managed numerous calculations to analyze the influence of each random variable of the problem inputs over the arterial pressure evolution.

Introduction

It is well known that arteries are subjected to many diseases such as atherosclerosis, aneurysm or hypertension [START_REF] Humphrey | Cardiovascular Solid Mechanics: Cells, Tissues, and Organs[END_REF]. The main purpose of current researches is to establish constitutive laws which describe the hyperelastic behavior of the arterial tissue. In this context, authors propose several mechanical models including a variable number of geometric and material parameters [START_REF] Humphrey | Cardiovascular Solid Mechanics: Cells, Tissues, and Organs[END_REF][START_REF] Baek | Theory of small on large: Potential utility in computations of fluid-solid interactions in arteries[END_REF] which are often determined by performing in vitro tests on the arterial specimens [START_REF] Humphrey | Cardiovascular Solid Mechanics: Cells, Tissues, and Organs[END_REF].

Accordingly, it is important that the obtained parameters (problem data) are well calibrated to ensure the accuracy of the problem solution in order to investigate the mechanical behavior of arteries. Note that a similar problem for the arterial geometric parameters in the reference configuration is reached [START_REF] Alastrué | Assessing the use of the "Opening Angle Method" to enforce residual stresses in patient-specific arteries[END_REF].

Several identification methods have been recently developed but few studies have reported parameters for human arteries, particularly in the in vivo case. [START_REF] Stalhand | Towards in vivo aorta material identification and stress estimation[END_REF] showed that in vivo measurable data can be used directly for parameter identification for a circular, hyperelastic, anisotropic and incompressible model that accounts for the residual stresses in the unloaded arterial wall. The model parameters are determined by stating a minimization problem for the model pressure. [START_REF] A C C E P T E D M A N U S C R I P T Accepted Manuscript 12 Olsson | Modeling initial strain distribution in soft tissues with application to arteries[END_REF] proposed a general method to compute the parameters of a residual stress field in the mechanical modelling of soft tissues. The authors also suggested a method to obtain this parameterization from in vivo measurements by a nonlinear parameter identification problem. More recently, [START_REF] Masson | Characterization of arterial wall mechanical behavior and stresses from human clinical data[END_REF] demonstrated the feasibility of material identification and wall stress computation for human common carotid arteries based on non-invasive in vivo clinical data. The reader also could consult [START_REF] Humphrey | Cardiovascular Solid Mechanics: Cells, Tissues, and Organs[END_REF] where the problem of the identification of the vascular tissue parameters is described.

Hence, it would be desirable to develop methods that allow parameter estimation in mechanical arterial models. However, estimating parameters is not straightforward in the in vivo cases and their values can be assessed within a certain range.

In this paper, we demonstrate the importance to include the stochastic uncertainties in the modeling of the arterial mechanical behavior through a parametric approach. For that, we used in vivo human data obtained from non-invasive measurements. The influence of the uncertain problem data on the arterial pressure response was investigated by considering a finite elastodynamical model. Thus, we focused on the probabilistic feature of the theoretical problem data to quantify the induced final error in the arterial pressure calculation.

A C C E P T E D

M A N U S C R I P T ACCEPTED MANUSCRIPT 4 2 Methods

Arterial measurements

In vivo experimental measurements have been performed to study the mechanical behavior of the human common carotid arteries (CCA). During 4 to 6 cardiac cycles, the CCA medial diameter (MD), considered as the outer diameter, and the intima-media thickness (IMT) were recorded using a high spatial resolution ultrasound echotracking system (Wall Track System, Pie Medical) [START_REF] Hoeks | Automated detection of local artery wall thickness based on M-line signal processing[END_REF][START_REF] Boutouyrie | Association between local pulse pressure, mean blood pressure, and large-artery remodeling[END_REF] over a line perpendicular to the longitudinal and transversal axes of the artery, selected on the 2D B-mode image. In addition, the CCA intraluminal pressure was also measured non-invasively with a pencil-type probe that incorporated a high-fidelity Millar strain-gauge transducer coupled with tonometry by applanation [START_REF] Boutouyrie | Association between local pulse pressure, mean blood pressure, and large-artery remodeling[END_REF]. The intraluminal blood pressure increases up to the systolic peak which indicates the maximum arterial pressure, then the CCA pressure curve decreases during the diastolic phase of the cardiac cycle. The bend in the descending part corresponds to the dicrotic wave which matches with the closure of the aortic valves Data used in this study are from a 39-year old healthy male subject.

Theoretical model

Consider a sector of a circular and thick cylinder representing the CCA defined by the angle Θ 0 (Figure 1). The dynamic deformation of the artery over the cardiac cycle may be described by two successive deformations. Starting from the stress free state (Ω 0 ), the artery is closed inducing residual stresses. The obtained configuration is the unloaded state (Ω 1 ). Then the CCA is subjected to dynamic radial expansion and axial stretch (Ω 2 ). In the cylindrical coordinate system relative to the basis ( )

r z , ,
θ e e e , the mapping is described by

0 r = r(R,t), θ = , z λ Z π ⎛ ⎞ Θ = Λ ⎜ ⎟ Θ ⎝ ⎠ , (1)
where (R,Θ,Z) and (r,θ,z) are respectively the reference and the deformed coordinates of a material particle, 0 Θ is the opening angle, Λ and λ are axial stretches ratios respectively from (Ω 0 ) to (Ω 1 ) and from (Ω 1 ) to (Ω 2 ). Let i R and i r (t) denote respectively the inner radii of the artery in the reference state and in the deformed state ( e R and e r (t) are the outer radii). The inner radius i r (t) is derived from the experimental measurements by i r (t) = MD(t) 2 IMT(t) -.

Using (1), it follows that the physical components of the deformation gradient tensor F are [ ] Consequently, the left and the right Cauchy-Green strain tensors, denoted B and C, have the same matrix representation

r z 0 r r diag , , diag , , R R θ ⎡ ⎤ ∂ π = λ Λ = λ λ λ ⎢ ⎥ ∂ Θ ⎣ ⎦ F , (2)
2 2 2 2 2 2 r z 0 r r diag ( ) , ( ) , ( ) diag , , R R θ ⎡ ⎤ ∂ π ⎡ ⎤ = = λΛ = λ λ λ ⎢ ⎥ ⎣ ⎦ ∂ Θ ⎣ ⎦ B C . (3)
Furthermore, the arterial material is considered as incompressible. The local volume ratio is given by

r z J det 1 θ = =λλ λ = F
and leads to

2 2 22 0 i i r(R, t) [r (t) (R R )] Θ = + - πλΛ . ( 4
)
Let us assume that the mechanical behavior of the artery is described by the following stored strain-energy density function [START_REF] Tang | 3D MRI-based multicomponent FSI models for atherosclerosis plaques[END_REF]) The corresponding response equation for the Cauchy stress tensor σ is

1 2 1 c d W a(I 3) b(I 3) [exp( (I 3)) 1] d 2 = -+ -+ --, (5)
1 2 p 2(W W ) = -+ + -1 σ 1 B B , (6)
where 1 denotes the identity tensor and

k k W W I ∂ ∂ = ( 1, 2) k = .
From ( 6), the equations of motion in the absence of body forces are reduced to

.. rr rr r r r θθ σ -σ ∂σ + =ρ ∂ , (7)
the dot denotes the time differentiation and ρ denotes the current mass density of the arterial material.

