domain: chim phys

text:
Estelle André

Nicolas Pannacci

Christine Dalmazzone

Annie Colin

A new way to measure viscosity in droplet-based microfluidics for high throughput analysis

In this work, we propose a new way to measure viscosity of samples in a microfluidic device. By analysing the shape of droplets after an expansion, we can measure the viscosity of the phase inside the droplet knowing the surface tension between the two liquids, the flow rate, the geometry of the channel and the viscosity of the continuous phase. This work paves the road for future high throughput studies in the framework of digital microfluidics.

Introduction

Combinatorial chemistry has opened new paths for synthesizing large libraries of novel materials and formulations. 1 High throughput characterization techniques become essential in order to benefit from these new synthesis methods. In fact, a systematic investigation of the relevant properties is required to select the convenient formulation or material. In this paper, we present a setup which allows to perform continuous rheological measurements on a microfluidic chip. Rheology is the study of the deformation and flow of a material in response to an applied stress. Viscosity is defined as the ratio between the shear stress and the shear rate. 2 For simple liquids, the shear stress is linearly related to the shear rate via the viscosity coefficient. In complex fluids, the existence of a mesoscopic length scale ranging between the molecular size and the whole sample 2 induces coupling between the structure of the fluid and the flow leading to a non-Newtonian behavior. Rheological behaviors are key parameters in many fields, ranging from medicine and food processing to the chemical and manufacturing industries. In the food industry, the stability of dressings is often obtained by increasing the viscosity. In the oil industry, in the field of enhanced oil recovery, the viscosity of the injected polymer solutions has to be higher than that of the oil in order to avoid fingering instability. 3,4 At the opposite, the viscosity of a medication must be low enough to be infused using a needle and a syringe. The development of these products thus requires the use of additives that tune the viscosity of the product to the range required by the final application. The formulation of the appropriate additives in a mixture is a tedious screening work that involves a series of long trials and tests. The use of high throughput microfluidic techniques, in this field would both increase efficiency and reduce costs of research and development for the chemical industry. 5 Let us underline that high throughput tests do not require to measure directly the property under scrutiny i.e. the viscosity of the sample in this study. Their aim is to define the area of a phase diagram where the properties are suited for applications. The measurement of a parameter varying as this property is sufficient to perform these tests. If required the property may be measured afterwards using classical tools.

Measuring rheological properties using high throughput techniques goes through miniaturization of the measurement setup. 6 The easiest type of rheometer to miniaturize, allowing for a continuous approach, are capillary rheometers. 7,8 Galambos and Forster 9 have proposed to use microfluidic devices and to take advantage of the features of specific microfluidics flows. After a T junction, two miscible fluids flowing side by side in the outlet channel are mixed by interdiffusion. Right after the T junction, the interface between the two fluids is still sharp since in their experimental conditions, diffusion is slower than convection. In the channel, the position of the interface is fixed by the ratio of the flow rates of the two fluids and by the ratio of their viscosities. These authors show that by measuring the position of this interface using fluorescence microscopy, they manage to compute the viscosity of one sample by knowing the flow rates and the viscosity of the other fluid. This elegant method does not require the implementation of an external pressure sensor. It has been improved by Guillot et al. 12,13 , Lee and Thipathi 14 and

Solomon and Vanapalli 15 . The tool is relatively easy to use owing to its simple setup and the absence of direct measurements of pressure. These techniques are efficient. However, they have to be coupled to a device allowing the preparation of samples of various compositions to be used in a screening approach. One may inject water and a concentrated solution of polymer at the inlet of a T junction. By varying the ratio of the two flow rates, one obtains, in the outlet channel, mixtures of various compositions. This process requires to flush the fluidic network between two compositions. At least twice the dead volume of the new composition has to be injected to avoid cross contamination of the preparations.

Droplet-based microfluidics is more suited than continuous microfluidics for the preparation of samples. It allows the manipulation of droplets or plug of small volumes (10 -6 to 10

-15 L) carried and isolated by an immiscible phase. These droplets can be generated at high frequencies (up to 100 kHz), merged with each other, split, trapped, and sorted with hydrodynamic, electrical, and optical-based droplet manipulation techniques. [16][17][18] In droplet-based systems, since Taylor diffusion and dilution of sample and reagents are absent, the temporal concentration information of samples can be preserved in droplets with high resolution and high fidelity. Such a feature is particularly suitable for high throughput formulations assays. The main drawback of this approach is the relative absence of characterization techniques. 19 Fluorescent probes or Raman scattering may be used to follow a chemical or biological reaction. Brosseau et al. 20 and Lee et al. 21 have extended these characterization techniques to another property than an optical property. Making use of the deformation of a droplet exiting a constriction, they have measured the surface tension and developed an analysis to characterize the features of surfactant adsorption. This type of analysis has also been used before by Cabral et al. 22 for the development of a microfluidic tensiometer.

In this work, we extend the previous approach to the measurement of the viscosity of the liquid present inside the droplet. The main originality of our work is to present a viscosimeter for droplet-based microfluidics. The first part of the article is devoted to the description of the materials and of the methods. The second part deals with the experimental results. It is a comprehensive study displaying the variation of the relaxation time and the maximal deformation of a droplet after a constriction as a function of the viscosities of the two phases, the surface tension, the size of the droplet and the velocity of the flow. From this study, we define an experimental protocol (see fourth part) allowing the measurement of the viscosity and apply it to characterize dilute polymer solutions. We show that this analysis may also be used for non-Newtonian fluids. We conclude by giving an example of high throughput experiments. The last part is devoted to conclusion and outlooks.

Materials & methods

Chemicals

The aqueous phase consists of deionized water-glycerol (Sigma-Aldrich) mixtures (60% and 68.4% (w/w), where 0% glycerol is only DI water) and the oil phase is a silicone oil (Polydimethylsiloxane, 20 and 500 mPa.s, Prolabo and VWR) or a mixture of both. Dodecyltrimethylammonium bromide (DTAB, Sigma Aldrich) was used as a surfactant at 1.7% (w/w) in the aqueous phase. This concentration is equal to twice the critical micellar concentration (CMC). Aqueous polymer solutions were also used. They consist of deionized water-PEG600 (Polyethylene glycol, BioUltra, 624 / , Sigma Aldrich) mixtures (51.9%, 63.3%, 69.9%, 74.6% and 78.3% (w/w), where 0% PEG600 is only DI water). We used shear thinning and elastic solutions. They consist of HPAM polymer solutions. HPAM are partially Hydrolysed PolyAcrylaMides. They consist of a succession of acrylamide monomers which form a linear chain between them. These polymers are partially hydrolysed and bear an electrical charge. Some of the amide functions are carboxyl or carboxylate functions. The degree of hydrolysis corresponds to the number of hydrolysed units on the total number of units of the polymer. Two solutions of HPAM of different molar masses were studied. The first polymer coined FLOPAAM 3230 has a molar mass of 9. 10 / and a degree of hydrolysis of 25 to 30%. The second polymer coined FLOPAAM 3630 has a more important molar mass, 18. 10 / and degree of hydrolysis of 25 to 30%. Both are sold by SNF. The HPAM solutions are prepared in the following manner: the polymer in powder form is solubilized to the desired concentration in deionized water with magnetic stirring overnight at room temperature. In both cases, we worked with dilute solutions (1000 ppm in DI water).

Pendant drop tensiometry

The determination of the interfacial tensions of the aqueous phase-oil phase interfaces is performed using the pendant drop method (Drop Shape Analyser -KRÜSS DSA 25). A glass cuvette is filled with the oil phase. Before each measurement, the cuvette is rinsed with the oil being tested. The syringe and the needle used to produce the droplet are rinsed with the mixture being tested. Drops of aqueous mixtures are formed at the tip of a needle into the oil reservoir. Before each series of measurements, the magnification of the video image is first determined fixing the needle diameter in order to access the drop dimensions. A numerical method based on the Young-Laplace equation is then used to vary a shape parameter known as the Bond number until the calculated drop shape coincides with the actual drop shape. The interfacial tension is calculated from this adapted shape parameter knowing the difference in densities between the two phases. In the case of the HPAM solutions, the two-phase densities are too close to be measured with the pendant drop method. The corresponding interfacial tensions were therefore measured using the Wilhelmy plate method. A thin platinum plate connected to a microbalance dives into a tank containing one or two liquids if the light phase is not air. The blade is positioned at the interface between the light phase and the heavy phase. The force on the plate due to wetting is Please do not adjust margins Please do not adjust margins measured using the microbalance and used to calculate the interfacial tension using the Wilhelmy equation. All of the results are given with a maximal error of 7%.

Rheology

The determination of the viscosity of the different phases is performed using a Physica MCR-301 (Anton Paar GmbH, Graz, Austria) rheometer. The rheometer was equipped with a temperature controller (C-PTD200-SN928212) and a coaxial cylinder with double air-gap (DG26.7/Q1 -SN36551) or a cone and plate geometry with a diameter of 4 cm and an angle of 1°59 (SN982166). Measurements are performed at 20°C. The shear rate is varied from 10 to 1000 s -1 and data points are taken every 15 s. The value of the viscosity is taken as an average of all the data points obtained over the shear rate range for the Newtonian case. All of the results are given with an error of 5%.

