Biomed Microdevices DOI 10.1007/s10544-013-9833-1
Impact of static pressure on transmembrane fluid exchange in high molecular weight cut off microdialysis Jiangtao Chu & Klas Hjort & Anders Larsson & Andreas P. Dahlin
# Springer Science+Business Media New York 2013
Abstract With the interest of studying larger biomolecules by microdialysis (MD), this sampling technique has reached into the ultrafiltration region of fluid exchange, where fluid recovery (FR) has a strong dependence on pressure. Hence in this study, we focus on the fluid exchange across the high molecular weight cut off MD membrane under the influence of the static pressure in the sampling environment. A theoretical model is presented for MD with such membranes, where FR has a linear dependence upon the static pressure of the sample. Transmembrane (TM) osmotic pressure difference and MD perfusion rate decide how fast FR increases with increased static pressure. A test chamber for in vitro MD under static pressure was constructed and validated. It can hold four MD probes under controlled pressurized conditions. Comparison showed good agreement between experiment and theory. Moreover, test results showed that the fluid recovery of the test chamber MD can be set accurately via the chamber pressure, which is controlled by sample injection into the chamber at precise rate. This in vitro system is designed for modelling in vivo MD in cerebrospinal fluid and studies with biological samples in this system may be good models for in vivo MD. Keywords Microdialysis . Fluid recovery . Transmembrane pressure . Colloid osmotic pressure
Electronic supplementary material The online version of this article (doi:10.1007/s10544-013-9833-1) contains supplementary material, which is available to authorized users. J. Chu : K. Hjort : A. P. Dahlin (*) Department of Engineering Sciences, Uppsala University, Box 534, 751 21 Uppsala, Sweden e-mail:
[email protected] A. Larsson Department of Medical Sciences, Clinical Chemistry, Uppsala University, Uppsala University Hospital, 751 85 Uppsala, Sweden
Index of parameter J The fluid permeate velocity through the MD membrane, length/time Qdialysate The flow rate of the dialysate, length3/time Qperfusate The perfusion rate of MD, length3/time Qr The flow rate of the transmembrane fluid permeate through the entire membrane, length3/time Pext The external pressure, pressure exerted by the sample fluid towards the inside of MD membrane, arbitrary pressure unit Pin The internal pressure, pressure exerted by the perfusate inside the MD membrane towards its outside, arbitrary pressure unit Pstatic The static pressure in the external of the probe, arbitrary pressure unit Pchamber The chamber pressure arbitrary pressure unit Pfluid The dynamic pressure given by the movement of the fluid in the chamber onto the MD probe, arbitrary pressure unit Posmotic The osmotic pressure of the MD sample in the chamber, arbitrary pressure unit Pstatic-in The static pressure inside the probe, arbitrary pressure unit Pperfusion The perfusion pressure exerted by the flow of the perfusate inside the probe, arbitrary pressure unit Pmembrane The pressure drop of the perfusate along the length of the membrane inside the Probe, arbitrary pressure unit Poutlet The pressure drop of the dialysate over the length of the probe outlet tubing, arbitrary pressure unit Posmotic-in The osmotic pressure of the perfusate, arbitrary pressure unit
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ΔP ΔPosmotic ρ g h1 h2
d l μ
L Rm ri ro FR
The transmembrane pressure, arbitrary pressure unit The osmotic pressure difference between the MD perfusate and the sample fluid, arbitrary pressure unit Density of the fluid, mass/length3 Gravitational acceleration constant The depth of the microdilaysis probe in the chamber fluid, length The height difference between the MD perfusate injection syringe and the probe, length The inner diameter of the outlet tubing of MD probe, length The length of the outlet tubing, length The dynamic viscosity of the transmembrane permeate, arbitrary pressure unit·time (Pa·s or cP) The length of the membrane, length The MD membrane resistance to the transmembrane permeate, length-2 The inner radius of the cylindrical membrane, length The external radius of the cylindrical membrane, length The fluid recovery of the MD sampling, (%)
1 Introduction Microdialysis (MD) is a well-established technique for in vivo studies of the chemistry of the central nervous system (CNS) (Ungerstedt et al. 1982), and for studies of the neurochemical behaviour (Ungerstedt 1991; Hillered et al. 2005). MD is a sampling technique, where a tubular shaped, semipermeable hollow fibre membrane is placed in the sampling area of interest. A perfusate which flows continuously through the inside of the tubular membrane carries away the collected analytes for further analysis (Plock and Kloft 2005). MD is mostly used for sampling small and hydrophilic molecules (Ungerstedt 1991; Hillered et al. 2005), such as glucose and lactate. Recently, interest has been raised in sampling molecules with larger masses (Ao and Stenken 2006; Clough et al. 2007), such as neuropeptides (Schutte et al. 2004; Pettersson et al. 2004), cytokines (Ao and Stenken 2006; Revuelto-Rey et al. 2012), and proteins (Kjellstrom et al. 1999; Clough 2005; Dahlin et al. 2012). With the increased popularity in using >100 kDa membranes for MD sampling and the fact that MD is routinely used as a clinical sampling tool used neurochemical brain monitoring in neuro intensive care patients (Plock and Kloft 2005; Ao and Stenken 2006; Hillered et al.