From (4), it easily follows that the second time differentiation of r(R, t) is

.. . 2 .. 3 h(t) h (t) r(R, t) 2r(R, t) 4r (R, t) = - , (8)
where

2 i h(t) r (t) = .
Consequently, integrating (7) between the inner radius ( ) i r t and the outer radius ( ) e r t , and using (8) leads to the following relation [START_REF] Humphrey | Elastodynamics and arterial wall stress[END_REF])

( ) ( ) ( ) ( ) ( ) ( ) e i . r t 2 .. rr e i e 2 2 i e i r t r, t r, t r (t) h (t) 1 1 P t P t dr [h(t) ln( ) ( )], r 2 r (t) 4 r (t) r (t) θθ σ -σ ρ = + + + - ∫ (9) A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPT 6
where ( ) i P t and ( ) e P t are respectively the inner and the outer pressure applied to the CCA.

Note that the outer pressure can be expressed as an exponential form [START_REF] Masson | Characterization of arterial wall mechanical behavior and stresses from human clinical data[END_REF][START_REF] Humphrey | Elastodynamics and arterial wall stress[END_REF] ( ) ( ) ( ) e e e 0 r t P t e.exp f , r t

⎛ ⎞ = ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ (10)
where 0 t is the diastolic time over the cardiac cycle and e and f are material parameters.

Probabilistic approach

In this section, we present the followed methodology to take into account the random uncertainties of geometric and mechanical parameters for the estimation of the arterial pressure i P (t) . The random variables considered here are the opening angle Θ Θ 0 0 , the axial stretches λ λ and Λ Λ, the inner radius of the artery R R i i , the density ρ ρ, the six parameters The construction of the probabilistic approach requires the description of random variables by probabilistic density functions (pdf for short). The pdf allows to carry out numerous and independent realizations of each random variable and consequently of the arterial pressure.

The entropy maximum principle is used here to construct the pdf [START_REF] Soize | Maximum entropy approach for modeling random uncertainties in transient elastodynamics[END_REF][START_REF] Jaynes | Information theory and statistical mechanics[END_REF].

Let X be a real random variable which represent the previous uncertain parameters, we assume that X is a stochastic modeling of the variable x. The uncertainty (or dispersion) measurement of X is given by the entropy of the probabilistic density function X p (11)

The entropy maximum principle allows to determine the pdf by searching the maximum of S(p X ) among the potential density functions under the only available (or used) information.

This latter can be, for instance, the support of random variable, the mean, the standard deviation, higher moments, etc. Each type of information defines a constraint for the optimization problem given by

A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPT 7 (12)
The first equation of the system (12) is the normalization condition which must be satisfied on the random variable support, whereas the second equation describes the available information.

For example, if the given information is the mean of X, g i (x) = x.

To solve the optimization problem, we introduce (1+n) Lagrange multipliers λ i associated to each constraint. It was shown in [START_REF] Kapur | Entropy Optimization Principles with Applications[END_REF]) that λ i can be obtained by minimizing a strictly convex function H given by Eventually, maximizing the entropy S(p X ) leads to minimizing the function H(λ i ). The pdf is completely known once λ i is known and it is written as ( 14)

n n 0 1 n 0 i [a' ,b' ] 0 i i i 1 i 1 H( , ,..., ) f (x) exp( g (x))dx = = λ λ λ = λ + + Π -λ -λ ∑ ∑ ∫ R , ( 13
The probabilistic approach leads to the construction of a confidence region whose bounds are defined by

- + c c p (1 p ) ; p p ζ ζ = - = (15)
where p -and p + are respectively the lower and upper limits and ζ is the fractile of order p c defined for a random variable X as

{ } c (p) x; p(X< x) = p ζ = (16)
The reader could consult [START_REF] Kree | Mécanique aléatoire[END_REF] where the probabilistic approach is more detailed.

Results and discussion

To construct the probabilistic density functions of random variables, let us consider the 5

random variables (Θ Θ 0 0 , λ λ, Λ Λ, ρ ρ, R R i i ).
As no statistic data is available to our knowledge, we have been based on the literature to construct the information that we have to use to determine the pdf. The different values found throughout different researches have permitted to define an Therefore, the pdf associated to Θ Θ 0 0 is given by

X [ a ' , b ' ] 0 X 1 X p (x) (x) exp( (a ', b ', m ) x (a ', b ', m )) = Π -λ -λ , ( 17
)
where m X is the mean of the random variable X.

Concerning the six remaining random variables (a a,b b,c c,d d,e e,f f), we have only defined a support for each parameter, since there was not enough information about these values to also define an average for each one of them regarding the common carotid artery application. In this case, the obtained pdf is uniform on the considered support and given as follows for a random variable X

X [ a ' , b ' ] 1 p (x) (x) b ' a ' = Π - . ( 18
)
In Table (1), we summarize the available information of the eleven random variables used in the modeling.

Considering the random variable of the opening angle and setting α = 180/Θ Θ 0 , the minimization of H(λ α0 , λ α1 ) leads to: λ α0 = -3.4564 and λ α1 = 2.5216 where λ αi (i = 0,1) are the Lagrange multipliers associated to α.

Similarly, the minimization of H(λ λ0 , λ λ1 ) leads to: λ λ0 = -5.0982 and λ λ1 = 4.4664. Figure 2 presents the pdf of each random variable of the series (Θ Θ 0 0 ,λ λ,ρ ρ,R R i i ) as well as their realizations according to the pdf. We can notice that all the obtained pdf have a similar form except the one associated with the random variable ρ ρ. This difference can be explained by the support of this variable which is smaller than the four other supports. The given support influences the minimization result. For this case, we obtain λ ρ0 = -3.9121 and λ ρ1 = 0.0001. Consequently, the pdf given by ( 17) is constant.

The eleven random variables are considered to manage numerous arterial pressure simulations, in total 2000 simulations were carried out. The first results given by the probabilistic approach showed a great dispersion in the estimation of the internal pressure which is essentially due to the large supports given by the available information. In fact, the interval bounds were chosen from different values reported in literature in order to construct a potential support for each random variable. Since the arterial pressure is sensitive to several random variables, the definition of the interval bounds should be more accurate to avoid great results deviation. Thus, we have made use of the first results in order to initialize the available information of random variables so that final results are more realistic and convincing.

A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPT

9

The starting up of the stochastic approach is based on random variable values obtained from the best realization which here corresponds to the selection number 1881 and presents the minimum error with the experimental data. Figure 3 These values are next considered as the averages of random variables whereas the support bounds are obtained by adding ± 5% to the average in order to take into account the uncertainty of parameters. The associated stochastic arterial pressure is the mean (or deterministic) model since it uses the averages of all the random variables as input data. Thus, if L -and L + are respectively the lower and upper bounds of the support of the random variable X, then L -= 0.95m X and L + = 1.05m X . The new averages and supports represent the updated available information to construct the pdf according ( 17) and ( 18).

Next, we present the results of Monte Carlo simulations (Kalos et al., 1992) of the arterial pressure taking into consideration the updating available information of the random variables.

Let recall that the mean model is known since experimental data are available and it was constructed in order to match them. Suppose that we have no data to suggest the good averages of the random variables, one may consider a percentage uncertainty for the description of the problem entries. In our case, we have considered a small uncertainty of 5%

for each of the eleven random variables.

