Computational Fluid Dynamics Study of the Dispersion Caused by Capillary Misconnection in Nano-Flow Liquid Chromatography.

It is well known that high-speed/high-efficiency separations in nano-flow liquid chromatography (LC) are very sensitive to the quality of the connections between the column and the rest of the instrument. In the present study, two types of connection errors (capillary misalignment and the occurrence of an inter-capillary gap) have been investigated using computational fluid dynamics. Interestingly, it has been found that large degrees of capillary misalignment (assuming an otherwise perfect contact between the capillary end-faces) can be afforded without introducing any significant dispersion over the entire range of investigated relative misalignment errors (0 ≤ ε/dcap ≤ 75%), even at the largest flow rates considered in nano-LC. On the other hand, when an inter-capillary gap is present, the dispersion very rapidly increases with the radial width Dc of this gap (extra variance ∼Dcn with n even reaching values above 4). The dependency on the gap length Lc is however much smaller. Results show that, when Dc ≤ 30 µm and Lc ≤ 200 µm, dispersion losses can be limited to the order of 1 nL2 at a flow of 1.5 µL/min, which is generally very small compared to the dispersion in the capillaries (20 µm i.d.) themselves. This result also reconfirms that zero-dead volume connectors with a sufficiently narrow bore can in theory be used without compromising peak dispersion in nano-LC, at least when the capillaries can be matched perfectly to the connector in- and outlet faces. The results are also indicative of the extra dispersion occurring inside microfluidic chips or in the connections between a microfluidic chip and the outer world.

Review of recent insights in the measurement and modelling of the B-term dispersion and related mass transfer properties in liquid chromatography.

In this contribution, we review the recent literature relating to the measurement and modelling of all diffusion-dominated processes contributing to the efficiency of a chromatographic column. In first instance, this involves the measurement and modelling of the overall effective diffusion coefficient Deff (determining the so-called B-term band broadening). The latter manifests itself most clearly during a so-called peak parking experiment. Using effective medium theory modelling, the measured Deff-value can subsequently be decomposed into its constituent contributions, of which the intra-particle or the mesoporous zone and the surface diffusion coefficient are the most important ones. As an accurate estimation of the diffusion processes also allows computing the C-term plate height contribution terms, the review ends with some recent insights obtained when using the established B- and C-term contributions to compute the degree of eddy-dispersion in contemporary packed bed columns.

Detailed computational fluid dynamics study of the parameters contributing to the viscous heating band broadening in liquid chromatography at pressures up to 2500 bar in 2.1 mm columns.

Over the past years viscous heating band broadening occurring in high pressure liquid chromatography has been studied extensively. In the present numerical study, we investigate the fine details of this band broadening contribution under extreme high-pressure conditions (2500 bar). To analyze the results, we first show that viscous heating leads to two clearly distinguishable band broadening effects, one originating from the radial differences in the species migration velocity and the other from the axial variations. It was found that the radial contribution is independent of the intrinsic band broadening of the bed (i.e. band broadening in absence of viscous heating) while it strongly depends on the radial dispersion coefficient and the retention enthalpy of the analytes. On the other hand, the axial contribution is strongly dependent on the bed intrinsic band broadening and it is found to be 4 to 5 times lower than the radial contribution. We also show the strong effect of the endfittings on the temperature gradients inside the column thus on the resulting viscous heating band broadening.

Computational fluid dynamics study of potential solutions to alleviate viscous heating band broadening in 2.1 millimeter liquid chromatography columns.

We report on a numerical simulation study of a number of potential column technology solutions to minimize the plate height contribution (Hvh) originating from the use of ultra-high pressures and their concomitant viscous heating effect. Looking as far as possible into the future of UHPLC, all main results are obtained for the case of a 2500 bar pressure gradient. However, to generalize the result, a correlation is given that can be used to interpolate the results to lower pressures with some 10% accuracy. For the considered case of a 2.1mm column, a liquid flow rate of 0.45 ml/min, an analyte with retention factor k(25°C)=3 and a retention enthalpy chosen such that ΔHR/R= -1000 K, it is found that, in order to keep the global plate height as measured at the column outlet (Hvh,glob,out) below 1 µm, the bed conductivity would need to be raised to λbed=2.4 W/m•K, i.e., 4 times higher than a typical packed bed of fully-porous or core-shell silica particles. An equivalent effect on the band broadening could be obtained if it would be possible to replace the steel column wall with a low conductivity material. In this case, a wall conductivity of 0.25 W/m•K, i.e., 64 times smaller than the conductivity of steel, would be needed to keep Hvh,glob,out below 1 µm. Results are also interpreted based on contour plots of the axial and radial velocity variation of a retained analyte.