2006; Clough et al. 2007; Lee et al. 2008) where in vivo intra cranial pressures could differ between 2 and 7 mmHg (torr) (Lundberg 1960) in healthy humans to more than 50 mmHg in treated patients. Membranes with such large pore sizes are designed to transmit fluid and as a consequence, the sample volume collected is different from the sample volume pumped into the MD system. In this case, the FR, which is defined as the volume of the dialysate that is collected divided by the volume of the perfusate that is delivered into the MD catheter, is not 100 %. A change of FR will alter the concentration of the analytes (Bungay et al. 2010). Also, a, FR that differs from 100 % is unfavourable since the idea of MD is to provide time resolved snapshots of the place where the membrane is placed with minimal effect on the microenvironment. For example, if there is a perfusion fluid leakage from the membrane, there will be a dilution effect in the microenvironment and the collected dialysate resulting in a MD sample that is a less representative image of the dynamic processes that are happening in vivo. Hence, there are good reasons to introduce a theoretical understanding on how pressure affects FR. Typically, transmembrane TM pressure is adjusted by changing the inside pressure components. Perfusion pressure could easily be varied by changing perfusion flow rates or by adjusting the altitude in where the dialysate is collected in respect to the membrane position (Li et al. 2008). TM osmotic pressure could be adjusted by adding colloids (Marklund et al. 2009), for instance dextran, in different concentrations in the perfusion fluid, to affect the MD FR (Dahlin et al. 2010). In pre-clinical and in vitro studies, one way to control the TM flow balance is by using different perfusion pumping methods such as push, pull or push-pull (Li et al. 2008; Slaney et al. 2011) and receive FR of 100 %. However, until now such pumping systems have been considered not suitable for clinical use. This makes it important to understand the influence of different pressure conditions by comparing theory with studies in well-controlled in vitro experiments. Ideally, the perfusate that enters into the MD catheter should also exit; e.g. no fluid exchange between the inside of the membrane and the outside- the sampling environment, should occur. This will lead to diffusion-based transportation of the molecules across the MD membrane since the convection flows are in equilibration. However, when using large pore sized membranes the fluid exchange between the perfusate and the sampling environment occur more prominently in the form of convection flow through the membrane, due to the low hindrance presented by the large sized pores. Those membranes are therefore much more sensitive to changes in TM pressure within the MD-sampling system, leading to higher uncertainties in dialysate volumes and analyte concentrations. TM pressure represents the pressure across the MD membrane and is dependent on both the inside and outside pressure components. The three main components of the TM
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pressure are: inside perfusion pressure of the perfusate, TM osmotic pressure difference, and the outside static pressure originating from the MD sampling environment. Previous studies (Rosdahl et al. 2000; Li et al. 2008; Marklund et al. 2009; Bungay et al. 2010) show that the TM pressure is the key influencing parameter on FR. There are very few studies on how the TM pressure and FR are affected by changed outside static pressures. Siaghy et al. (1999) presented an in vitro MD system where the outside static pressure was varied by increasing or decreasing the sampling volume where the MD membrane was placed. However, in Siaghy’s study, a simple definition of two pressure components during the MD process was considered: external and internal pressure. It is not clear what the origin of these two pressures is; and there is no identification of any pressure component with a specific type or nature, which should be responsible for the TM pressure. As the result of this study, even though a membrane with 20 kDa MWCO probe was used the results showed an increasing tendency for FR along with increased static outside