Device design

The microfluidic channel geometries are designed using the layout editor CleWin. These geometries (Fig. 1) consist of a flow focusing junction including the oil phase and aqueous phase inlets. A third inlet is added to control the velocity and the spacing of the droplets. The height of the channels that make up this first part of the geometry is H = 120 µm. A chamber where the deformation of the droplet occurs (Fig. 2) is designed before the outlet of the device. The width of this chamber is three times greater than the width of the inlet channel. The height of the chamber may differ from the height of the channels that make up the first part of the geometry. Two different geometries were used. The first one refers to the "confined droplet situation" and is coined "C". In this case, the width of the inlet channel is W 1 = 120 µm, the width of the chamber is W 2 = 310 µm and the channel height remains the same all along the chip and equals to H = 120 µm. The second geometry refers to the "unconfined droplet situation" and is coined "D". In this case, the width of the inlet channel is W 1 = 333 µm, the width of the chamber is W 2 = 960 µm and the channel height is equal to H = 120 µm in the first part of the microsystem (Fig. 1 green and red enlarged areas) and to H = 240 µm in the deformation chamber (Fig. 1 purple enlarged area). The droplets flow in this chamber. (Fig. 1 purple enlarged area and Fig. 2). It is the place where their deformation is recorded. In the experiments, the radius of the droplets is varied between 20 µm to 85 µm. The velocity of the droplets range between 10 mm/s to 260 mm/s. In the following, we will define a geometrical parameter as R*=2a o /W 1 where a o is the radius of the droplet, W 1 the width of the inlet channel at the entrance of the chamber. Brosseau et al. 20 use the same geometrical parameter in their analysis.

Microfabrication

Microfluidic devices are produced using standard photolithography techniques using photomasks (Photext). In brief, a negative mold of the structure is prepared by photolithography of SU8-2100 (Micro Chem) on a silicon wafer. Polydimethylsiloxane (PDMS, RTV 615, Momentive) was poured over the mold, cured in an oven for at least 2h at 65°C and peeled off the mold. The holes for the tubing connections are punched with a biopsy needle. To seal the device, glass-PDMS or PDMS-PDMS surfaces were oxidized using air plasma. The resulting device can either be treated with a solution of octadecyltrichlorosilane (OTS) in hexadecane to render the Please do not adjust margins Please do not adjust margins channel walls hydrophobic 23 or poly(acrylic acid) can be grafted on the channel walls to render them hydrophilic 24 . In order to vary the height of the device between the channel and the chamber, two patterned PDMS surfaces can be sealed by adding EtOH between the two surfaces just after the plasma treatment. The two surfaces can thus be aligned manually in a timescale of 30 min. The aligned surfaces are then placed in an oven overnight. The channel height was measured by image analysis cutting the channel after experimentation.

Microfluidics

The fluids are injected from reservoirs using a pressure driven flow controller (Fluigent MFCS EZ). Reservoirs and the microfluidic chip are connected via PEEK (PolyEtherEtherKetone) tubing of outer diameter 500 µm or FEP (Fluorinated Ethylene Propylene) tubing of outer diameter 1/16''.

High-speed microscopy

The microfluidic device is mounted on an inverted microscope (Axio Observer Mat, Zeiss) and imaged using a x20 microscope objective. The pictures of the droplets are recorded with a high-speed camera (i-SPEED 2, Olympus) at a frame rate of 2000 or 4000 pictures per second. The movies of droplets are recorded at the entrance of the deformation chamber.

Image processing and data analysis

The droplet trajectory and shape are obtained by image processing of the high-speed movies through plug im ! 25 an open software platform for data processing from IFPEN already used for other case studies 26 . All parameters of interest rely on the detection of the twodimensional projection of the contour of the droplet. The droplet contour is defined as the outside edge of the droplet meniscus. Different parameters are extracted from this analysis: the droplet width w, the droplet length l and the droplet centre positions x, y (Fig. 2). Then a home-made Matlab program is used to obtain the parameters of interest.

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For each droplet, the deformation D is defined as:

(1) and is obtained as a function of the position in the channel (Fig. 3 (a)). For each measurement, the values obtained for 3 droplets are considered. The uncertainty on the measurement is ∆ 0.003.

Following Gires et al. 27 , the maximal deformation in the expansion D max is obtained by a fitting of the deformation curve with the following equation:

⁄ (2)
p i are the fitting parameters. This fitting is performed only on the data for those where the droplet is in the expansion chamber. The position x max corresponding to the maximal deformation is also extracted. The droplet instantaneous velocity is defined as:

(3)

i.e. the division of the difference in position of the center between two frames i and i+1 by the time between two frames t f . The droplet velocity is then plotted as a function of its position in the channel (Fig. 3 (b)) and the resulting curve is fitted with the following equation:

Experimental results

We first focus on simple systems and study the deformation of droplets made of silicone oil. The continuous phase is a waterglycerol mixture.

In some situations, dodecyltrimethylammonium bromide (DTAB) is used as a surfactant. It is dissolved in the aqueous phase. In the following, we discuss first the measurement of the relaxation time.

Relaxation time

Fig. 4 gathers all the experiments performed. In those experiments, the radius of the droplet a o is typically comprised between 40 and 85 µm, the height of the chamber H between 120 and 240 µm, the geometrical parameter * 2 / between 0.4 and 1.3, the velocity of the droplet at the maximal deformation U Dmax between 10 and 260 mm/s and the interfacial tension between 9.3 and 28 mN/m. The viscosity of the internal phase varies between 20 and 100 mPa.s, the one of the external phase between 10 and 20 mPa.s and the ratio of viscosity between the two phases ⁄ between 1 and 10.

All the data collapse on a master curve. The relaxation time is given by:

(5)

Strikingly, the characteristic time involved in the relaxation of the shape of the droplet does not depend upon the interfacial tension.

We have checked this point experimentally by comparing measurements performed in presence and in absence of surfactants. In our experiments, we used DTAB at a concentration of 0.07 mol/L which is above the CMC (CMC = 0.03 mol/L 36 ). Let us anticipate that in this situation the interface of the drops was always covered by surfactants (see next section). The radius of the droplets in presence of surfactant is 76 µm, the velocity 125 mm/s, the viscosity of the dispersed phase 19 mPa.s, the viscosity of the continuous phase 11.8 mPa.s, the relaxation time is 1.6 ms). In this situation, the surface tension was 9.3 mN/m. In absence of surfactant, the radius of the droplets in presence of surfactant is 78 µm, the velocity 136 mm/s, the viscosity of the dispersed phase 19 mPa.s, the viscosity of the continuous phase 11.8 mPa.s, the relaxation time is 1.6 ms. The surface tension is equal to 27.7 mN/m.

Deformation

Fig. 5 and Fig. 6 display the measurements of the maximal deformation as a function of the combination of the capillary number, the geometrical parameter and the ratio of viscosity. The capillary number is defined as: This number varies between 0.01 and 0.12 in these experiments. We have not been able to collapse all the data on a single curve independent of the confining regime. The data have been separated on two graphs. Fig. 5 deals with confined droplets ( * 0.7) whereas Fig. 6 focuses on unconfined droplets ( * 0.7). We split our analysis at * 0.7. This may seem striking. The change of behavior does not always occur for critical parameters equal to 1. For example, turbulence occurs for Reynolds number much higher than 1. Here we think that the presence of a lubrication film between the wall of the channel and the droplet induce a change of behavior for R* less than 1.

When the droplet is confined in the channel, a lubrication film is formed between the channel wall and the droplet. The majority of the studies concerning the calculation of the thickness of this film in the case of two-phase flows concern gas-liquid systems. Since Bretherton 28 which provided an estimate of the lubrication film thickness for very low capillary numbers in circular-section channels, the models have extended to wider ranges of capillary numbers and to square channels. Whatever the model considered and the conditions, the thickness of this film increases with a power of the capillary number with 0.

Thus, the lower the interfacial tension or the higher the viscosity of the continuous phase, the thicker the film. The presence of this film can create additional dissipation forces that will hinder the deformation of the droplet. Thus, the larger the capillary number, the more the droplet is hindered in its deformation and the more the exponent associated with the capillary deviates from 1 by decreasing. Knowing this, it is still mathematically possible to look for a scaling law (Fig. 5). The maximal deformation scales as:

0.7 . * . . ( 7
)
This function has been determined by fitting the experimental data with a mean squared procedure. The coefficient of determination here is r 2 = 0.92. This value is mainly due to the fact that, as we explained previously, it is not possible to find a general scaling law valid for all viscosities and interfacial tensions as the exponents vary with these properties.

This conclusion differs in the unconfined droplet situation (Fig. 6). The maximal deformation scales as:

1.6 * .

(8)

The coefficient of determination is higher and equal to 0.96. The exponent of is equal to -0.1. This slight dependence allows the measurement of the viscosity of the internal phase.