An explicit expression for the retention factor and velocity dependency of the mobile zone mass transfer band broadening in packed spheres beds used in liquid chromatography.

The present study proposes a ready-to-use analytical expression to calculate the mobile zone mass transfer contribution (hCm) in packed bed columns. For this purpose, first high-accuracy computations of the band broadening in a perfectly ordered sphere array (fcc-arrangement, external porosity ε=0.40) were made using computational fluid dynamics (CFD), covering a broad range of zone retention factors (2≤k''≤18) and reduced velocities (0≤νi≤48). Subsequently, these data were used to determine the value of the geometrical constants in a number of possible analytical expressions for the hCm-contribution. This fitting exercise showed the traditional literature approach, using the Wilson-Geankoplis correlation to calculate the dimensionless Sherwood (Sh) number for the mass transfer, leads to fitting errors on the hCm-term as large as 150%. Instead, a new correlation for Sh is established. In addition, we also explored the difference in fitting accuracy between hCm-expressions based on either a plug-flow or a laminar flow profile assumption. Surprisingly, no significant difference in fitting accuracy between both assumptions was observed. Finally, a best-fit analytical expression is proposed that can represent the CFD-computed band broadening data with an average absolute fitting error of Δh=0.005, corresponding to a relative error of 2.5% on the hCm-term and of only 0.3% on the total plate height in a perfectly ordered sphere packing. Defining the presently investigated fcc-ordered sphere array with external porosity=40% as the reference geometry for a perfect sphere packing, the established expression can be used as a new yardstick expression against which the degree of eddy-dispersion can be measured.

The stability of blood eosinophils in stable chronic obstructive pulmonary disease: a retrospective study in Belgian primary care.

BACKGROUND: Blood eosinophil counts (BEC) were recently included in the 2019 Global Initiative for Obstructive Lung Disease (GOLD) guideline as an easily accessible theragnostic biomarker for Chronic Obstructive Pulmonary Disease (COPD). However, the stability of BEC remains insufficiently studied. METHODS: We conducted a retrospective study in six primary care practices in Belgium on data from Electronic Health Records of stable COPD patients, to characterise the stability of blood eosinophils over time. We report the percentage of patients with BEC persistently below or above the 2019 GOLD guideline thresholds (100 and 300 cells/µL). For each patient the mean, standard deviation (SD) and relative standard deviation (RSD) of the BEC were calculated to determine the intra-patient variability. RESULTS: Ninety-eight patients were included, yielding 1082 eosinophil measurements (median 8 measurements/patient), with BEC ranging between 0 and 1504 cells/µL. Four (4.1%) patients had BEC persistently below 100 cells/µL, 34 (34.7%) had measurements persistently above this threshold. Approximately half of the patients (51.0%) had BEC persistently below 300 cells/µL and 3 (3.1%) patients had counts persistently above this threshold. 28.6% of patients crossed both threshold values throughout the registration period. The mean BEC per patient ranged between 15 and 846 cells/µL with an intra-patient SD between 5 and 658 cells/µL. The mean intra-patient RSD was 0.46. There was a significant strong positive correlation (Pearson analyses) between the mean BEC and SD (r = 0.765; n = 98). Simple linear regression was used to further describe the influence of the mean eosinophil count on the SD (B = 0.500; 95%CI 0.415-0.586; n = 98; p < 0.001). CONCLUSION: BEC can be variable in individual COPD patients. Therefore, the use of a single measurement to guide therapeutic decisions remains debatable. Further prospective research remains necessary to validate the reproducibility of this biomarker.