pressure. Stenken et al. (1993) developed an in vitro MD hydrodynamic system, in which the flow of both the perfusate and the sample through a cross-flow MD probe can be well characterized. Their study results showed that the in vitro calibration of MD probe is an appropriate method for use in hydrodynamic in vivo environments. Well defined in vitro experiments are the starting point for development of new methods that eventually will be used in vivo. However the extrapolation of in vitro data back to biological functions is very challenging and requires the in vitro system to be as similar to the in vivo system as possible. A complete mimic of in vivo by in vitro systems is of course impossible to achieve but certain parameters could be set in vitro, such as temperature, ion strength, and pH, in order to make the model extrapolation more closely resemble than of the in vivo. A parameter most often overlooked in in vitro systems is the static outside pressure exerted by the sample. The main reasons for not considering static sample pressures in in vitro MD is that low MWCO membranes used for small molecules are not sensitive to pressure in the same way as membranes at or above 100 kDa. Also, the outside static pressure mostly remains on a constant level throughout the experiment and finally, a pressurized in vitro experiment is more complex to carry out since it requires additional instrumentation and equipment. In this study, a systematic analysis is made on the TM pressure, yielding a quantification model for TM fluid exchange, and hence fluid recovery control. We present an in vitro MD system that can hold four MD probes under controlled pressurized sampling conditions. The function of the chamber is validated, and it is used for investigating how the FR is affected by the pressure components in the MD sampling system.
2 Theory Figure 2 gives a schematic presentation of the pressure system in the chamber. Since the influence of pressure on fluid recovery, and hence TM fluid exchange, is the major point of this study, all pressure components which affect the fluid exchange across the membrane directly or indirectly should be considered. They can be divided into external pressure, Pext, outside the membrane and towards its inside; and internal pressure, Pin, pressure inside the probe and towards the outside of the membrane. The TM pressure ΔP is given by ΔP=Pext− Pin. Hence, with a positive ΔP there will be a TM net flow, Qr, into the MD catheter. If we keep the relative positions constant in the system and assume the atmospheric pressure constant, we can simplify the model and get the dependence of ΔP on the different system parameters as: ΔP ¼ Pchamber −Poutlet þ ΔPosmotic
ð1Þ
where Pchamber is the pressure in the chamber monitored by a pressure sensor, Poutlet is the pressure drop of the dialysate along the outlet tubing and ΔPosmotic=Posmotic-in−Posmotic. We can measure the fluid recovery, FR=Qdialysate/Qperfusate, which has a direct coupling to the TM netflow since Qr= Qdialysate−Qperfusate. By using Poiseuille’s law to model the Poutlet and Darcy’s law to model ΔP, we can express the FR as below. For more details, please see the ESI. FR ¼ a þ
b b ΔPosmotic þ Pchamber ð2aÞ Qperfusate Qperfusate
where the constants are given by a¼
1 256lL 1þ ro Rm d 4 ln ri
and b ¼
1 μRm ro 128μl ln þ 2πL ri πd 4
ð2bÞ
with l being the length of the outlet tubing, L the length of the membrane, Rm the MD membrane resistance to the TM permeate, d the inner diameter of the outlet tubing of MD probe, r0 the external radius of the cylindrical membrane, ri the inner radius of the cylindrical membrane, and μ the dynamic viscosity of the TM permeate. For detailed definition and unit information of TM pressure system components and experimental parameters, see the index of parameter attached in the appendix. For detailed evolution from the MD TM pressure system to Eq. (2a), see the theory section in the Supplementary Information. From Eq. (2a), it is clear that by setting the osmotic condition, and hence ΔPosmotic, and the flow rate, Qperfusate, the fluid recovery, FR, can be studied as a function of the chamber pressure, Pchamber. This is the basis for the FR studies of the experimental, results and discussions.