Analysis of the data

Let us now discuss the obtained results. At the end of this section, we will define an experimental procedure to measure the viscosity of the sample located inside the droplet. We have first shown that the relaxation time does not depend upon the interfacial tension. To understand this point it is required to analyze the relaxation of a droplet submitted to a flow. The modelling of this process has been first addressed by Taylor 29 . In Taylor's model a droplet of viscosity  int is placed in a fluid with a viscosity  ext . The system is submitted to a pure hyperbolic flow in the (x,y) plane. In this situation, the extension rate along the flow direction x , dU ⁄ is a constant. U is the velocity of the surrounding fluid. The steady deformation (i.e. the deformation of the drop when steady state is achieved) is proportional to the extension rate and is given by: . in the confined droplet situation. The colorbar specifies the value of the viscosity ratio . Please do not adjust margins Please do not adjust margins (9)

 is the interfacial tension, is the steady deformation of the droplet i.e after the relaxation process. Note that a sharp constriction induces an inhomogeneous extensional velocity field. The use of a geometry involving a uniform extensional flow rate would allow us to use this formulation and to measure the viscosity through the measurement of D steady knowing the interfacial tension. Even though some optimized geometries have been proposed by Zografos et al. 30 , they remain devoted to one phase flow and induce a homogeneous elongational rate only in the middle plane of the channel. As they are complex to set up experimentally, we decided to use a sharp constriction. As we just mentioned, a sharp constriction induces an inhomogeneous extensional velocity field. This theoretical model has been generalized to inhomogeneous extensional velocity fields by Barthes-Biesel et al. 31 where:

2 3 (12)
Note that the capillary time does not depend upon the velocity.

To solve this set of equations, numerical simulations are required to compute the eigenvalues <e 1 > and <e 2 >. These numerical simulations are out the scope of this work. To go further, we proceed through hypothesis and restrict our analysis to our experimental situation. We assume that varies exponentially with the distance to the inlet of the chamber. This point is in agreement with the recent numerical simulations of Trégouët et al. 33 The correspondence between time and space in microfluidic devices allows us to write:

t / (13)
where U is the velocity of the droplet, L a characteristic length, D o the initial value of the deformation and t the time. We define a convection time ⁄ .

Note that we assume here that the velocity of the dispersed phase is proportional to the velocity of the droplet. The dynamics of droplets in microfluidic devices has been extensively studied by Gallaire and co-workers. In a review 34 , they show that the velocity of a drop differs slightly from the velocity of the fluid in rectangular geometry. In this situation, the flow in the gutters of the geometry governs the differences of velocity. The ratio ⁄ scales as ⁄ where B is a constant. U is the velocity of the drop and V d the mean velocity of the dispersed phase. In all the cases, the differences between U and V d are less than 6%. In our analysis, we neglect this non-linear variation and assume that the velocity of the drop U is proportional to the mean velocity of the fluid V d .

The solving of this set of equations shows that:

⁄ ⁄ (14)
where C 1 and C 2 are two constants and also shows that:

(15)

for ≫ and ≫ . Our experiments follow this hypothesis since the time scale involved in the relaxation process is 2.5 to 32 times higher than the time calculated for the capillary relaxation.

Experimental data displayed on Fig. 4 suggest that our experiments follow the framework of the previous analysis. They show that the relaxation of the droplet involves a single time scale inversely proportional to the velocity. The characteristic length L involved in the spatial development of the flow is proportional to the width of the inlet channel at the entrance of the deformation chamber. This analysis is confirmed quantitatively by the fact that the time scale involved in the extensional velocity field is the same than the relaxation time of the deformation. In Fig 3, the relaxation time involved in the extensional flow is 0.5 ms. 0.5 ms is also the relaxation time of the deformation in this situation while the corresponding capillary time is equal to 0.08 ms. These results clearly show that in our experiments, the relaxation time cannot be used to measure interfacial tension or viscosity since it is ruled by convection processes. We have tried to vary the size of the channel, of the droplets, to accelerate the flow but we did not succeed to obtain a range of parameter where the convection time is shorter than the capillary one . might be measured in the first part of the deformation of the drop around D max i.e. in the short time situation. This measurement is tricky and requires the knowledge of the viscosity of the liquid trapped in the drop to calculate the eigen values of the strain rate tensor and determine precisely D steady . This analysis points out that the only way to fit the entire curve of relaxation is to use numerical simulations. The extraction of the interfacial tension and viscosity of the internal phase require to assume values, fit the data and make back and forth between experiments and numerical simulations. This procedure has been used recently by Trégouët et al. 33 to measure the interfacial tension. This journal is © The Royal Society of Chemistry 20xx

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In this work we chose an experimental approach and decide to use a calibration curve. We determine the value of the maximal deformation D max experimentally. We assume that this value is a function of the physical quantities that control the problem i.e. the droplet velocity and radius, the interfacial tension and the viscosity of the two fluids. Looking for a scaling law, we expect that the capillary number, the geometrical parameter and the ratio of viscosity are involved in this relationship linking the maximal deformation to the previous dimensionless numbers. Brosseau et al. 20 found a relationship involving the capillary number and the geometrical parameter only, keeping the ratio of viscosity constant. However, Park and Dimitrakopoulos showed through simulations that this number has an influence on the deformation of the droplet. 35 In our experiments, we varied this ratio of viscosity to complete the relationship between the maximal deformation and the dimensionless numbers controlling the phenomenon.

Measurements of the maximal deformation evidence two regimes. We recall that in the confined droplet situation (i.e. for * 0.7), the maximal deformation scales as 0.7 . * .

. . But the exponents vary with the properties of the fluids. In the unconfined droplet situation (i.e. for * 0.7), the maximal deformation scales as 1.6 * . . The exponent of is equal to -0.1. Note that the exponent of Ca has been set to one in this analysis as we expect linear effects involving the velocity.

From this law, we propose a procedure to measure the internal viscosity of a droplet. We will first measure the interfacial tension at equilibrium of the droplet. We will assume that this parameter does not vary too much due to elongation. In other words, we will assume that the elasticity of the monolayer is negligible and that no surface gradients are involved during the relaxation. This hypothesis is in agreement with previous studies performed with solutions of surfactants above the critical micellar concentration (CMC) in microfluidic systems. 36 It is also supported by our experimental data. In our experiments, we used DTAB at a concentration of 0.07 mol/L which is above the CMC (CMC = 0.03 mol/L 36 ). The measurements performed in presence and in absence of surfactant collapse on the same master curve on Fig. 6. Note that we have checked following Wang et al. 37 and Moiré et al. 36 that in this situation the interface of the drops was always covered by surfactants. The kinetics of adsorption in microfluidic devices has been studied carefully by Wang et al. 37 and Alvarez et al. 38 . DTAB are small molecules and it is it is demonstrated in the literature that the limiting step is not the adsorption but rather the convection diffusion process. Following Wang and Alvarez, the time scale involved in the diffusive process is , where h p is the mass transfer distance in a stationary flow and h c the mass transfer distance in presence of flow. h p is given by h p = /C, where is the surface concentration and C the surfactant monomer bulk concentration. Following the data of Wang and assuming a rigid interface, h c is given by 2 / 3 ⁄ where a o is the radius of the droplet or of the jet and Pe is the Péclet number defined as / 2

. U is the characteristic velocity in the external phase and D eff is the effective diffusion coefficient that takes into account the contribution of the micelles to the mass transfer. Following Glawdel and Ren 39 , 1 1 / where / 1, c is the surfactant concentration, CMC is the micellar concentration and Na is the aggregation number of micelles.

In our situation,  DTAB = 1.89 10 -6 mol/m 2 , D eff = 4 10 -11 m 2 /s. 36 The mass transfer distance in stationary flow h p is equal to 0.062 mm. The mass transfer distance under flow h c varies between 1 and 3 mm in our experiments. The diffusion time is thus equal to 10 -4 s which is much less than the time scale involved in our experiments (a few milliseconds in our experiments). We may thus consider that the surfaces are saturated by surfactant after the formation and during the expansion of the droplet. This situation differs from the one presented by Brosseau et al. 20 The surfactant used by Brosseau et al. is very specific with a high molecular weight. For these reasons the authors are able follow the kinetics of adsorption in microfluidic device.

Note that this situation is not the generic one. For surfactants with moderate molecular weight, the adsorption of the surfactant at the interface is almost instantaneous in microfluidic device as shown by Wang and Moiré. We anticipate that our method will be not valid in presence of surfactant if the time scale of adsorption or of diffusion is longer than a few ms.

To continue with the procedure, we will measure the velocity of the droplets, its maximal deformation and compute its viscosity.

We underline that our procedure holds for both Newtonian and non-Newtonian systems. We will comment this point in the following section in which we display such a study.