The checkerboard model for the Eddy-dispersion in Laminar flows through porous media. Part II: Application to ordered and disordered 2-D flow systems.

We report on a series of high-accuracy computational fluid dynamics band broadening simulations in three different 2-D flow systems: a 2-D pillar array and 2-D lumped packed bed geometries with different checkerboard velocity bias patterns. These media display a local maximum in the relationship between the eddy-dispersion plate height and the mobile phase velocity. The occurrence of such a dispersion maximum has not been reported before but appears to be a characteristic of regular chromatographic media with alternating velocity bias, at least in 2-D geometries. This newly observed behavior can be fully understood and modelled using the checkerboard model established in part I of the present study.

The checkerboard model for the eddy-dispersion in laminar flows through porous media. Part I: Theory and velocity field properties.

The additivity assumption underlying Giddings' coupling model for the eddy-dispersion in laminar flows through heterogeneous media is critically analyzed and a potential solution for its non-additivity in the high velocity limit is presented. Whereas the unit cell in Giddings' model only consists of a single velocity bias step, the unit dispersion cell of the newly proposed model comprises two consecutive velocity bias steps. Consequently, the unit cell of this new model allows to account for the occurrence of an internal velocity bias rectification at high reduced velocities and is therefore additive in both the low and high velocity limit. First, a mathematical expression for the velocity- and diffusion-dependency of the model's dispersion characteristics has been established. Subsequently, the physical behavior of the model is discussed. It is shown the relation between the eddy-dispersion plate height h and the reduced velocity ν can be expected to display a local maximum in systems where the transversal dispersion purely occurs by molecular diffusion, as is the case in perfectly ordered flow-through media. In disordered media, where the transversal dispersion also contains a significant advective component, the model predicts a velocity-dependency that is qualitatively similar to that described by Giddings' coupling model but, all other conditions being equal, converges to a significantly smaller horizontal asymptote at high reduced velocity. The latter might shed new light on earlier eddy-dispersion studies pursuing a quantitative agreement between experimental data and the Giddings model.

A multiscale modelling study on the sense and nonsense of thermal conductivity enhancement of liquid chromatography packings and other potential solutions for viscous heating effects.

We report on a numerical study of the thermal conductivity and temperature distribution in analytical packed bed and monolithic HPLC columns to assess the feasibility of a number of potential solutions to the viscous heating problem that would normally impede high efficiency separations when moving to extreme operating pressures (e.g., 2500 bar). Computational fluid dynamic (CFD) simulations were employed to study heat transfer on three hierarchical levels of the column: meso­pore level, through-pore level and column level. At the first level, realistic values were determined for the conductivity of the porous zone (kpz), depending on the internal structure of the porous zone and the mobile phase used (acetonitrile, water or a mixture of both). These kpz-values were in turn used at the second level to determine realistic values for the effective conductivity of the bed (keff). It was shown that the presence of a solid core only has a minor effect on the packed bed conductivity. Using highly conducting materials as core material can be expected to maximally lead to a 60% increase in bed conductivity. Contrarily, in monolithic beds, the presence of a core material would form one continuous phase of highly conducting material, thus greatly enhancing the conductivity of the bed. At the third level, the temperature field in the entire column (bed and column housing) was resolved for three typical boundary conditions: isothermal, adiabatic and still-air oven. The effect of different physical properties (inlet pressure, mobile phase composition, bed conductivity, wall conductivity and column ID) on these temperature fields was investigated. It was shown that, theoretically, besides 1 mm ID columns also "core-shell monoliths" can provide a solution to viscous heating (by increasing the bed conductivity). Other possible solutions are proposed and discussed.

Optimizing design and employing permeability differences to achieve flow confinement in devices for spatial multidimensional liquid chromatography.