1500 simulations of Monte Carlo were carried out by generating random values of the uncertain variables according to the pdf that is constructed after the starting up step.

Convergence of the Monte Carlo simulations can be observed by the calculation of the mean and the standard deviation (SD) of the mean arterial pressure random response. The mean arterial pressure can be defined as MAP = (SAP+2 DAP)/3 where SAP and DAP are respectively the systolic and diastolic arterial pressure.

The convergence of the stochastic method is reached in the 500th realization (Figure 4). The mean of MAP appears to be equal to 0.0102 MPa (76.5 mmHg) whereas the SD is equal to 0.0024 MPa. On the other hand, the MAP corresponding to the experimental data is 0.0093 MPa (69.8 mmHg). Note that, according to the strong law of large numbers theory (Andrews, 1988) the obtained arterial pressure at convergence is the same as that found by the mean model, the obtained set of parameters is therefore equal to that previously given by the deterministic case.

A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPT 10
The different independent trials enable us to define a predicted confidence region in which the probability to have a realization is equal to p c = 95%. This can be done by ordering the MAP from the lower value p -to the upper value p + . For example, in our case p -= 0.0062 MPa and p + = 0.0176 MPa. It should be emphasized that a physiological constraint was taken into account in our modeling to ensure the limitation of the systolic and diastolic pressures to physiological values (McDonald, 1958). This non violation condition allows the final solution to be realistic and concluding.

In Figure 5, we present the evolution of the maximal and minimal arterial pressures in the confidence region for a confidence probability equal to 95%. The line and dashed curves are respectively associated with the data and the mean model whereas the dotted curves represent the boundaries of the confidence region.

Eventually, we can notice that an uncertainty of 5% in the problem input description can lead to an error estimated to 21.42%. This error is obviously higher when the uncertainty percentage is 10% or 15% for example. This remark justifies the use of stochastic approach for the modeling of arterial mechanical behavior.

The different carried out realizations can be summarized graphically by a histogram to describe the MAP distribution. Here, we split the range of the pressure into 40 classes in abscissa, and in vertical axis, we note the frequency to have a value of the MAP. When the number of classes increases, the bars become less large and therefore the curve fitting of the pdf is more continuous. This enables us to have information about the pdf corresponding to the global random response. In Figure 6, we present the real pdf of the MAP in comparison with the Gaussian pdf constructed by using the mean and standard deviation obtained from Monte Carlo convergence. We can notice that the real pdf describing the MAP evolution is similar to Gaussian pdf.

On the other hand, we present some results of the stochastic approach by considering the only uncertainty of each random variable in order to analyze the influence of every parameter independently of the other uncertain parameters. During simulations, the considered random variable is described by its associated pdf constructed as aforementioned, whereas the 10 others parameters are maintained constant to their values obtained by the deterministic model.

In Figure 7, we show the distribution of the arterial pressure for each random case. The bold curve represents the mean model whereas the other curves describe the stochastic simulations.

We can notice that the arterial pressure random response is more influenced by some data than others. The vertical arrow in the first figure indicates the range width of the pressure variation. We can see that the arterial pressure is much more sensitive to the opening angle Nevertheless, the effect of the parameters a a and b b is negligible in the considered support. This analysis illustrates the necessity to take into consideration the uncertainties of the parameters to have a good prediction of the region confidence of the random final result.

Conclusion

Through a simple case study, we have demonstrated that a parametric analysis should be considered to take into account the random uncertainties of the problem inputs. The probabilistic approach allows the evaluation of the arterial pressure dispersion and provides a 95% confidence interval which covers the potential random responses. This approach is worth to be adapted for more accurate biomechanical constitutive relations such as anisotropic models by considering the contribution part of the collagen fibers in the artery to improve the description of the arterial mechanical behavior. To our knowledge, this is the first time that material and geometric parameters of artery have been estimated using in vivo human data based on stochastic model.

A C C E P T E D M

A N U S C R I P T

  are respectively the radial, circumferential and axial stretch ratios.

  strain invariants and (a, b, c, d) the material parameters.

  (a a,b b,c c,d d, ,e e, ,f f) governing the strain-energy density function and the outer pressure ( ) e P t . As a result, we have 11 random variables to examine.

  )where[a', b'] is the support of the pdf of the random variable X and [a ',b'] (x) Π is the indicator function which is equal to 1 if x belongs to [a', b'] and 0 if not.

  support for each random variable. For instance, we have considered that the mean of the opening angle Θ Θ 0 0 is equal to 130°(Delfino et al., 1997) and that Θ

  radius variation than the axial stretches (λ λ, Λ Λ). Concerning the mechanical parameters, the random variable f f has more influence on the solution than the others.

Figure 1 .

 1 Figure 1

Figure 2 .

 2 Figure 2. Probabilistic density function of the random variable (left), 3000 realizations of the random variable following the pdf (right).

Figure 3 .Figure 4 .Figure 5 .Figure 7 .

 3457 Figure 3. Arterial pressure evolution

  depicts the evolution of the arterial pressure obtained with this realization. Both stochastic and experimental curves are close except around t = 0.35 s where the error is nearly 7%. The global error, noted between the stochastic model and the data, is equal to 2.28%. The results are recapitulated in the table 2.

  Stergiopulos, N., Moore, J.E., Meister, Jr. and J.J., 1997. Residual strain effects on the stress field in a thick wall finite element model of the human carotid bifurcation. J.

	ACCEPTED MANUSCRIPT
	Delfino, A., Biomechanics 30, 777-786.
	Kalos, M.H., Whitlock, P.A., 1992. Monte-Carlo Methods Volume 1: Basics. John Wiley and
	Sons, Chistester.
	Andrews, D.W.K., 1988. Laws of Large Numbers for Dependent Non-Identically Distributed
	Random Variables. Cambridge University press.
	McDonald, Donald A., 1958. Blood flow in arteries. Edward Arnold (Publishers) LTD,
	London, UK.
	13

Table 1 .

 1 Available information for the random variables.

	22

Table 2 .

 2 Mean model results.

	Θ 0			ρ	R i	a	b	c
		λ	Λ
	(degree)			[Kg.mm -3 ]	[mm]	[MPa]	[MPa]	[MPa]
	138.846°	0.985	0.826	1.002e -6	3.609	0.0014	1.103e -12	0.0114
		e
	d		f
		[MPa]
	16.438	1.45e -4	3.856


Britta Höchsmann
email: b.hoechsmann@blutspende.de

Markus Rojewski

Hubert Schrezenmeier

Gisela Baur

Paroxysmal nocturnal hemoglobinuria (PNH): higher sensitivity and validity in diagnosis and serial monitoring by flow cytometric analysis of reticulocytes 1

Keywords: PNH, Paroxysmal nocturnal hemoglobinuria, flow cytometry, immunophenotyping, Glycosylphophatidyl-inositol anchor, GPI deficiency, reticulocytes

Paroxysmal nocturnal hemoglobinuria (PNH): higher sensitivity and validity in diagnosis and serial monitoring by flow cytometric analysis of reticulocytes

Britta Höchsmann, Markus Rojewski, Hubert Schrezenmeier

Introduction:

Paroxysmal Nocturnal Hemoglobinuria (PNH) is an acquired hematopoietic stem cell disease [START_REF] Dacie | Paroxysmal nocturnal haemoglobinuria[END_REF][START_REF] Oni | Paroxysmal nocturnal hemoglobinuria: Evidence of monoclonal origin of abnormal red cells[END_REF]. Pathophysiologically it is based on somatic mutations of the X-linked phosphatidyl-inositol-glycan (PIG-A) gene [START_REF] Myata | The cloning of PIG-A, a component in the early step of GPI-anchor biosynthesis[END_REF][START_REF] Mortazavi | The spectrum of PIG-A mutations in aplastic anemia/paroxysmal nocturnal hemoglobinuria: a high incidence of multiple mutations and evidence of a mutational hot spot[END_REF] which result in a partial or absolute deficiency of GPI-linked proteins [START_REF] Bessler | Paroxysmal nocturnal hemoglobinuria is caused by somatic mutations in the PIG-A gene[END_REF]. The lack of GPI-linked proteins leads to the clinical features chronic intravascular hemolytic anemia and thromboembolism [START_REF] Helley | French Society of Hematology: Evaluation of hemostasis and endothelial function in patients with paroxysmal nocturnal hemoglobinuria receiving eculizumab[END_REF][START_REF] Hill | Effect of eculizumab on haemolysisassociated nitric oxide depletion, dyspnoea, and measures of pulmonary hypertension in patients with paroxysmal nocturnal haemoglobinuria[END_REF]. The role of GPI-AP in bone marrow failure which is often associated with PNH is less clear [START_REF] Hillmen | Natural history of paroxysmal nocturnal hemoglobinuria[END_REF].

Measurement of GPI-anchored proteins expression by flow cytometry is nowadays the gold standard for laboratory diagnosis of PNH and has replaced the Ham test and the sucrose lysis test (sugar water test) [START_REF] Nebe | Flow Cytometric Analysis of GPI-deficient Cells for the Diagnosis of Paroxysmal Nocturnal Hemoglobinuria and PNH-Syndrome[END_REF][START_REF] De Latour | Paroxysmal nocturnal hemoglobinuria: natural history of disease subcategories[END_REF]. Flow cytometry allows a sensitive and specific detection of even small GPI-deficient populations and a quantification of PNH cell populations in various cell lineages. This quantification is especially important, as the estimated size and type of the involved cell lineages correlates with different clinical manifestations of the disease [START_REF] Richards | The role of flow cytometry in the diagnosis of PNH in the clinical laboratory[END_REF]. For instance patients with more than 20% type III deficiency on red cells mostly have clinically significant hemolysis, while nearly half of pts with more than 50% GPI-deficiency on the granulocytes suffer from venous thrombosis in the first ten years after initial diagnosis [START_REF] Hall | Primary prophylaxis with warfarin prevents thrombosis in PNH[END_REF]. Therefore the size of the GPI-AP deficient population on granulocytes is a prognostic factor for vascular events, which have been shown to be the key determinant of prognosis with the most important impact on life expectancy. Remarkably, clone size and cell lineage involvement can change over time [START_REF] Hillmen | Natural history of paroxysmal nocturnal hemoglobinuria[END_REF][START_REF] Schrezenmeier | Paroxysmal nocturnal haemoglobinuria: a replacement of haematopoietic tissue?[END_REF][START_REF] Parker | Diagnosis and management of paroxysmal nocturnal hemoglobinuria[END_REF]. This leads to the need of follow up investigations to initiate appropriate therapeutic approaches. Beside initial diagnosis flow cytometry in particular enables serial monitoring during the course of the disease [START_REF] Hernandez-Campo | Detailed immunophenotypic characterization of different major and minor subsets of peripheral blood cells in patients with paroxysmal nocturnal hemoglobinuria[END_REF][START_REF] Richards | Immunophenotypic analysis of PNH cells[END_REF][START_REF] Nebe | Flow cytometric analysis of GPI-deficient cells for the diagnosis of paroxysmal nocturnal hemoglobinuria (PNH)[END_REF][START_REF] Schrezenmeier | Paroxysmal nocturnal haemoglobinuria: a replacement of haematopoietic tissue?[END_REF]. This allows ontime determination of therapeutic decisions like initiation of prophylactic anticoagulation [START_REF] Hall | Primary prophylaxis with warfarin prevents thrombosis in PNH[END_REF] or application of the C5-antibody eculizumab, which has allready proven to reduce hemolytic activity and thrombembolic events (16 -19). Additionally therapeutic effects may be monitored via flow cytometric analysis of GPI-deficiency.

Disappearance of the GPI-deficient populations indicates effective therapy after stem cell transplantation while increase of the GPI-deficient erythrocyctepopulations upon eculizumab therapy is presumable due to a decrease of hemolytic activity with the result of a prolonged red blood cell (RBC)-survival [START_REF] Hill | Recent developments in the understanding and management of PNH[END_REF]. Although flow cytometric analysis of GPI-AP is the gold standard for diagnosis of PNH for years, there are no detailed international or even nationwide rules to determine minimal demands for PNH diagnosis based on flow cytometry. There exists just a general advice of the International PNH Interest Group (IPIG) to examine at least erythrocytes and granulocytes for diagnosis of PNH [START_REF] Parker | Diagnosis and management of paroxysmal nocturnal hemoglobinuria[END_REF]. No consensus recommendations are available for the choice of GPI-AP markers or even the cell populations which should be examined. Thus, results from different laboratories are often difficult to compare and false negative or false positive results are not a rare event. Moreover most tests are influenced by hemolytic crises or RBC transfusions as they rely on GPIdeficiency of erythrocytes. Therefore, in this study we retrospectively analysed the results of our routine diagnostics of the last 5 years to assess the most suitable GPI-markers and cell populations for a sensitive, valid and rapid GPI-AP flow cytometric analysis for diagnosis and serial testing.

Design and Methods:

Patients:

Flow cytometric GPI-AP analysis was performed in 803 patients suffering from PNH or suspected GPI-deficient populations. The reason for flow cytometric analysis as reported by the treating physician were the following diagnoses or suspected diagnoses: PNH in 67 patients, hemolysis in 77 patients, Aplastic Anemia or trilineage cytopenia in 291 patients, MDS in 44 patients, single lineage or bilineage cytopenia in 76 patients, unclear thromboembolic events or ischemias in 49 patients, other hematologic diseases in 25 patients and insufficient information in 174 patients. In the majority of the patients, blood was sent for routine diagnostic assessment to our reference diagnostic laboratory at the Institute of Clinical Transfusion Medicine and Immunogenetics Ulm for analysis of GPI deficiency as a diagnostic routine procedure in patients with bone marrow failure, hemolytic anemia, iron deficiency anemia, thrombosis or abdominal pain of unknown origin. Some of the analyses were performed as diagnostic test in clinical trials after informed consent and ethical committee approval of the trial. Patients were included in the follow-up analysis if at least two GPI-AP assessments with a minimum interval of three months were available (n=155 pts). At time of initial GPI-AP-analysis blood count was available in 89 of the 155 follow up pts.; in this pts group 48/89 pts showed neutropenia with < 0.5 G/l and 70/89 pts had thrombopenia with < 100 G/l. Patients with eculizumab treatment were censored at the date of first eculizumab application and GPI-AP assessment of these patients during eculizumab therapy were not included in the analyses presented here. Five patients who received allogeneic stem cell transplantation were not censored for analysis.