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3 Experimental 3.1 Chemicals Perfusion fluid, referred to as Ringer’s solution, composed of aqueous solution of 147 mM NaCl, 2.7 mM KCL, 1.2 mM CaCl2 and 0.85 mM MgCl2, was prepared in house and all chemicals were obtained from Merck (Darmstadt, Germany). Dextran T500, molecular weight 500 kDa, (batch no. HE518) was purchased from Pharmacosmos (Holbaek, Denmark) and used to prepare dextran Ringer’s solution in different concentrations to be used as perfusion fluid or sample fluid. The dextran solutions were prepared in weight to volume concentrations. Deionized water was produced in-house. 3.2 Blood plasma sample Venous blood samples were collected in Vacutainer tubes containing lithium-heparin (LH PST™ II, BD Vacutainer Systems, Plymouth, UK) or EDTA (K2-EDTA, BD Vacutainer Systems) from healthy blood donors. The samples were centrifuged at 1,500 g for 10 min at room temperature and the supernatants from individual donors were pooled in batches of approximately 75 mL, according to the anticoagulant used. The collection of plasma samples was approved by the local Ethical Board at Uppsala University (01-367).
of part II. These four holes were used for insertion of MD probes. The diameter of the hole was 3.78 mm (1/8 in.) and chosen to fit standard Polyetheretherketone (PEEK) tubing. Two additional holes with the same diameter (3.78 mm) were also drilled in the centre of each short edge of part II, which were used for liquid sample injection and pressure sensing respectively. Loctite super glue (LOCSG5G, Henkel Norden AB, Stockholm, Sweden) was used to assemble the three separate parts together. Glue was applied onto the top and bottom surface of part II, then part I and III were hold against part II immediately after the application of the glue, using six screw clamps. The glue was allowed to cure for 24 h in room temperature. After this step, six PEEK tubing (denoted a, b, c, d, e and f) with outer diameter (o.d.) 3.78 mm, and inner diameter (i.d.) 1.59 mm (Valco Instruments Co. Inc. and VICI AG, Schenkon, Switzerland), were inserted and glued into the six drilled holes using the previous glue. The tubing on the long edges (a, b, c, d) were adjusted to be positioned 45 mm extending out of the drilled holes, while tubing at opening e and f extended 10 mm out from the holes. 3.4 MD in vitro experiment set-up
The chamber was constructed from three rectangular shaped Polymethylmethacrylate (PMMA) parts (I, II, III) as shown in Fig. 1. Part I and III were identical and served as lid and bottom plate respectively. For part II, the rectangular shaped void in the middle with the dimensions of 50×30×8 mm became the chamber after the three parts (I–III) were assembled together, resulting in a chamber volume of 12 mL. Four holes with diameter of 3.2 mm were drilled, 10 mm away from each other along the centre line on one of the two long edges
Four MD catheters of model CMA 71 (10 mm membrane length, 100 kDa MWCO, outlet tubing dimensions: length 220 mm and i.d. 1.5 mm; CMA MD, Solna, Sweden) were inserted into the chamber via the tubing through the openings a, b, c and d, as shown in Fig. 1. The joint heads of the probe stopped at the protruding ends of the PEEK tubing and a small section of silica tubing with length of 20 mm was used to wrap and connect them together. In the chamber, the probes were positioned in parallel with 10 mm spacing between each other. The probe at position a and d were positioned 10 mm away from the openings e and f, respectively. The probes protruded into the chamber with their ends staying at 20 mm depth into the chamber, where the total depth of the chamber is 30 mm. The membranes on the MD probes were positioned exactly in
Fig. 1 The structure and construction of the in vitro MD test chamber: a– d four CMA 71 MD catheters inserted into the chamber, with the inlets connected to syringe pumps, e injection of MD sample into the chamber, with the inlets connected to syringe pumps, f pressure sensing port, with
the other end connected to a pressure sensor. (I)-(III) are three rectangular parts made of PMMA, with (II) having a rectangular void in the middle and six holes drilled through at positions (a–f). The features of layer (II) are shown on the right side with their respective dimensions
3.3 Construction of pressurization chamber