In spatial multi-dimensional liquid chromatography (LC) devices the flow of each dimension has to remain in the corresponding region, otherwise the separation efficiency is undermined. Adequate flow-confinement measures are necessary. Here, the use of permeability differences across different compartments of spatial two-dimensional (2D) and three-dimensional (3D) LC devices as a method to guide fluid flow and reduce analyte loss during the first, second- and third-dimension development was investigated with computational fluid dynamics (CFD) simulations. In case of 2DLC devices, it was shown that porous barriers with a permeability on the order of 10-12 m2 suffice to keep the total sample spillage from an open 1D channel under 1%. In case of 3DLC devices, it was shown that flow confinement could be achieved using an open 1D channel in combination with a highly-permeable monolith (permeability on the order of 10-12 m2) in the second-dimension (2D) and a less permeable packing with a permeability on the order of 10-15 m2 (e.g. 1 µm particles) in the third-dimension (3D). Additionally, the impact of the 3D flow-distributor has been studied and a novel design, capable of limiting the spillage to the other dimensions to the absolute minimum, is proposed.

Experimental and numerical study of band-broadening effects associated with analyte transfer in microfluidic devices for spatial two-dimensional liquid chromatography created by additive manufacturing.

Conventional one-dimensional column-based liquid chromatographic (LC) systems do not offer sufficient separation power for the analysis of complex mixtures. Column-based comprehensive two-dimensional liquid chromatography offers a higher separation power, yet suffers from instrumental complexity and long analysis times. Spatial two-dimensional liquid chromatography can be considered as an alternative to column-based approaches. The peak capacity of the system is ideally the product of the peak capacities of the two dimensions, yet the analysis time remains relatively short due to parallel second-dimension separations. Aspects affecting the separation efficiency of this type of systems include flow distribution to homogeneously distribute the mobile phase for the second-dimension (2D) separation, flow confinement during the first-dimension (1D) separation, and band-broadening effects during analyte transfer from the 1D separation channel to the 2D separation area. In this study, the synergy between computational fluid dynamics (CFD) simulations and rapid prototyping was exploited to address band broadening during the 2D development and analyte transfer from 1D to 2D. Microfluidic devices for spatial two-dimensional liquid chromatography were designed, simulated, 3D-printed and tested. The effects of presence and thickness of spacers in the 2D separation area were addressed and leaving these out proved to be the most efficient solution regarding band broadening reduction. The presence of a stationary-phase material in the 1D channel had a great effect on the analyte transfer from the 1D to the 2D and the resulting band broadening. Finally, pressure limit of the fabricated devices and printability are discussed.

A Training Game for Students Considering Family Medicine: an Educational Project Report.

The Groningen Institute Model for Management in Care Services aims to prepare medical students for their complex tasks as family physicians, based on the CanMEDS framework. Although initially developed for pharmacy students, the present paper reports on the eight-year experience with GIMMICS for family physician students at the Vrije Universiteit Brussel. The Groningen Institute Model for Management in Care Services is a training game that simulates real-life situations in a structured and supervised setting. It offers students the possibility to practice clinical, practical, and communicational skills. Students install and manage their group practices, hold consultations with simulated patients, participate in several assignments and collaborate with pharmacy students. Feedback sessions showed that the training game is well-received by the students. A self-assessment questionnaire comprised of 23 questions on significant aspects of the seven CanMEDS roles showed significantly higher scores at the end of the game for 17 questions (p<0.05, Wilcoxon signed-rank test ). GIMMICS is a valuable linking pin between the different learning methods in medical education and clinical practice, helping students to improve themselves in the CanMEDS roles. However, simulation-based medical education requires significant time and resource investment.

Numerical and analytical investigation of the possibilities to enhance the thermal conductivity of core-shell particle packed beds.

We report on a numerical study of the thermal conductivity of core-shell particle packed bed columns. Covering a variety of packing structures and a broad range of mobile phase and porous zone conductivities, it was in all cases found that switching to particles with a highly conducting core (e.g., with a gold or copper core instead of a silica core) would produce a much smaller increase of the effective heat conductivity of the bed (keff) than previously expected in literature. We found maximal increases on the order of some 20-70%, which is much lower than the potential increases up to 2000% assumed in literature. The overestimation in literature could be attributed to the fact that this literature was based on an incorrect extrapolation of the Zarichnyak-model which was the heat conductivity model predominantly used up till now. On the other hand, the computed relationships between keff and the core conductivity obtained in the present study are in good agreement with an analytical solution derived from the effective medium theory, a theory which is physically much more relevant for the case at hand than the Zarichnyak-model. The results also show that the observed increase in effective bed conductivity between fully porous and core-shell particle beds frequently observed in literature is not only due to the presence of the core, but that differences in the shell layer conductivity can play an equally important role. In addition, it could also be demonstrated that, if ways could be found to increase the conductivity of the shell layer, this would produce a much stronger increase of the overall bed conductivity than will ever be possible by increasing the conductivity of the cores.