A new method to measure the viscosity in droplets a/The Newtonian situation

We prepared solutions of PEG at various concentrations. We measured the rheological properties of these solutions using classical rheometry tools. The solutions are Newtonian in the range of studied shear rate. We then used the microfluidic device D and studied the deformation of droplets containing these solutions. We measured the velocity of the droplets and their deformation in the chamber as previously described. Fig. 7 displays the measurement of the viscosity extracted from the microfluidic analysis as a function of the viscosity measured using a rheometer. The value extracted from the microfluidic analysis is clearly proportional to the one measured using a rheometer. The discrepancy between both is

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Please do not adjust margins mainly due to the low value of the exponent of , that induces a large error bar. These data prove that this method is performant to study the relative evolution of the viscosity of a solution as a function of the concentration of a viscosity enhancing agent. In the framework of high throughput analysis, such correlation is sufficient to find a functioning point for a formulation. If required, the viscosity of the most efficient sample may be measured using a classical rheometer afterwards.

b/The non-Newtonian situation

Tests were carried out in microsystem D with silicone oil as the continuous phase and aqueous solutions of FLOPAAM 3630 and 3230 at 1000 ppm as the dispersed phase. The silicon oil is a Newtonian fluid and its viscosity is 20 mPa.s. Both FLOPAAM solutions are shear thinning solutions. Their rheological curves have been measured in cone plate geometry. These fluids follow a power law equation. Their viscosity is given by in the measured shear rate range (i.e between 10 s -1

and 1000 s -1 ). We get A = 0.64 and n = -0.71 in the FLOPAAM 3630 situation and A = 0.52 and n = -0.64 in the FLOPAAM 3230 situation. FLOPAMM 3230 solution does not exhibit measurable first normal stress difference. At the opposite, for shear rate higher than 50 s -1 , first normal stress differences are of the order of the shear stresses in the FLOPAAM 3630 situation. This last solution is thus shear thinning but also highly elastic. We used the previous approach to measure the rheological curve for these two solutions. We prepared droplets of polymer solutions. The mechanism of drop formation depends upon the elasticity of the solution. When a droplet is produced in a continuous phase, a jet of liquid connecting the arrival of dispersed phase to the droplet before its complete detachment is formed. In the Newtonian situation, the diameter of the filament decreases exponentially (regime dominated by the inertia of the continuous phase), then linearly until rupture of the filament to form the droplet (regime dominated by capillary forces).

In the elastic case, an intermediate regime is observed during which the state of the filament results from the equilibrium between elastic forces and capillary forces: the capillary pressure tends to thin the filament, while the elastic forces induced by the stretching fluid resist this thinning. The filament radius also decreases exponentially over time but more slowly. In addition, before its complete breakup, the filament adopts a particular structure consisting of a string of spherical drops connected by fluid bridges called beads-on-astring. After the complete stall of the droplet, the small drops move very quickly in the centre of the channel, coalesce and integrate with the droplet that has just unhooked. Thus, we are not bothered by the presence of satellite drops during the subsequent analysis of the deformation of the droplet.

For each test involving one of the two polymers, the speed of the drop is varied between 130 and 170 mm/s in the FLOPAAM 3230 situation and between 90 and 140 mm/s in the FLOPAAM 3630 situation. The drop radius is 63 μ ± 5% for the FLOPAAM 3230 and 70 μ ± 3% for the FLOPAAM 3630. The deformation of the drop, its speed and its size are measured in the same way as for the Newtonian fluids. Then, using the correlation found for Newtonian fluids, the corresponding viscosity ratio is determined by: . * .

( Please do not adjust margins Please do not adjust margins For Newtonian fluids, the mean shear rate borne by a drop in an unconfined geometry is given by: (17)

In the following, we will assume that this equation is also valid in the non-Newtonian situation. This may be surprising. We underline that such approach is used classically in all the rheometers. Fig. 8 displays the obtained results. We note a good agreement between the measured viscosity into the drops and the one measured using a conventional rheometer. We anticipate that in some situation the discrepancy is higher than 40%. However, such measurements are enough accurate in a high throughput approach.

Towards high throughput measurements

In order to show that our technics is promising for high throughput measurements, we developed a microdevice allowing us to measure the viscosity of a mixture as a function of the concentration of its constituents. The geometry we have chosen is shown in Fig. 9. The geometry is similar to the previous ones, but instead of a single arrival of dispersed phase, the geometry has two, one for each of the two solutions involved in the mixture. We inject into the microsystem two aqueous solutions of glycerol at different concentrations. Solution A is composed of 64 % (w/w) of glycerol and solution B with 89 % (w/w) of glycerol. These two solutions are injected at different flow rate ratios using syringe pumps to obtain different dispersed phase viscosities. In order to get a homogenous solution before preparing the droplets, it is required to mix the two fluids. This process is very complex in microfluidics. Two fluids that are injected into a microchannel flow side by side and are only mixed by diffusion. The characteristic time for diffusion is given by /4

where W is the width of the channel and D diff the diffusion coefficient. A microfluidic channel with a length of * is thus required to ensure mixing by diffusion, V being the fluid velocity. For an average speed of 5 mm/s and a diffusion coefficient D diff equal to 5.10

-11 m 2 /s, we obtain a length of 1 m, which can not be realized in a fluidic circuit. In order to solve this issue, we use a passive mixer with herringbones that break the flow laminarity and promote mixing between two fluids by increasing the contact surface. This set up is classically used in microfluidic devices. We chose the same herringbones cycles than those of Stroock 43 . They are composed of twice six herringbones. These herringbones are asymmetric, the angle they make with the x-axis of the channel is 45° and the ratio between the shortest and the longest side is of 1:2. In addition, the herringbones are drawn in positive at the top of the channel for better mixing performance. 44 Following the analysis of Stroock, we use 9 cycles of 12 herringbones to ensure the mixing. After this mixing zone, the solution enters the droplet formation zone. Droplets are produced and send into an expansion chamber. We measure the viscosity using our approach and the scaling law obtained previously. Fig. 10 shows the viscosity value as a function of the theoretical viscosity given by the flow rate ratios. A good match of these two values is found.

The results presented in this section provide a first step towards a high-throughput analysis of the viscosity of microfluidic droplets. Indeed, thanks to the mixer, we have shown that it is possible to put in contact two different compounds and to mix them to then have access to the viscosity of the resulting mixture.

Conclusion

In this work we have analyzed the flow of droplets inside an expansion. Following the work of Brosseau et al. 20 , we have shown that the maximal deformation in the unconfined situation depends upon the capillary number, a geometrical parameter and on the viscosity ratio between the internal phase and the external one. Please do not adjust margins Please do not adjust margins

We have thus proposed to use an experimental scaling law to describe the evolution of the maximal deformation D max as a function of the capillary number, the geometrical number and the ratio of viscosity.

We have shown that this analysis was relevant and allowed us to measure the relative evolution of the viscosity of Newtonian and non-Newtonian polymer solutions. This paves the road for high throughput analysis in the framework of digital microfluidics.

Fig. 2

 2 Fig. 2 Diagram of the chamber where the deformation occurs. The upper part depicts the top view of the chamber. In the lower part, the diagram coined "C" refers to the side view of the chamber in the "confined droplet situation" and the diagram coined "D" refers to the side view of the chamber in the "unconfined droplet situation".

  Fig. 3 displays typical results.

Fig. 3

 3 Fig. 3 (a) Typical deformation profile of a droplet passing through the expansion. We can follow the evolution of the deformation as the droplet is in the entrance channel, enters the expansion and relaxes to a spheroid shape. The maximal deformation of the droplet is extracted from this curve. (b) Typical velocity profile of a droplet passing through an expansion. The droplet speed at the maximal deformation is extracted from this curve. (c) Typical deformation profile of a droplet as a function of time. The insert depicts the logarithm of the deformation as a function of time, this graph is used to determine the relaxation time of the droplet. (d) Typical profile of the extension rate as a function of time. The insert depicts the logarithm of the normalized extension rate as a function of time, this graph is used to determine the convection time of the droplet. (For this figure, fluids are a silicone oil 20 cSt for the droplet phase and a DI water-glycerol mixture 60% (w/w) for the continuous phase. The radius of the droplet is 76 m and we use set up C. The surface tension is 28 mN/m, the initial velocity of the droplet is 246 mm/s).

  The speed of the droplet at the maximal deformation U Dmax is extracted from this fitting. Then combining fitted data of deformation and velocity, the deformation of the droplet is obtained as a function of time. The relaxation time of the droplet τ is obtained by a linear fitting of the curve representing the logarithm of the deformation as a function of time (Fig.3 (c)). For the following, we define ⁄ as the extension rate of the droplet and plot it as a function of time (Fig.3 (d)). We also define a convection time obtained by a linear fitting of the curve representing the logarithm of the normalized extension rate as a function of time (Fig.3(d) Insert).

Fig. 4

 4 Fig. 4 Collapse of the droplet relaxation time on a master curve. Data are from all the experiments performed in the confined and the unconfined droplet situation. The colorbar specifies the value of the geometrical parameter R*.

Fig. 5

 5 Fig. 5 Collapse of the droplet maximal deformation on a master curve 0.7 . * .

Fig. 6

 6 Fig. 6 Collapse of the droplet maximal deformation on a master curve 1.6 * . in the unconfined droplet situation. The colorbar specifies the value of the viscosity ratio .

)

  Sarrazin et al. 40 showed that the velocity profile in the droplet follows a parabolic shape similar to the profile of the Poiseuille flow in which it flows. A droplet positioned near the centre of a Poiseuille flow undergoes internal recirculation. The fluid flows to the front of the drop near its centre and to the back near the interface. Hudson et al. 41 used the method presented by Nadim and Stone 42 to determine the flow field inside a droplet created by a Poiseuille flow in a rectangular channel. The expressions characterizing the flow field in the droplet are valid only for unconfined droplets which do not feel the presence of the walls of the channel.