The pattern of lineage involvement and the suitability of various lineages and markers in the peripheral blood for detection of GPI-deficient populations were statistical analysed retrospectively in all patients. For follow-up the size of GPIdeficient populations as well as the evolution of lineage involvement was investigated.

Two Color Flow Cytometry:

Immunophenotyping was performed as previously described. [START_REF] Schrezenmeier | Paroxysmal nocturnal haemoglobinuria: a replacement of haematopoietic tissue?[END_REF] 1296 flow cytometric examinations performed between March 2003 and August 2008 were analysed. Peripheral blood (PB) was obtained by venous puncture using Na-EDTA or citrate as anti-coagulant. All incubations were performed at room temperature in the dark. We used the flow cytometric analysis of CD58 and CD59 on reticulocytes and erythrocytes and of CD66b/CD24 and CD16 on granulocytes as mandatory markers for our screening panel. The expressions of CD14 and CD48 on monocytes as well as CD48/CD19 and CD48/CD3 on lymphocytes were used as optional markers to fully assess lineage involvement.

In 584 cases a combination of CD66b/CD24, CD16 and FLAER, a fluorochromlabelled modified bacterial toxin which binds directly to the GPI-anchor was used to confirm the diagnosis. Staining of the reticulocytes by the RNA dye thiazol orange allowed a separate analysis of erythroctes and reticulocytes.

Staining of erythrocytes and reticulocytes (no wash, stain, no lyse protocol):

A volume of 100 µL of 1:10 diluted PB in PBS without Ca 2+ /Mg 2+ (PAA Laboratories, Paching, Austria) was used for each assay. As isotype control, diluted PB was incubated with 20 µL of IgG*PE, clone X40 (BD Immunocytometry Systems, Heidelberg, Germany). Detection of GPI-deficient erythrocytes and reticulocytes was performed by staining 100 µL of diluted PB with either 20 µL of CD58*PE, clone AICD58 (Beckman Coulter Immunotech, Krefeld, Germany) or 20 µL of CD*59 PE, clone p282 (H19) (BD Pharmingen, Heidelberg, Germany). After 20 min, cells were washed once by addition of 1 mL PBS without Ca 2+ /Mg 2+ followed by centrifugation at 5900 g for 0.5 -1 min. The cells of all three assays were resuspended in 1 mL of ReticCOUNT Reagent (BD Immunocytometry Systems) and incubated for 20 min -1 h to stain RNA of reticulocytes before analysis by flow cytometry (figure 1).

Staining of granulocytes, monocytes (no wash, stain, lyse protocol):

To consider the contribution of different autofluorescences, separate isotype controls were performed for granulocytes, monocytes Therefore, two assays of PB, containing 0.8x10 6 -1.6x10 6 Immunotech), incubation for 7 -15 min, addition of 1 mL aqua followed by vigorous mixing and incubation for another 5 -15 min. After lysis of erythrocytes, cells were washed twice using 1 mL PBS without Ca 2+ /Mg 2+ and resuspended 300 -800 µL PBS without Ca 2+ /Mg 2+ for flow cytometry analysis.

Staining of granulocytes (wash, lyse, stain protocol):

For detection of GPI-deficient granulocytes by FLAER (FITC labeled aerolysin, Protox Biotech, Victoria, Canada), a volume of PB blood containig approximately 2x10 5 neutrophiles was washed with the 5-fold volume of PBS without Ca 2+ /Mg 2+ and the supernatant was discarded. Erythrocytes were lysed as described above using half the volume of OptiLyse B and aqua and washed twice, using PBS without Ca 2+ /Mg 2+ . Half of the remaining cells were stained with 2 -5 µL of a 1:10 dilution of IgG*PE, clone X40 (BD Immunocytometry Systems) in PBS, the other half of the cells was stained with a 1:50 dilution of CD16*PE, clone 3G8 (BD Pharmingen) in PBS and 0.5 -5 µL FLAER, respectively. After 20 -30 min, 1 mL of PBS without Ca 2+ /Mg 2+ was added, supernatant was removed after centrifugation at 5900 g for 30 sec -1 min and cells were resuspended in 300 -800 µL of PBS without Ca 2+ /Mg 2+ .

Normal rangecut off values of GPI-deficiency

In the 5year observation period every week healthy blood donors (overall n= 268) were tested for GPI-deficiency to establish cut-off values (mean + 2 SD) for GPI-deficient cells. In respect of variabilities in antibody efficiency we updated this cut off every 6 months with the results of the last 50-60 examined healthy donors. The valid cut offs at the end of the 5-year observation period (overall results of the 268 healthy donors were put in parantheses) were: reticulocytes CD58: 0.5% (1.0%), reticulocytes CD 59: 1.9% (2.0%), erythrocytes CD58: 0.1% (0.2%), erythrocytes CD59: 0.5% (0.8%), granulocytes CD66b/CD24: 0.1% (0.7%), granulocytes CD16: 1.0 % (1.2%), granulocytes FLAER*,CD16: 0.3 % (1.2%); monocytes CD14: 2.5 % (3.3%), monocytes CD48: 1.1% (1.1%); For flow cytometric diagnosis of a PNH cell population at least two cell lineages with significant GPI-deficient populations were required. Significant GPI-deficient populations are defined if all examined markers (minimum: 2) were exceeding the cut off value.

Statistical analysis:

Statistical analyses of the data were carried out in Microsoft Office Access 2003 and GraphPad PRISM, version 4.00. Used tests were linear regression, including correlations, coefficient of correlation and confidence interval as well as scatter plots. A p-value off less than 0.05 was considered as statistically significant.

Results:

Patient characteristics

Patient characteristics for the examined 803 pts (416 male; 382 female) were as follows: the patient age ranged from 0.4 to 90.7 years (median age: 32.4 years) with no relevant differences between men (52%) and women (48%) (table 1). At initial GPI-AP-flow cytometry 176 of all patients (22%) were diagnosed with PNH typical GPI-deficient populations (figure 2). The groups with and without PNH diagnosis at time of initial GPI-AP-analysis do not differ significantly in age and sex distribution. For detailed patient characteristics see table 1.

In the follow up cohort 155 pts and 625 flow cytometric analyses were evaluated (median number of analyses per patient: 3; range from 2 to 26) for a median follow up duration of 1039 days. Patient characteristics of the follow up group are summarized in table 1.

Blood count was evaluable in 89 of these pts at the time of initial assessment and in 120 pts at time of the last examination. Thrombocytopenia < 100 G/l was obtained in 62% at the initial examination and in 43% at the last examination. Leukocytopenia < 0.5 G/l was initially obtained in 36% and decreased to 18% at the final investigation (see data supplements).

Flow cytometric results

Analysis of different GPI-anchored markers in the same cell lineage

Primarily, we compared all flow cytometric results (including the follow-up analyses) within each separate cell lineage to assess the correlation of the various GPI-linked markers. We found a highly significant correlation between the markers CD58 and CD59 on reticulocytes (r 2 = 0.95, p < 0.0001; n=1284) and erythrocytes (r 2 = 0.86, p < 0.0001; n = 1284), between CD24/66b and CD16 or between CD24/66b and CD16, FLAER on granulocytes (r 2 = 0.76, p < 0.0001; n = 1248) and between CD14 and CD48 on monocytes (r 2 = 0.62, p < 0.0001; n = 599) (figure 3). If we restricted the analysis to the first GPI-AP-flow cytometric analysis in each patient, the correlation did not change considerably (figure 3).