Two-dimensional insertable separation tool (TWIST) for flow confinement in spatial separations.

Spatial comprehensive two-dimensional liquid chromatography (xLC×xLC) may be an efficient approach to achieve high peak capacities in relatively short analysis times, thanks to parallel second-dimension separations [1,2]. A key issue to reach the potential of xLC×xLC is to achieve adequate flow control and confinement of the analytes to the desired regions, i.e. confinement in the first-dimension direction and subsequently homogeneous flow in the second dimension. To achieve these goals we propose the TWIST concept (TWo-dimensional Insertable Separation Tool), a modular device that includes an internal first-dimension (1D) part that is cylindrical and rotatable. This internal part features a series of through-holes, each of which is perpendicular to the direction of the 1D flow. The internal part is inserted in the cylindrical casing of the external part. The internal diameter of the casing is marginally larger than the external diameter of the internal part. The external part also comprises a flow distributor and second-dimension (2D) channels. During the 1D injection and development, the channel is placed in a position where the through-holes are facing the wall of the external part, such that the liquid remains confined within the 1D channel. Thereafter, to realize the transfer to the second dimension (2D injection), the 1D channel is rotated, so that the holes of the internal part are aligned with the holes on the external part, allowing a transversal flow of the 2D mobile phase from the distributor through the 1D channel and eventually into the 2D area.

Numerical investigation of band spreading generated by flow-through needle and fixed loop sample injectors.

The present study reports on a computational fluid dynamics study of the band broadening occurring in injector systems frequently used in contemporary liquid chromatography instruments. The aim of this work is to determine band broadening originating purely from the injection volume in absence of any other possible contribution (e.g. band broadening due to the injection valve) and to unravel the mechanism behind it. Simulations of the dispersion process in flow through needle injectors were performed. In addition, fixed loop injectors were also simulated and comparison with flow through needle injectors was made. The results are also represented in a dimensionless form, allowing to generalize them to different experimental conditions. It was shown that two different injection regimes exist (the convection regime and the diffusion regime), both leading to narrow injection bands, while operating the injection needle in between the two regimes leads to broad injections bands. It was also found that the band broadening in the flow-through needle injector is strongly affected by the holding time between sample uptake and the actual injection. As a result, fixed, full loop injectors produced narrower injection bands compared to flow-through needle injectors operated with a realistic holding time.

A microfluidic distributor combining minimal volume, minimal dispersion and minimal sensitivity to clogging.

A new type of microfluidic flow distributor (referred to as the mixed mode or MM-distributor) is proposed. Its performance characteristics are determined using computational fluid dynamics (CFD), both in the absence and the presence of clogging, which is an important problem in microfluidic systems. A comparison is made with two existing, well-performing distributor types: the bifurcating (BF) distributor and an optimized diverging distributor, the so-called radially interconnected (RI) distributor. It was found that, in the absence of clogging, the MM-distributor produces only a little more dispersion than the bifurcating (BF) distributor, but much less than the radially interconnected (RI) distributor. The dispersion in an MM-distributor also follows a similar dependency on its width (power ≅ 2) as the BF-distributor. The dispersion in the RI-distributor on the other hand displays a very disadvantageous 4th-order dependency on its width, prohibiting its use to distribute the flow across wide beds (order of millimeters or centimeters). These observations hold independently of the flow rate. With increasing degree of clogging, the MM-distributor rapidly becomes advantageous over the BF-distributor, owing to the fluid contact zones that are provided after each bifurcation step. This means that overall, and when the occurrence of clogging cannot be excluded, the MM-type distributor seems to offer the best possible compromise between the ability to cope with local clogging events and the dispersion in the absence of clogging.