Fig. 8 :Fig. 7

 87 Fig.8: Droplets viscosities measured by the microfluidic approach as function of the calculated mean shear rate into the droplets. Fluids are FLOPAAM 3230 (green dots) and 3630 (red dots) at 1000 ppm. The dots are measured using our set up and the lines are the viscosity from the rheometer.

Fig. 9 :

 9 Fig.9: Geometry of the high-throughput microsystem. The geometry is similar to the previous one but there are two inlets of dispersed phase A and B and a mixing zone.

Fig. 10

 10 Fig.10Measurement of the viscosity extracted from the microfluidic analysis as a function of the viscosity measured using a rheometer of glycerol mixtures at various concentrations (69.2 %, 76.9 %, 80.6 % and 84.2 % (w/w)).

  and summarized by Rallison 32 and Trégouët et al.

		33 .
	Following this last work, the steady deformation must be
	calculated with the mean values of the eigenvalues <e1> and
	<e2> of the deformation-rate tensor averaged over the drop
	through:
	t		(10)
	Barthes-Biesel et al.	31 assume that the transient regime is
	captured by a first-order relaxation towards the steady state
	:
		t	(11)

This journal is © The Royal Society of Chemistry 20xx J. Name., 2013, 00, 1-3 | 3

This journal is © The Royal Society of Chemistry 20xx J. Name., 2013, 00, 1-3 | 9

Acknowledgements

We thank S. Perrin, C. Burnichon, B. Betro and N. Palazzo for their experimental advices and M. Moreau for the software platform plug im !.

Conflicts of interest

There are no conflicts to declare.


G Leonardi

M Striani

S Quaglini

A Cavallini

S Montani

Towards semantic process mining through knowledge-based trace abstraction

Keywords: Semantic process mining, knowledge-based trace abstraction, medical applications

Many information systems nowadays record data about the process instances executed at the organization in the form of traces in a log. In this paper we present a framework able to convert actions found in the traces into higher level concepts, on the basis of domain knowledge. Abstracted traces are then provided as an input to semantic process mining. The approach has been tested in the medical domain of stroke care, where we show how the abstraction mechanism allows the user to mine process models that are easier to interpret, since unnecessary details are hidden, but key behaviors are clearly visible.

Introduction

Most commercial information systems, including those adopted by many health care organizations, record information about the executed process instances in a log [START_REF] Van Der Aalst | Process Mining. Data Science in Action[END_REF]. The log stores the sequences (traces [START_REF] Van Der Aalst | Process Mining. Data Science in Action[END_REF] henceforth) of actions that have been executed at the organization, typically together with key execution parameters, such as times, cost and resources. Logs can be provided in input to process mining [START_REF] Van Der Aalst | Process Mining. Data Science in Action[END_REF][START_REF] Van Der Aalst | Workflow mining: a survey of issues and approaches[END_REF] algorithms, a family of a-posteriori analysis techniques able to extract non-trivial knowledge from these historic data; within process mining, process model discovery algorithms, in particular, take as input the log traces and build a process model, focusing on its control flow constructs. Classical process mining algorithms, however, provide a purely syntactical analysis, where actions in the traces are processed only referring to their names. Action names are strings without any semantics, so that identical actions, labeled by synonyms, will be considered as different, or actions that are special cases of other actions will be processed as unrelated.

Relating semantic structures, such as ontologies, to actions in the log, not only can solve the synonyms issue, but also can enable trace comparison and process mining techniques to work at different levels of abstraction (i.e., at the level of instances and/or concepts) and, therefore, to mask irrelevant details, to promote reuse, and, in general, to make process analysis much more flexible and reliable.

In fact, it has been observed that human readers are limited in their cognitive capabilities to make sense of large and complex process models [START_REF] Aguilar | Evaluation measures for business process models[END_REF][START_REF] Vanderfeesten | On a quest for good process models: The cross-connectivity metric[END_REF], while it would be often sufficient to gain a quick overview of the process, in order to familiarize with it in a short amount of time. Of course, deeper investigations can still be conducted, subsequently, on the detailed (ground) process model.

Interestingly, semantic process mining, defined as the integration of semantic processing capabilities into classical process mining techniques, has been recently proposed in the literature (see Section 5). However, while more work has been done in the field of semantic conformance checking (another branch of process mining) [START_REF] Alves De Medeiros | Semantic process mining tools: Core building blocks[END_REF][START_REF] Grando | Semantic process mining for the verification of medical recommendations[END_REF], to the best of our knowledge semantic process model discovery needs to be further investigated.

In this paper, we present a knowledge-based abstraction mechanism (see Section 2), able to operate on log traces. In our approach:

actions in the log are mapped to the ground terms of an ontology; a rule base is exploited, in order to identify which of the multiple ancestors of an action should be considered for abstracting the action itself. Medical knowledge and contextual information are resorted to in this step; when a set of consecutive actions on the trace abstract as the same ancestor, they are merged into the same abstracted macro-action, labeled as the common ancestor at hand. This step requires a proper treatment of delays and/or actions in-between that descend from a different ancestor.

Our abstraction mechanism is then provided as an input to semantic process mining (see Section 3). In particular, we rely on classical process model discovery algorithms embedded in the open source framework ProM [START_REF] Van Dongen | The proM framework: a new era in process mining tool support[END_REF], made semantic by the exploitation of domain knowledge in the abstraction phase.

We also describe our experimental work (see Section 4) in the field of stroke care, where the application of the abstraction mechanism on log traces has allowed us to mine simpler and more understandable (from the clinical point of view) process models.

Knowledge-based trace abstraction

In our framework, trace abstraction has been realized as a multi-step mechanism. The following subsections describe the various steps.

Ontology mapping

As a first step, every action in the trace to be abstracted is mapped to a ground term of an ontology, formalized resorting to domain knowledge.

In our current implementation, we have defined an ontology related to the field of stroke management, where ground terms are patient management actions, while abstracted terms represent medical goals. Figure 1 shows an excerpt of the stroke domain ontology, formalized through the Protègè editor. In particular, a set of classes, representing the main goals in stroke management, have been identified, namely: "Administrative Actions" (such as hospital admission and discharge), "Brain Damage Reduction","Causes Identification", "Pathogenetic Mechanism Identification", "Prevention", and "Other". These main goals can be further specialized into subclasses, according to more specific goals (e.g., "Parenchima Examination" is a subgoal of "Pathogenetic Mechanism Identification", while "Early Relapse Prevention" is a subgoal of "Prevention"), down to the ground actions, that will implement the goal itself.

Some actions in the ontology can be performed to implement different goals. For instance, a Computer Assisted Tomography (CAT) can be used to monitor therapy efficacy, or to assess therapy starting time (see class "Prevention" in figure 1). The proper goal to be used in the abstraction phase will be selected on the basis of the context of execution, as formalized in the rule base, described in the following subsection.

All ground actions are being mapped to SNOMED concepts1 . The ontology partially showed in Figure 1 is therefore being integrated with the most comprehensive and precise clinical health terminology product in the world, accepted as a common global language for health terms. The figure, as an example, reports the CAT SNOMED code, which is an attribute of the CAT action.

Rule-based reasoning for ancestor selection

As a second step in the trace abstraction mechanism, a rule base is exploited to identify which of the multiple ancestors of an action in the ontology should be considered for abstracting the action itself. The rule base encodes medical knowledge. Contextual information (i.e., the actions that have been already executed on the patient at hand, and/or her/his specific clinical conditions) is used to activate the correct rules. The rule base has been formalized in Drools [START_REF] De Maio | Mastering JBoss Drools 6 for Developers[END_REF].

As an example, referring to the CAT action mentioned above, the rules reported below state that, if the patient has experienced a severe brain damage and suffers from atrial fibrillation, s/he must initiate a proper therapy. Such a therapy starts with ASA (a class of anti-inflammatory drugs), and continues with daily AC (anti-coagulant drug) administration. Before the first AC, a CAT is required, to assess AC starting time, which could be delayed in case CAT detects a hemorrhagic transformation. After a few days of AC administration, another CAT is needed, to monitor therapeutic results. Therefore, depending on the context, CAT can implement the "Timing" or the "Monitoring" goal (see Figure 1). Forward chaining on the rules below (showed as a simplified pseudocode with respect to the system internal representation, for the sake of simplicity) allows to determine the correct ancestor for the CAT action.

rule "SevereDamage" when ( Damage(value > threshold) && AtrialFibrillation(value=true) ) then logicalInsertFact (DamFib); end rule "Fibrillation1" when existInLogical(DamFib) && isBefore("CAT", "AC") then setAncestorName("CAT", "Timing"); end rule "Fibrillation2" when existInLogical(DamFib) && isAfter("CAT", "AC") then setAncestorName("CAT", "Monitoring"); end

Trace abstraction

Once the correct ancestor of every action has been identified, trace abstraction can be completed.

In this last step, when a set of consecutive actions on the trace abstract as the same ancestor, they have to be merged into the same abstracted macro-action, labeled as the common ancestor at hand. This procedure requires a proper treatment of delays, and of actions in-between that descend from a different ancestor (interleaved actions henceforth).

Trace abstraction has been realized by means of the procedure described in Algorithm 1 below.