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the middle of the chamber with a 10 mm distance away from both two long edges. The perfusate inlets of the four MD probes were connected to Hamilton gaslight 2.5 mL syringes (1002TLL, Hamilton Bonaduz AG, Bonaduz, Switzerland), which were mounted on a CMA 400 syringe pump (CMA MD, Solna, Sweden). Pressurization of the chamber was achieved by a syringe pump which delivers liquid into the chamber through opening e, as illustrated in Fig. 1. The liquid injection constitutes of a Hamilton gaslight 10 ml syringe (model 1010RN, Hamilton Bonaduz AG, Bonaduz, Switzerland) with a EFD Precision tip (model 5114-0.25-B, Verick International, Brampton, Ontario,USA). The syringe was connected with 500 mm long Polytetrafluoroethylene (PTFE) tubing with o.d. 1.59 mm (1/16 in.), i.d. 0.79 mm (Valco Instruments Co. Inc. and VICI AG, Schenkon, Switzerland). The PTFE tubing was connected to the PEEK tubing at position e using the same silica tubing which was used for the connection between MD probe joint head and the PEEK tubing. The syringe was mounted onto a Harvard PhD 2000 infusion syringe pump (Harvard apparatus, Holliston, MA, USA). A Digitron 2081P manometer (Digitron instrumentation Ltd, Devon, England) was used as the pressure sensor to monitor the pressure in the chamber through opening f. The measuring portal of the manometer was connected to the PEEK tubing at position f, at first by a section of 34 mm long PEEK tubing which has an i.d. 1.59 mm, then by a section of 438 mm long silica tubing which has an i.d. 2.9 mm. The reading of the manometer was the measured air pressure subtracted by atmospheric pressure. 3.5 MD sampling process Before insertion of the MD probes into the chamber and also prior to the MD process, the catheters were flushed in DI water using Ringer’s solution as perfusion fluid, at a flow rate of 15 μL/min. As shown in Fig. 1, the four MD probes were inserted into the chamber through openings a, b, c and d. MD test sample (Ringer’s solution or Plasma) was injected through opening e into the chamber, while for opening f, the pressure sensing channel, was kept open to allow excess air to be removed. After the chamber was filled with sample, channel f was connected to the pressure sensor. The whole PMMA part of the device was immersed into a temperature control water bath (Lauda Dr. R. Wobser GMBH & CO., LaudaKönigshofen, Germany), to keep the chamber temperature at 37.5 °C. Before collection of dialysate fractions, the MD probes were flushed with perfusate using a flow rate of 15 μL/min for 5 min followed by 15 min equilibration time using the same flow rate as for the following MD experiment. Pressurization of the chamber was conducted by injecting MD test sample into the chamber at various pumping rates.
Dialysate fractions were collected in pre-weighted microvials, which were positioned at the same height as the MD probe centre position. The pressure sensor read-outs were recorded with various time intervals. 3.6 MD sample collection Experiments details in this study are listed in Table 1, indicating in which figure the test results are presented. As Table 1 presents and compares, the varying test parameters include: MD test sample (Ringer’s solution, dextran Ringer’s solution, Plasma); Perfusion fluid (Ringer’s solution, dextran Ringer’s solution); MD perfusion fluid injection rate (pump injection rates at 0.5, 1, and 2 μL/min); MD chamber pressurization injection rate (representing the MD sample injection rate which pressurizes the test chamber. In total 11 sets of experiments were done. For each set of experiments, data (e.g. MD dialysate collection) were collected at 3–6 different pressure points for all four probes. The pumping rates in the pressurization injection rate column of Table 1 lead to different pressure points or pressure ranges in the chamber pressure column correspondingly. In each experiment, the pressurization injection rate started with zero, which means that there were none MD sample injections from the pressurization syringe into the chamber while the MD test was running. After that, the pressurization injection rate was gradually increased to achieve correspondingly increased pressure inside the chamber. For test sets 2, 3, 4 in Table 1, the pressurization injection rate was adjusted and set, aiming to achieve a certain pressure point. Instead, for the rest of the tests, the pressurization injection rates were fixed values with stepwise increase and the resulted chamber pressures were measured. For each test, a dialysate fraction volume ranging from 50 to 230 μL was collected from each individual MD probe, depending on respective test conditions. After collection, the collection vials were weighed.