A theoretical study on the advantage of core-shell particles with radially-oriented mesopores.

We report on a first-principles numerical study explaining the potential advantage of core-shell particles with strictly radially-oriented mesopores. Comparing the efficiency of these particles with fully porous and core-shell particles with a conventional (i.e., randomly oriented) mesopore network, the present numerical study shows a similar strong reduction in minimal reduced plate height (hmin) as was very recently observed in an experimental study by Wei et al. (respectively a hmin-reduction on the order of about 1 and 0.5 reduced plate height-units). As such, the present work provides a theoretical basis to understand and confirm their experimental findings and quantifies the general advantage of "radial-diffusion-only" particles. Determining the effective longitudinal diffusion (B-term contribution) in a series of dedicated, independent simulations, it was found that this contribution can be described by a very simple, yet fully exact mathematical expression for the case of "radial- diffusion-only" particles. Using this expression, the significant increase in efficiency of these particles can be fully attributed to their much smaller B-term band broadening, while their C-term band broadening (representing the mass transfer resistance) remains unaffected.

Impact of thyroid autoimmunity on cumulative delivery rates in in vitro fertilization/intracytoplasmic sperm injection patients.

OBJECTIVE: To predict the impact of thyroid autoimmunity (TAI) on the probability of delivery after a defined number of treatment cycles, using analysis of cumulative delivery rates in patients with and without TAI. DESIGN: Retrospective cohort study performed at the Center for Reproductive Medicine and Department of Endocrinology, University Hospital of Brussels, approved by the institutional review board of the hospital. SETTING: University hospital. PATIENT(S): All patients who started their first IVF/intracytoplasmic sperm injection cycle at our fertility center between January 1, 2010 and December 31, 2011 were included. MAIN OUTCOME MEASURE(S): Live birth delivery after 25 weeks' gestation was taken as the primary endpoint of our study Cumulative delivery rates were calculated for both groups until six treatment cycles. INTERVENTION(S): All patients (in both groups) received the usual IVF treatment protocols (i.e., antagonist or agonist protocol). RESULT(S): In total 2,406 women who consulted our center were included. We included 333 patients with TAI and 2019 patients without TAI. In the TAI group the crude cumulative delivery rate after six cycles was 47%, whereas the expected cumulative delivery rate was 65%. In our control the crude cumulative delivery rate after six cycles was 47%, whereas the expected cumulative delivery rate was 76%. CONCLUSION(S): Our study did not confirm an influence of TAI status in patients undergoing fertility treatment on cumulative delivery rates after six IVF/intracytoplasmic sperm injection cycles.

Design and evaluation of microfluidic devices for two-dimensional spatial separations.

Various designs of chips for comprehensive two-dimensional spatial liquid chromatography were investigated. The performance of these chips was initially evaluated using computational fluid dynamics (CFD). A bifurcating distributor with an angle of 140° between branches was implemented in order to achieve a homogeneous velocity field. The cross-sectional area of the channels of the flow distributor was fixed at 0.5 × 0.5 mm, which allows a robust micromilling technique to be used for chip manufacturing. Experiments were performed with chips featuring purposely introduced imperfections in the structure of the bifurcating flow distributor to study its capacity of overcoming potential local clogging. Split peaks were observed when 75% of one of the flow channels was obstructed, in line with the CFD predictions. The main bottlenecks for the performance of the spatial two-dimensional chips were identified, viz. sample injected in the first dimension diverging into the flow distributor and channel discretization (i.e., remixing of first-dimension separation peaks because of finite number of second-dimension channels). Solutions to the former problem were studied by applying a flow resistance in the vertical segments that formed the outlets of the flow distributor and by simulating the presence of constrictions. It was found that a flow resistance of 1.0×10(11) m(-2) reduced the amount of sample diverging into the flow distributor by a factor of 10. The presence of a constriction of 90% of the segment area and 50% of the segment length decreased the diverging flow by a factor of 5. The influence of the linear velocity was significant. Solutions to the channel discretization problem were sought by investigating different designs of spatial two-dimensional chips.