The function abstraction takes in input a log trace, the domain ontology onto, and the level in the ontology chosen for the abstraction (e.g., level = 1 corresponds to the choice of abstracting the actions up to the sons of the ontology root). It also takes in input three thresholds (delay th, n inter th and inter th). These threshold values have to be set by the domain expert in order to limit the total admissible delay time within a macro-action, the total number of interleaved actions, and the total duration of interleaved actions, respectively. In fact, it would be hard to justify that two ground actions share the same goal (and can thus be abstracted to the same macro-action), if they are separated by very long delays, or if they are interleaved by many/long different ground actions, meant to fulfill different goals (where the term "long" may correspond to different quantitative values in different application domains).

The function outputs an abstracted trace.

For every action i in trace, an iteration is executed (lines 3-27). First, a macro-action m i , initially containing just i, and sharing its starting and ending times, is created. m i is labeled referring to the ancestor of i (the one identified by the rule based reasoning procedure) at the abstraction level provided as an input. Accumulators for this macro-action (total -delay, num -inter and total -inter, commented below) are initialized to 0 (lines 4-10). Then, a nested cycle is executed (lines 11-25): it considers every element j following i in the trace, where a trace element can be an action, or a delay between a pair of consecutive actions. Different scenarios can occur:

if j is a delay, total -delay is updated by summing the length of j (lines [START_REF] Ferreira | Improving process models by mining mappings of low-level events to high-level activities[END_REF][START_REF] Grando | Semantic process mining for the verification of medical recommendations[END_REF][START_REF] Grigori | Business process intelligence[END_REF].

Algorithm if j is an action, and j shares the same ancestor of i at the input abstraction level, then j is incorporated into the macro-action m i . This operation is always performed, provided that total -delay, number -inter and totalinter do not exceed the threshold passed as an input (lines 15-19). j is then removed from the actions in trace that could start a new macro-action, since it has already been incorporated into an existing one (line 18). This kind of situation is described in Figure 2 (a). if j is an action, but does not share the same ancestor of i, then it is treated as an interleaved action. In this case, num -inter is increased by 1, and total -inter is updated by summing the length of j (lines 20-23). This situation, in the end, may generate different types of temporal constraints between macro-actions, as the ones described in Finally, the macro-action m i is appended to abs trace, that, in the end, will contain the list of all the macro-actions that have been created by the procedure (line 26). Complexity. The cost of abstracting a trace is O(actions * elements), where actions is the number of actions in the input trace, and elements is the number of elements (i.e., actions + delay intervals) in the input trace.

Semantic process mining

In our approach, process mining, made semantic by the exploitation of the abstraction mechanism illustrated above, is implemented resorting to the well-known process mining tool ProM, extensively described in [START_REF] Van Dongen | The proM framework: a new era in process mining tool support[END_REF]. ProM (and specifically its newest version ProM 6) is a platform-independent open source framework that supports a wide variety of process mining and data mining techniques, and can be extended by adding new functionalities in the form of plug-ins.

For the work described in this paper, we have exploited ProM's Heuristic Miner [START_REF] Weijters | Process Mining with the Heuristic Miner Algorithm[END_REF]. Heuristic Miner is a plug-in for process model discovery, able to mine process models from logs. It receives in input the log, and considers the order of the actions within every single trace. It can mine the presence of short-distance and long-distance dependencies (i.e., direct or indirect sequence of actions), with a certain degree of reliability. The output of the mining process is provided as a graph, known as the "dependency graph", where nodes represent actions, and edges represent control flow information. The output can be converted into other formalisms as well.

Currently, we have chosen to rely on Heuristics Miner, because it is known to be tolerant to noise, a problem that may affect medical logs (e.g., sometimes the logging may be incomplete). Anyway, testing of other mining algorithms available in ProM 6 is foreseen in our future work.

Experimental results

In this section, we describe the experimental results we have conducted, in the application domain of stroke care.

First, we will present a case study, meant to showcase in an immediate fashion the effects of abstraction of the quality of the mined process model.

Then, we will discuss a more complete validation work, able to properly quantify the abstraction effects themselves.

In both studies the available log was composed of more than 15000 traces, collected at the Stroke Unit Network (SUN) collaborating centers of the Lombardia region, Italy. The number of traces varied from 266 to 1149. Traces were composed of 13 actions on average.

Case study

In the case study, we wanted to test whether our capability to abstract the log traces on the basis of their semantic goals allowed to obtained process models where unnecessary details are hidden, but key behaviors are clear. Indeed, if this hypothesis holds, in our application domain it becomes easier to compare process models of different stroke units (SUs), highlighting the presence/absence of common paths, regardless of minor action changes (e.g., different ground actions that share the same goal) or irrelevant different action ordering or interleaving (e.g., sets of ground actions, all sharing a common goal, that could be executed in any order) 2 .

Figure 3 compares the process models of two different SUs (SU-A and SU-B), mined by resorting to Heuristic Miner, operating on ground traces. Figure 4, on the other hand, compares the process models of the same SUs as figure 3, again mined by resorting to Heuristic Miner, but operating on traces abstracted according to the goals of the ontology in figure 1. In particular, abstraction was conducted up to level 2 in the ontology (where level 0 is the root, i.e.. "Goal").

Generally speaking, a visual inspection of the two graphs in figure 3 is very difficult. Indeed, these two ground processes are "spaghetti-like" [START_REF] Van Der Aalst | Process Mining. Data Science in Action[END_REF], and the extremely large number of nodes and edges makes it hard to identify commonalities in the two models.

The abstract models in figure 4, on the other hand, are much more compact, and it is possible for a medical expert to analyze them.

In particular, the two graphs in figure 4 are not identical, but in both of them it is easy to a identify the macro-actions which corresponds to the treatment of a typical stroke patient.

However, the model for SU-A at the top of figure 4 exhibits a more complex control flow (with the presence of loops), and shows three additional macroactions with respect to the model of SU-B, namely "Extracranial Vessel Inspection", "Intracranial Vessel Inspection" and "Recanalization". This finding can be explained, since SU-A is a better equipped SU, where different kinds of patients, including some atypical/more critical ones, can be managed, thanks to the availability of different skills and instrumental resources. These patients may require the additional macro-actions reported in the model, and/or the repetition of some procedures, in order to better characterize and manage the individual patient's situation.

On the other hand, SU-B is a more generalist SU, where very specific human knowledge or technical resources are missing. As a consequence, the overall model control flow is simpler, and some activities are not executed at all. Interestingly, our abstraction mechanism, while hiding irrelevant details, allows to still appreciate these differences.

Validation

For the validation study, we asked a SUN stroke management expert to provide a ranking of some SUN stroke units (see Table 1, column 2), on the basis of the quality of service they provide, with respect to the top level SU (referred as H0 in the experiments). Such a ranking was based on her personal knowledge of the SUs human and instrumental resource availability (not on the process models); therefore, it was qualitative, and coarse-grained, in the sense that more than one SU could obtain the same qualitative evaluation. The expert identified 6 SUs (H1-H6) with a high similarity level with respect to H0; 5 SUs (H7-H11) with a medium similarity level with respect to H0; and 4 SUs (H12-H15) with a low similarity level with respect to H0. The ordering of the SUs within one specific similarity level is not very relevant, since, as observed, the expert's ranking is coarse-grained. It is instead important to distinguish between different similarity levels. We mined the process models of the 16 SUs by resorting to Heuristic Miner, both working on ground traces, and working on abstracted traces. We then ordered the two available process model sets with respect to H0, resorting to two different process model distances, i.e., the one described in [START_REF] Dijkman | Graph matching algorithms for business process model similarity search[END_REF], and the one presented in [START_REF] Montani | Improving structural medical process comparison by exploiting domain knowledge and mined information[END_REF], globally obtaining four rankings.

These two distance measures are quite dissimilar. In particular, the distance in [START_REF] Dijkman | Graph matching algorithms for business process model similarity search[END_REF] provides a normalized version of the graph edit distance [START_REF] Bunke | On a relation between graph edit distance and maximum common subgraph[END_REF] for comparing business process models, and defines syntactical edit operation costs for node substitution (relying on edit distance between action names), node insertion/deletion, and edge insertion/deletion. On the other hand, the distance in [START_REF] Montani | Improving structural medical process comparison by exploiting domain knowledge and mined information[END_REF] moves towards a more semantic and knowledge-intensive approach: when actions are represented in an ontology, as it is our case, it can adopt Palmer's distance [START_REF] Palmer | Verb Semantics for English-Chinese Translation[END_REF] for calculating action node substitution costs. Palmer's distance between two actions is set to the normalized number of arcs on the path between the two actions themselves in the ontology. So, given the semantics of our ontology, two different actions can be considered as more or less distant on the basis of their goal. Moreover, the distance in [START_REF] Montani | Improving structural medical process comparison by exploiting domain knowledge and mined information[END_REF] also considers edge substitution, which is disregarded in [START_REF] Dijkman | Graph matching algorithms for business process model similarity search[END_REF]. Indeed, Heuristic Miner labels edges with information that can be relevant in graph comparison, such as reliability [START_REF] Weijters | Process Mining with the Heuristic Miner Algorithm[END_REF], while statistical temporal information can be easily extracted from the log and saved as arc properties.