Marker analysis between different cell lineages

In a second step we compared the sizes of various GPI-marker negative populations in different cell lineages. This analysis was initially performed for all GPI-AP-flow cytometric results in patients with flow cytometric diagnosis of PNH.

The following significant correlations were obtained: CD58-negative reticulocytes and CD58-negative erythrocytes (n = 457, r 2 = 0.63, p < 0.0001), CD59-negative reticulocytes and CD59-negative erythrocytes (n = 455, r 2 = 0.61, p < 0.0001), CD59-negative reticulocytes and CD24/D66b-negative granulocytes (n = 450, r 2 = 0.60, p < 0.0001), CD59-negative reticulocytes and CD14-negative monocytes (n= 381, r 2 = 0.68, p < 0.0001), CD59-negative erythrocytes and CD24/66bnegative granulocytes (n = 449, r 2 = 0.33, p < 0.0001), CD14-negative monocytes and CD24/66b-negative granulocytes (n = 423, r 2 = 0.84, p < 0.0001), CD 48-negative monocytes and CD24/66b-negative granulocytes (n = 421, r 2 = 0.48, p < 0.0001), (Figure 4).

In a second step the analysis was restricted to the first flow cytometric analysis of each patient with flow cytometric diagnosis of PNH. There were no significant differences between both analyses (figure 4).

Marker analysis for detection of small GPI-deficient populations

To elucidate the importance of individual markers for the flow cytometric diagnosis of PNH all markers were separately analyzed. Depending on the size of the CD24/CD66b-negative granulocyte population we defined two different subgroups based on a CD24/CD66b-negative-granulocyte population < 10% or > 10% at the first investigation. The largest median GPI-deficient population in the subgroup with < 10% CD24/66b-negative granulocyte populations was observed for CD14 on monocytes, CD16 or CD16, FLAER on granulocytes and CD59 on reticulocytes. In the subgroup with > 10% CD24/CD66b-negative-granulocyte population the largest median GPI-deficient population was shown for CD14 on monocytes, CD24/66b and CD16 as well as CD16, FLAER on granulocytes and CD59 on reticulocytes (figure 5).

Follow up analysis

We analysed repeated measurements of GPI-AP expression on reticulocytes, erythrocytes, granulocytes and monocytes in 155 pts (figure 6) in order to study the dynamics of GPI-AP deficient cell populations over time. Since it has been demonstrated that treatment with eculizumab changes the relative proportion of GPI-AP deficient red cells [START_REF] Hill | Sustained response and long term safety of eculizumab in PNH[END_REF], patients who received eculizumab treatment were censored at start of this treatment. Median number of analyses per pt was 3 and the median follow up duration was 1039 days (minimum 90 days, maximum 1903 days). Initially 75 (48%) of these pts were diagnosed with PNH.

The longitudinal studies revealed different patterns of GPI-AP-expression during the follow up period (figure 2

Discussion:

Flow cytometry of GPI-AP is considered to be the gold standard of PNH diagnosis. CD55-and CD59-expression on erythrocytes are most frequently used for screening of PNH (6 -7, 9 -14, 21, 22). Our presented data show that addition of further antibodies against GPI-linked antigens on different cell lineages considerably improves the sensitivity and validity of the method. Among the markers evaluated we recommend a panel including at least the following markers: CD58 and CD59 for reticulocytes and erythrocytes a combination of CD24/66b and eventually FLAER on the granulocytes and CD14 on monocytes.

It has been shown that detection of GPI-deficient reticulocytes is more sensitive than analysis of erythrocytes. And reticulocytes better correlates with proportion of GPI-deficient white cells. The remarkable worse correlation between erythrocytes and granulocytes compared to the correlation of reticulocytes and granulocytes (figure 4) and the larger GPI-deficient populations in reticulocyte than erythrocyte (figure 5) are probably caused by RBC transfusions, hemolytic crises and a shorter life span of PNH erythrocytes [START_REF] Rosse | Immune lysis of normal human and paroxysmal nocturnal hemoglobinuria (PNH) red blood cells[END_REF][START_REF] Navenot | Investigation of the survival of paroxysmal nocturnal hemoglobinuria red cells through the immunophenotyping of reticulocytes[END_REF]. As reticulocytes are less affected by these events their examination for GPI-AP-deficiency is especially suitable for diagnosis of involvement of the red cell lineage if there are small GPI-deficient granulocyte populations below 10%. Nevertheless the most international recommendations for flow cytometry still favour erythrocyte analysis. Our data emphasize the importance of reticulocyte analysis. Even if reticulocyte clone size correlates well with white cell clone size both should be tested to confirm the flow cytometric diagnosis of PNH because alteration of GPI-AP on leukocytes can be a sign of granulocytic/monocytic dysplasia and immaturity (31, data supplements) in the context of various myeloid diseases or cytolysis. Due to our results participation of leukocytes is detected best by examination of CD14-deficiency on monocytes (figure 5). Therefore additional examination of monocytes provides a higher detection sensitivity of GPI-AP deficiency especially in pts with small GPI-deficient granulocyte populations < 10%. In fact the marker combination CD24/66b and CD16 seems to be suitable in sensitivity and validity to detect GPI-deficient granulocytes in our analysis.

Follow-up examination is recommended by the International PNH Interest Group (IPIG) in case of bone marrow failure syndromes [START_REF] Parker | Diagnosis and management of paroxysmal nocturnal hemoglobinuria[END_REF] even in case of initially normal flow cytometric analysis. Moreover, regular follow up studies are indicated in case of known PNH to detect substantial changes in GPI-AP deficient population size or cell lineage involvement, as both situations may prompt therapeutic consequences or may demonstrate effect of therapeutic interventions. Therefore, we evaluated our panel on different cell lineages for longitudinal monitoring of GPI-deficient populations to determine the frequency of significant changes in cell lineage involvement and GPI-deficient population size.

Our definition of a relevant change in GPI-deficient population size (</> 50% GPI-deficiency on granulocytes) is based on data published by Hall et al. [START_REF] Hall | Primary prophylaxis with warfarin prevents thrombosis in PNH[END_REF] demonstrating that pts with a GPI-deficient population on granulocytes > 50% have a significant higher risk of thromboembolic events. Our results again support the importance of GPI-AP measurement on reticulocytes to obtain results independent of hemolytic crisis and RBC transfusions.

The described flow cytometry panel could be used for serial monitoring during follow up to detect evolution of GPI-AP deficient populations and to assess therapy effects. Although follow-up investigations were performed only in a minority of patients with initially normal results (80 out of 627pts), in 7 of the follow up patients PNH was newly diagnosed. Based on our follow up data with a relevant proportion of newly developing GPI-AP deficient populations and significant changes in the size of GPI-AP deficient populations repeated GPI-AP-analysis in regular intervals should be performed, like it is recommended by the International PNH Interest Group (IPIG). [START_REF] Parker | Diagnosis and management of paroxysmal nocturnal hemoglobinuria[END_REF]. Another interesting fact in our follow up data is the absence of spontaneous remissions of PNH typical GPI-AP deficient populations which had been reported. A study with 35 pts referred a rate of 15 % spontaneous remissions [START_REF] Hillmen | Natural history of paroxysmal nocturnal hemoglobinuria[END_REF] in PNH pts but available GPI-AP flow cytometric results and even HAM-test were limited in this study. All observed remissions in our patient group happened in the context of stem cell transplantation or intensified immunosuppressive therapy especially in patients with AA-PNH-syndrome. The reported 3 patients with classical PNH and decrease of the GPI-AP deficient population on granulocytes below 50% developed an increase over 50 % GPI-deficient cells on the granulocytes during further follow up.