We exploited both these metrics because we wished to verify the effect of trace abstraction independently of the simplicity or completeness of the distance definition.

Results are shown in table 1.

Column 1 in table 1 shows the levels of similarity with respect to the reference SU. Column 2 shows the ranking according to the human medical expert; columns 3 and 4 show the ranking obtained by relying on the distance in [START_REF] Dijkman | Graph matching algorithms for business process model similarity search[END_REF], mining the process models on ground and abstracted traces, respectively. Similarly, columns 5 and 6 show the results obtained by relying on the distance in [START_REF] Montani | Improving structural medical process comparison by exploiting domain knowledge and mined information[END_REF], mining the process models on ground and abstracted traces, respectively. In particular, abstraction was conducted at level 1 in the ontology (where level 0 is the root).

When working on ground traces, the distance in [START_REF] Dijkman | Graph matching algorithms for business process model similarity search[END_REF] correctly rates two process models in the high similarity group (33%), one process model in the medium similarity group (20%), and one process model in the low similarity group (25%, column 3). When working on abstracted traces, on the other hand, the distance in [START_REF] Dijkman | Graph matching algorithms for business process model similarity search[END_REF] correctly rates three process models in the high similarity group (50%), one process models in the medium similarity group (20%), and one process model in the low similarity group (25%, column 4).

When working on ground traces, the distance in [START_REF] Montani | Improving structural medical process comparison by exploiting domain knowledge and mined information[END_REF] correctly rates two process models in the high similarity group (33%), zero process model in the medium similarity group (0%), and one process model in the low similarity group (25%, column 5). When working on abstracted traces, on the other hand, the distance in [START_REF] Montani | Improving structural medical process comparison by exploiting domain knowledge and mined information[END_REF] correctly rates four process models in the high similarity group (66%), two process models in the medium similarity group (40%), and two process model in the low similarity group (50%, column 6).

In summary, when working on abstracted traces, both distances lead to rankings that are closer to the qualitative ranking provided by the human expert, but the improvement is larger when adopting the distance in [START_REF] Montani | Improving structural medical process comparison by exploiting domain knowledge and mined information[END_REF], probably because it is able to take into account semantic information. We plan to verify this statement by means of further experiments in the future.

For the sake of completeness, we have also tested the effect of abstraction by evaluating the capability of the two distances in locating the high level SUs (i.e., the SUs with a high similarity with respect to H0) as the first six items of the overall ranking. To this end, we calculated the nDCG 6 [START_REF] Croft | Search Engines: Information Retrieval in Practice[END_REF] index on the rankings of Table 1. Also in this experiment, we were able to verify that the use of abstraction leads to results that are closer to the (ideal) ones provided by the human expert (see Table 2), with a larger improvement when adopting the distance in [START_REF] Montani | Improving structural medical process comparison by exploiting domain knowledge and mined information[END_REF].

Table 1. Ordering of 15 SUs, with respect to a given query model. Correct positions in the rankings with respect to the expert's qualitative similarity levels are highlighted in bold.

Similarity Medical expert [START_REF] Dijkman | Graph matching algorithms for business process model similarity search[END_REF] ground [START_REF] Dijkman | Graph matching algorithms for business process model similarity search[END_REF] abs [START_REF] Montani | Improving structural medical process comparison by exploiting domain knowledge and mined information[END_REF] ground [START_REF] Montani | Improving structural medical process comparison by exploiting domain knowledge and mined information[END_REF] [11] ground [START_REF] Dijkman | Graph matching algorithms for business process model similarity search[END_REF] abs [START_REF] Montani | Improving structural medical process comparison by exploiting domain knowledge and mined information[END_REF] ground [START_REF] Montani | Improving structural medical process comparison by exploiting domain knowledge and mined information[END_REF] abs 0.621 0.798 0.781 0.925

Table 3, on the other hand, reports our results on the calculation of fitness [29] on the process models mined for our 16 SUs, at different levels of abstraction. Fitness evaluates whether a process model is able to reproduce all execution sequences that are in the log. If the log can be replayed correctly, fitness evaluates to 1. In the worst case, it evaluates to 0. Fitness calculation is available in ProM. As it can be observed from the table, the more the traces are abstracted, the more the fitness values increase in the corresponding mined models.

In conclusion, our abstraction mechanism, while hiding irrelevant details, allows to still appreciate relevant differences between models, such as, e.g., the presence/absence of important actions, as commented in section 4.1. Moreover, when working on abstracted traces, the adoption of different distance definitions leads to SU rankings that are closer to the qualitative ranking provided by the human expert. Finally, very interestingly, abstraction proves to be a means to significantly increase the quality of the mined models, measured in terms of fitness, which is a well known and largely adopted indicator.

Related works

The use of semantics in business process management, with the aim of operating at different levels of abstractions in process discovery and/or analysis, is a relatively young area of research, where much is still unexplored.

One of the first contributions in this field was proposed in [START_REF] Casati | Semantic analysis of business process executions[END_REF], which introduces a process data warehouse, where taxonomies are exploited to add seman-tics to process execution data, in order to provide more intelligent reports. The work in [START_REF] Grigori | Business process intelligence[END_REF] extends the one in [START_REF] Casati | Semantic analysis of business process executions[END_REF], presenting a complete architecture that allows business analysts to perform multidimensional analysis and classify process instances, according to flat taxonomies (i.e., taxonomies without subsumption relations between concepts). Hepp et al. [START_REF] Hepp | Semantic business process management: A vision towards using semantic web services for business process management[END_REF] propose a framework able to merge semantic web, semantic web services, and business process management techniques to build semantic business process management, and use ontologies to provide machine-processable semantics in business processes [START_REF] Hepp | An ontology framework for semantic business process management[END_REF]. The work in [START_REF] Sell | Adding semantics to business intelligence[END_REF] develops in a similar context, and extends OLAP tools with semantics (exploiting ontologies rather than (flat) taxonomies).

The topic was studied in the SUPER project [START_REF] Pedrinaci | Semantic business process management: Scaling up the management of business processes[END_REF], within which several ontologies were created, such as the process mining ontology and the event ontology [START_REF] Pedrinaci | Towards an ontology for process monitoring and mining[END_REF]; these ontologies define core terminologies of business process management, usable by machines for task automation. However, the authors did not present any concrete implementations of semantic process mining or analysis.

Ontologies, references from elements in logs to concepts in ontologies, and ontology reasoners (able to derive, e.g., concept equivalence), are described as the three essential building blocks for semantic process mining in [START_REF] Alves De Medeiros | Semantic process mining tools: Core building blocks[END_REF]. This paper also shows how to use these building blocks to extend ProM's LTL Checker [START_REF] Van Der Aalst | Process mining and verification of properties: An approach based on temporal logic[END_REF] to perform semantic auditing of logs.

The work in [START_REF] Alves De Medeiros | An outlook on semantic business process mining and monitoring[END_REF] focuses on the use of semantics in business process monitoring, an activity that allows to detect or predict process deviations and special situations, to diagnose their causes, and possibly to resolve problems by applying corrective actions. Detection, diagnosis and resolution present interesting challenges that, on the authors' opinion, can strongly benefit from knowledge-based techniques.

In [START_REF] Alves De Medeiros | An outlook on semantic business process mining and monitoring[END_REF][START_REF] Alves De Medeiros | Process mining towards semantics[END_REF] the idea to explicitly relate (or annotate) elements in the log with the concepts they represent, linking these elements to concepts in ontologies, is addressed. This "semantic lifting" approach, to use a term borrowed from the Web scenario, is also investigated in [START_REF] Azzini | Using semantic lifting for improving process mining: a data loss prevention system case study[END_REF], to discover the process that is actually being executed.

In [START_REF] Alves De Medeiros | Process mining towards semantics[END_REF] an example of process discovery at different levels of abstractions is presented. It is however a very simple example, where a couple of ground actions are abstracted according to their common ancestor. However, the management of interleaved actions or delays is not addressed, and multiple inheritance is not considered. A more recent work [START_REF] Jareevongpiboon | Ontological approach to enhance results of business process mining and analysis[END_REF] introduces a methodology that combines domain and company-specific ontologies and databases to obtain multiple levels of abstraction for process mining. In this paper data in databases become instances of concepts at the bottom level of a taxonomy tree structure. If consecutive tasks in the discovered model abstract as the same concepts, those tasks are aggregated. However, also in this work we could find neither a clear description of the abstraction algorithm, nor the management of interleaved actions or delays.

Moreover, most of the papers cited above (including [START_REF] Alves De Medeiros | Semantic process mining tools: Core building blocks[END_REF][START_REF] Alves De Medeiros | Process mining towards semantics[END_REF]) present theoretical frameworks, and not yet a detailed technical architecture nor a concrete implementation of all their ideas.

Referring to medical applications, the work in [START_REF] Grando | Semantic process mining for the verification of medical recommendations[END_REF] proposes an approach, based on semantic process mining, to verify the compliance of a Computer Interpretable Guideline with medical recommendations. In this case, semantic process mining refers to conformance checking rather than to process discovery (as it is also the case in [START_REF] Alves De Medeiros | Semantic process mining tools: Core building blocks[END_REF]). These works are thus only loosely related to our contribution.

Besides the contributions listed above, most of which can be categorized as normative/deductive approaches, it is worth citing some interesting emergent approaches as well [START_REF] Syamsiyah | DB-XES: enabling process discovery in the large[END_REF][START_REF] Azzini | Consistent process mining over big data triple stores[END_REF]. The work in [START_REF] Syamsiyah | DB-XES: enabling process discovery in the large[END_REF] affords the problem of dealing with very big log files, proposing solutions for scalable process discovery and extending XES [START_REF] Verbeek | Xes, xesame, and prom 6[END_REF], a log file format introduced to solve problems with the semantics of additional attributes; the work in [START_REF] Azzini | Consistent process mining over big data triple stores[END_REF] moves even forward, presenting a methodology designed to implement consistent process mining algorithms in a Big Data context, managing semantic heterogeneity.

Another interesting research direction adopts abstraction as a way to establish a relationship between the events typically recorded in the log by the information system, and the high-level actions which are of interest when mining business process models. In particular the work in [START_REF] Ferreira | Improving process models by mining mappings of low-level events to high-level activities[END_REF] looks for mappings between events and actions. The set of possible mappings can be large, and one should focus on the mapping which has the highest coverage, meaning that the chosen mapping should be applicable to the largest possible number of traces in the log. The range of a mapping, i.e., the set of actions that appear in the mapping, is also a very important factor. In particular, the authors adopt a greedy approach, where they try to merge those mappings which, by themselves, already have the largest range and highest coverage among their peers. The work in [START_REF] Tax | Event abstraction for process mining using supervised learning techniques[END_REF], on the other hand, shows that supervised learning (namely Condition Random Fields) can be leveraged for the event abstraction task when annotations with high-level interpretations of the low-level events are available for a subset of the traces. Conditional Random Fields are trained on the annotated traces to create a probabilistic mapping from low-level events to high-level actions. This mapping, once obtained, can be applied to the unannotated traces as well. In [START_REF] Mannhardt | From low-level events to activities -A pattern-based approach[END_REF], the authors align the behavior defined by activity patterns with the observed behavior in the log. Activity patterns encode assumptions on how high-level actions manifest themselves in terms of recorded low-level events. The work in [START_REF] Günther | Activity mining by global trace segmentation[END_REF] exploits trace segmentation. Trace segmentation is based on the idea that subsequences of events, which are supposed to be the product of a higher-level action, are identified. From the co-occurrence of events in the log, the authors derive the relative correlation between their event classes. All event classes found in the log are successively combined into clusters, representing higher-level types. In this hierarchy of event classes, an arbitrary level of abstraction can be chosen to process the log.

Most of these constributions (see, e.g., [START_REF] Ferreira | Improving process models by mining mappings of low-level events to high-level activities[END_REF][START_REF] Günther | Activity mining by global trace segmentation[END_REF]), however, adopt non-semantic approaches. Moreover, as stated in the Introduction, in our work we assume that traces are sequences of actions (i.e., with respect to event traces, they have already been pre-processed). Therefore, this line of research is only loosely related to ours.

In conclusion, in the current research panorama, our work appears to be very innovative, for several reasons:

many approaches, illustrating very interesting and sometimes ambitious ideas, just provide pure theoretical frameworks, which can be very important to inspire more engineering-style work. However, concrete implementations of algorithms and complete architectures of systems are often missing, leaving open research opportunities for contributions like the one we have presented; in semantic process mining, more work has been done in the field of conformance checking (also in medical applications), while process discovery still deserves attention (also because many approaches are still at the theoretical level, as commented above); as regards trace abstraction, it is often proposed as a very powerful means to obtain better process discovery and analysis results, but technical details of the abstraction mechanism are usually not provided, or are illustrated through very simple examples, where the issues related to the management of interleaved actions or delays do not emerge.

Concluding remarks and future work

In this paper, we have presented a framework for knowledge-based abstraction of log traces. In our approach, abstracted traces are then provided as an input to semantic process mining. Semantic process mining relies on ProM algorithms; indeed, the overall integration of our approach within ProM is foreseen in our future work. Our case study in the field of stroke management suggests that the capability of abstracting the log traces on the basis of their semantic goal allows to mine clearer process models, where unnecessary details are hidden, but key behaviors are clear.

Moreover, in our validation study we mined the process models of some SUs by resorting to Heuristic Miner, both working on ground traces, and working on abstracted traces. We then ordered the two available process model sets with respect to the model of the best equipped SU in the SUN network, resorting to two different process model distances, i.e., the one described in [START_REF] Dijkman | Graph matching algorithms for business process model similarity search[END_REF], and the one presented in [START_REF] Montani | Improving structural medical process comparison by exploiting domain knowledge and mined information[END_REF], globally obtaining four rankings. We verified that, when working on abstracted traces, both distances lead to rankings that are closer to the qualitative ranking provided by a domain expert, but the improvement is much larger when adopting the distance in [START_REF] Montani | Improving structural medical process comparison by exploiting domain knowledge and mined information[END_REF], probably because it is able to take into account semantic information. Finally, abstraction proves to be a means to significantly increase the quality of the mined models, when measured in terms of fitness.

In the future, we would like to test the approach in different application domains as well, even if we know that the task will require time and may present some issues. Indeed, domain knowledge acquisition is typically time consuming: our work on formalizing the stroke ontology and the rules required multiple sessions of work with physicians. Moreover, the domain of stroke management can count on internationally recognized guidelines, which are well detailed: therefore, the acquired knowledge can be considered as comprehensive and accurate; this may not hold in different domains. The domain choice will therefore be critical, and possibly we will select a non medical application.

We also plan to apply the abstraction mechanism to subsets of the log, obtained by clustering techniques or possibly by domain expert rating, in order to test the effect of abstraction on a more homogeneous input.

The quality of the mined process models could also be evaluated by resorting to conformance checking techniques.

We will also consider how to cobine our approach with the pattern-based abstraction described in [START_REF] Mannhardt | From low-level events to activities -A pattern-based approach[END_REF].

Finally, an abstraction mechanism directly operating on process models (i.e., on the graph, instead of the log), may be considered, possibly along the lines described in [START_REF] Günther | Fuzzy mining -adaptive process simplification based on multi-perspective metrics[END_REF], and abstraction results will be compared to the ones currently enabled by our framework.

Fig. 1 .

 1 Fig. 1. An excerpt from the stroke domain ontology. The annotation shown for CAT (computer assisted tomography) reports its SNOMED code

Figure 2 (

 2 b) (Allen's during[START_REF] Allen | Towards a general theory of action and time[END_REF]) and Figure2(c) (Allen's overlaps[START_REF] Allen | Towards a general theory of action and time[END_REF]).

Fig. 2 .

 2 Fig.2. Different trace abstraction situations: (a) two actions are abstracted to a single macro-action macro1, with a delay in between; (b) two actions are abstracted to a macro-action macro1, with an interleaved action in between, resulting in a different macro-action macro2 during macro1; (c) two actions are abstracted to a macro-action macro1, with an interleaved action in between, which is later aggregated to a fourth action, resulting in a macro-action macro2 overlapping macro1.

Fig. 3 .Fig. 4 .

 34 Fig.3. Comparison between two process models, mined by resorting to Heuristic Miner, operating on ground traces. The figure is not intended to be readable, but only to give an idea of how complex the models can be

  1: Multi-level abstraction algorithm

abs trace = abstraction(trace, onto, level, delay th, n inter th, inter th); abs trace = ∅; for every i ∈ actions in trace do if (i.startF lag = yes) then create : mi as ancestor(i, level); mi.start = i.start; mi.end = i.end; total delay = 0; num inter = 0; total inter = 0; for (every j ∈ elements in trace) do if (j is a delay) then total delay = total delay + j.length; else if (ancestor(j, level)=ancestor(i, level)) then if (total delay < delay th ∧ num inter < n inter th ∧ total inter < inter th) then mi.end = max(mi.end, j.end); j.startFlag = no; end else num inter = num inter + 1; total inter = total inter + j.length; end end end append mi to abs trace; end return abs trace;

Table 2 .

 2 nDCG6 index calculation on the rankings provided by the two metrics.

	abs

Table 3 .

 3 Fitness values calculated on the mined process models, when operating at different levels of abstraction

	SU Ground Abs. level 2 Abs. level 1
	H0 0.58	0.83	0.87
	H1 0.43	0.73	0.97
	H2 0.47	0.72	0.87
	H3 0.40	0.85	0.95
	H4 0.42	0.91	0.93
	H5 0.42	0.83	0.87
	H6 0.52	0.76	0.95
	H7 0.52	0.79	0.92
	H8 0.75	0.78	0.92
	H9 0.46	0.85	0.92
	H10 0.41	0.83	0.87
	H11 0.44	0.61	0.90
	H12 0.49	0.67	0.89
	H13 0.46	0.84	0.91
	H14 0.43	0.85	0.90
	H15 0.54	0.78	0.90

http://www.snomed.org/snomed-ct, last accessed on 02/08/2018

It is however worth noting that, within our framework, it is still possible to mine the process models from ground traces, and investigate them in detail as a further analysis step, if needed.