Generally, expression of GPI-anchored proteins should be analysed in all situations suspicious of PNH and in bone marrow failure syndromes. According to our data measurement of at least two different GPI-anchored proteins on granulocytes, erythrocytes and reticulocytes provides a simple and rapid method to detect even small GPI-deficient populations. Measurement of erythrocytes only includes the pitfall of false negative results or false low values of GPIdeficient populations. On the contrary examination of GPI-deficiency on reticulocytes additionally prevents false positive interpretation of significant GPIdeficient populations on the leukocytes (data supplements). GPI-AP-deficiencies without clinical PNH were reported in the context of other hematologic diseases or after immunosuppressive therapy [START_REF] Taylor | Antibody selection against CD52 produces a paroxysmal nocturnal haemoglobinuria phenotype in lymphocytes by a novel mechanism[END_REF] as well as in healthy individuals [START_REF] Young | The problem of clonality in aplastic anemia: Dr Dameshek's riddle, restated[END_REF][START_REF] Bessler | Somatic mutations and cellular selection in paroxysmal nocturnal haemoglobinuria[END_REF]. Our data demonstrate that in patients with small GPI-deficient populations these can in particular be detected on monocytes. In conclusion we recommend a flow cytometric screening panel with the markers CD58 and CD59 on reticulocytes and erythrocytes as well as with the markers CD24/66b and CD16 on granulocytes for initial diagnosis and monitoring during follow up. In case of significant GPI-AP-deficient population in a minimum of one cell lineage the analysis should be extended to the markers CD14 and CD48 on monocytes.

Furthermore we advise a serial monitoring for PNH-pts as well as for pts with bone marrow failure syndromes without a present GPI-AP-deficiency every 6 months or in case of significant clinical symptoms.

Recently Richards et al [START_REF] Richards | Development and evaluation of a stabilized whole-blood preparation as a process control material for screening of paroxysmal nocturnal hemoglobinuria by flow cytometry[END_REF] showed that a relevant proportion of laboratories doing PNH-testing by flow cytometry have significant problems with regard to false-positive and false-negative results. On the other hand due to the advent of a new targeted therapy option early diagnosis and serial monitoring of PNH is gaining importance for a better patient management [START_REF] Schrezenmeier | Eculizumab opens a new era of treatment for paroxysmal nocturnal hemoglobinuria[END_REF]. As a consequence, there is the urgent need for optimized flow cytometric protocols in PNH diagnosis. In conclusion, this analysis has demonstrated that the described flow cytometric method offers significant benefits in sensitivity and validity in PNH testing and can be therefore recommended for a wider use.

Authorship and Disclosures

BH and HS took primary responsibility for the paper and designed research. BH and MR performed laboratory work. BH, HS and MR analysed the data and wrote the paper. BH and HS were advisors for and received honoria from Alexion. MR reported no potential conflicts of interest.

Running head:

B. Höchsmann and H. Schrezenmeier et al.

Flow cytometric analysis for PNH

Figure 1:Staining of the reticulocytes by the RNA dye thiazol orange allowed a separate analysis of erythrocytes and reticulocytes. Comparision of the results in a healthy control and a PNH-patient. In the healthy control separation of two populations according to erythrocytes (left upper quadrant) and reticulocytes (right upper quadrant) without significant GPI-deficiency. In the PNH patient separation of four poulations according to erythrocytes and reticulocytes without (upper quadrants) and with (lower) significant GPI-deficiency.

Figure 2: Flow sheet patient of the different patient groups at time of initial GPI-APanalysis and during follow up. Significant changes of GPI-deficient populations during follow up was observed in groups B, D1, D2 with an expansion of GPI-AP deficient populations (including new PNH-diagnosis) and in groups E1, E2 and F with an decrease of GPI-AP deficient populations (including disapearance of PNH diagnosis criteria).

Figure 3: Correlation between the used GPI-AP markers within one cell line. Black = all analyses. Red = restricted to the first analysis per patient. Broken black lines = confidence interval of all analyses. Broken red lines = confidence interval of the first analysis per patient. All correlations were highly significant (p < 0.0001) in the group with all analyses as well as in the group with only the first analysis (p < 0.0001). The range of the correlation coefficient was r2 =0.61 -0.95. Figure 4: Correlation between the used GPI-AP markers on the different cell lines. Black = all analyses. Red = restricted to the first analysis per patient. Broken black lines = confidence interval of all analyses. Broken red lines = confidence interval of the first analysis per patient. All correlations were highly significant in the group with all analyses (p < 0.0001) as well as in the group with only the first analysis (p < 0.0001). The range of the correlation coefficient was r2 =0.33 up to 0.88. The lowest value for r2 (r2 =0.33) was observed between CD59 on erythrocytes and CD24/CD66b on granulocytes, whereas the correlation between CD59 on reticulocytes and CD24/CD66b on granulocytes was r2 =0.60.

Figure 5: Scatter blots with marker deficient cells in % in pts with > 10% GPI-deficient granulocyte population (B + D) and in pts with < 10% GPI-deficient granulocyte population (A + C). ECD58 = CD58-deficiency on erythrocytes, ECD59 = CD59deficiency on erythrocytes, RCD58 = CD58-deficiency on reticulocytes, RCD59 = on reticulocytes, GCD24/66b = CD24/66b-deficiency on granulocytes, GFLAER or GCD16 = CD16 and/or FLAER or CD16-deficiency on granulocytes, MCD14 = CD14-deficiency on monocytes, MCD48 = CD48 deficiency on monocytes. Blue line median size of GPIdeficient population. Table 1: Patient characteristics of all pts at initial analysis and separated in the groups with and without flow cytometric PNH diagnosis at initial GPI-AP analysis as well as of the patient groups A -F regarding to number, sex distribution, age, follow up duration, GPI-AP-examination number and GPI-AP examination number up to a significant change during follow up.

(2-26)

Relevant change during follow up was defined as *(B) new flow cytometric diagnosis of PNH during follow up after a normal GPI-AP-expression at first investigation; *(D) increase of GPIdeficient granulocyte population from < 50% to > 50%) and/or involvement of additional cell lineages during follow up; * (E) decrease of GPI-deficient granulocyte population from > 50% to < 50%) or disappearance of GPI-deficiency in a cell lineage during longitudinal analysis; *(F) disappearance of the PNH-typical GPI-AP deficiency below our criteria for flow cytometric PNH diagnosis.

Data supplements 2: a case report of false positive interpretation of significant GPI-deficient populations on leucocytes: patient was diagnosed in an external labaratory to have a significant PNH and eculizumab therapy was started. After the patient developed an ischemic stroke a blood sample was taken and sent to us for confirmation of the diagnosis. Due to the large GPIdeficient populations on the monocytes in combination with the almost normal reticulocytes we suspected immature myeloid cells. Consecutively a bone marrow assessment confirmed an AML M7 with a blast excess and a chemotherapy was started.

Monocytes Reticulocytes

  leucocytes each, were incubated with 20 µL of IgG*FITC and 20 µL of IgG* PE clone X40 (both BD Immunocytometry Systems). Analysis of granulocytes was performed by staining PB with 10 µL of CD24*FITC, clone SN3 (DAKO, Hamburg, Germany), 10 µL of CD66b*FITC, clone 80H3 (Beckman Coulter Immunotech) and 20 µL of CD11b*PE, clone D12 (BD Immunocytometry Systems). In a separate assay, the corresponding amount of PB was incubated with 10 µL of CD16*FITC, clone NKP15 and 20 µL of CD11b*PE, clone D12 (both BD Immunocytometry Systems). For analysis of monocytes, PB was incubated either with 20 µL of CD14*FITC, clone MOP9 and 20 µL of CD33*PE, clone P67.6 (both BD Immunocytometry Systems) or 20 µL of CD48*FITC, clone J4.57 (Beckman Coulter Immunotech) and 20 µL*CD33, clone P67.6 (BD Immunocytometry Systems), respectively.. After 20 -30 min, cells were washed once by addition of 1 mL PBS without Ca 2+ /Mg 2+ and centrifugation by 5900 g for 0.5 -1 min. Lysis of erythrocytes was performed by resuspension of the cell pellets in 100 µL OptiLyse B (Beckman Coulter

  , figure 6, figure 7): (A) no significant GPI-AP deficiency fulfilling our criteria for flow cytometric PNH diagnosis during the whole investigation period; (B) new flow cytometric diagnosis of PNH during follow up after a normal GPI-AP-expression at first investigation; (C) flow cytometric diagnosis of PNH at initial analysis with stable size of GPI-deficient granulocyte population during follow up (defined as GPI-deficient granulocyte population stable < 50% or > 50 %); (D) flow cytometric diagnosis of PNH at initial analysis with expansion of the GPI-deficient granulocyte population (defined as increase of GPI-deficient granulocyte population from < 50% to > 50%) (D1) and/or involvement of additional cell lineages (D2) during follow up; (E) flow cytometric diagnosis of PNH at initial analysis and decrease of the GPIdeficient granulocyte population (defined as decrease of GPI-deficient granulocyte population from > 50% to < 50%); (E1) or disappearance of GPIdeficiency in a cell lineage (E2) during longitudinal analysis; (F) disappearance of the PNH-typical GPI-AP deficiency below our criteria for flow cytometric PNH diagnosis. The cut off granulocyte clone size of </> 50% as sign of a relevant quantitative change in clone size was chosen because of published data about the impact of this relative proportion for thromboembolic events (15). Patient characteristics, number of examinations and duration of follow up are summarized in table 1. In detail 9% of the 80 pts with no PNH-typical GPI-AP deficiency in the first analysis developed flow cytometric PNH diagnosis during follow-up (group B). In 3 of these 7 cases detected during follow up diagnosis was based on significant GPI-AP deficient populations on monocytes and granulocytes. 28% of the follow up patients showed a significant change of GPI-AP deficiency on granulocytes or lineage involvement. Moreover 5 out of the 75 pts initially diagnosed with PNH developed an emerging GPI-deficient population on an additional cell lineage or showed less involved cell lineages during follow up (group D2 and E2). In 11 % of all cases with flow cytometric diagnosis of PNH a significant change of GPI-deficient granulocyte population occurred (group D1 and E1). In the group of the 7 pts with decrease of GPI-deficient granulocyte population or disappearance of significant GPI-AP deficiency in a cell line (E1 and E2) 2 pts received allogeneic stem cell transplantation and 2 pts were treated with ATG-based immunosuppressive therapy. Only 3 of these 7 pts suffered from a classical PNH, while 4 were diagnosed with associated bone marrow failure syndromes. All 3 pts with classical PNH showed a decrease of GPI-AP deficient population on granulocytes and no change in cell lineage involvement. Additionally 8 pts (11 %) fulfilled no longer the flow cytometric criteria of PNH during follow up (group F). Half of these 8 pts received an ATGbased immunosuppression and 4 pts (one was treated for MDS) received an allogeneic stem cell transplantation before the PNH-typical GPI-AP deficient population pattern disappeared. A spontaneous loss of significant GPI-deficiency clones, i.e. disappearance without prior therapy, was observed in none of the follow up pts. All such cases were obtained in association with therapy response and blood count improvement.

Figure 6 :

 6 Figure 6: examples of follow up courses for each follow up subgroup A-F. (A) flow cytometric criteria for PNH at initial diagnosis and during follow up not fullfilled; (B) new flow cytometric diagnosis of PNH during follow up; (C) stable GPI-deficiency during follow up; (D) increase of GPI-deficiency during follow up; (E) decrease of GPIdeficiency during follow up; (F) flow cytometric diagnosis criteria for PNH lost during follow up.

Figure 7 :

 7 Figure 7: Scatter blots of GPI-marker deficiency in % during follow up. ECD59 = CD59deficiency on erythrocytes, RCD59 = on reticulocytes, GCD24/66b = CD24/66bdeficiency on granulocytes, MCD14 = CD14-deficiency on monocytes. Blue line: median size of GPI-deficient population. First examination = results of group B (no flow cytometric PNH-diagnosis at first GPI-AP-analysis, but fulfilling flow cytometric PNH diagnosis criteria during follow up) at time of initial GPI-AP-analysis. Initial diagnosis = results of group C + D + E + F (flow cytometric PNH diagnosis at first GPI-AP analysis) at time of first GPI-AP-analysis and results of group B at time of first flow cytometric PNH diagnosis. Last follow up: results of all patients with flow cytometric PNH diagnosis at time of last GPI-AP analysis.

Figure 1 :

 1 Figure1:Staining of the reticulocytes by the RNA dye thiazol orange allowed a separate analysis od erythrocytes and reticulocytes. Comparision of the results in a healthy control and a PNH-patient. In the healthy control separation of two populations according to erythrocytes (left upper quadrant) and reticulocytes (right upper quadrant) without significant GPI-deficiency. In the PNH patient separation of four poulations according to erythrocytes and reticulocytes without (upper quadrants) and with (lower) significant GPI-deficiency.

Figure 2 :

 2 Figure 2: Flow sheet patient of the different patient groups at time of initial GPI-AP-analysis and during follow up. Significant changes of GPI-deficient populations during follow up was observed in groups B, D1, D2 with an expansion of GPI-AP deficient populations (including new PNH-diagnosis) and in groups E1, E2 and F with an decrease of GPI-AP deficient populations (including disapearance of PNH diagnosis criteria).

Figure 3 :Figure 4 :Figure 5 :

 345 Figure 3: Correlation between the used GPI-AP markers within one cell line. Black = all analyses. Red = restricted to the first analysis per patient. Broken black lines = confidence interval of all analyses. Broken red lines = confidence interval of the first analysis per patient. All correlations were highly significant (p < 0.0001) in the group with all analyses as well as in the group with only the first analysis (p < 0.0001). The range of the correlation coefficient was r2 =0.61 -0.95.

Figure 6 :Figure 7 :

 67 Figure 6: examples of follow up courses for each follow up subgroup A-F. (A) flow cytometric criteria for PNH at initial diagnosis and during follow up not fullfilled; (B) new flow cytometric diagnosis of PNH during follow up; (C) stable GPIdeficiency during follow up; (D) increase of GPI-deficiency during follow up; (E) decrease of GPI-deficiency during follow up; (F) flow cytometric diagnosis criteria for PNH lost during follow up.