4 Results and discussion 4.1 Validation of the test chamber Pressures in human bodies vary from −10 up to 150 mmHg depending on site and condition. The intracranial pressure (ICP) of a normal adult at rest is 7–15 mmHg (Nikaina et al. 2012). These are relatively small pressures that required a stable and perfectly sealed pressure chamber system . The chamber pressure capabilities were evaluated in a Ringer’s− Ringer’s fluid system with a perfusion fluid rate of 1 μL/min and pressurization injection flow rates of 0, 1, 2 and 3 μL/min. The results are presented in Fig. 3, where chamber pressure is plotted as a function of pressurization injection rate. At no
Biomed Microdevices Table 1 All experiments conducted in this study. The experiments are grouped depending on the variation of test parameters: MD test sample, MD perfusion fluid, MD perfusion fluid injection rate. Each set of tests
include several test cycles. All sample (not test 11) and perfusion fluids contain Ringer’s solutions. When the solution is spiked with Dextran T500, it is marked with the dextran concentration in % (w/v)
Test set
MD sample (dextran conc. in Ringer)
MD perfusion fluid (dextran conc. in Ringer)
MD perfusion rate (μL/min)
Pressurization injection rate (μL/min)
Chamber pressure (mmHg)
Test results presented in Figure
1 2 3 4
– – – –
– – – –
1 0.5 2 1
0, 1, 2, 3 0, 1.2, 4, 8, 11, 17 0, 2.5, 7, 11, 18 0, 0.8, 2.5, 6.5, 12,18
1.2–7 0,5, 10, 20, 30, 50 0, 5, 10, 20, 30, 50 0, 5, 10, 20, 30,50
Fig. Fig. Fig. Fig.
5 6 7 8 9 10 11
– – – 1% 3% 5% Plasma
1 3 5 3 3 3 3
1 1 1 1 1 1 1
0, 3, 5 0, 3, 5 0, 3, 5 0, 3, 5 0, 3, 5 0, 3, 5 0, 3, 4, 5
0, 17.3, 24.3 0, 15.2, 22.5 0, 20.1, 28.7 0, 23.9, 42.5 0, 25, 48.2 0, 28.5, 54.1 4.86–42.5
Fig. 4(b) Fig. 4(b) Fig. 4(b) Fig. 4(c) Figs. 4(c) and 5 Fig. 4(c) Fig. 5
% % % % % % %
3 4(a) 4(a) 4(a)
Each test cycle uses a specific MD sample injection (chamber pressurization) rate, to get the corresponding chamber pressure point (for test set 2–10) or pressure range (for test set 1 and 11) For test set 2–10, during the first test cycle, zero pressurization injection rate corresponds to the experimental procedure as: no pressurization injection and left the pressurization port open to atmosphere, so the chamber pressure stays as zero. Whereas for test set 1 and 11, during the first test cycle, there was no pressurization injection but the pressurization port was sealed. As a consequence for these two cases, the chamber pressure was observed to start with a small value and increase very slowly. Apart from these two different zero pressurization injection procedures, for all other test cycles, the initial experimental conditions were set to identical (with pressurization port connected to continuous fluid injection) At the end of each test cycle, the dialysate fraction were collected and weighed, and then a fluid recovery data point can be calculated. After statistical treatment of several (for instance, in the cases of test set 2, 3, 4, 12 fluid recovery points were generated for each every pressurization injection rate. Since three repeating for each test cycle were performed on four probes) such data points, The results from each test set were presented in the corresponding figure, as indicated in the last column of this table
pressurization injection rate, the chamber pressure was 1.54± 0.28 mmHg (s.e.m) whereas a pressurization injection rate of 3 μL/min resulted in a chamber pressure of 7.16±0.17 mmHg. A two way ANOVA test (with confidence interval as 5 %) was done, with the aim to find out if the positioning of the probe was a factor which influenced the individual probe’s FR behaviour, and to verify the observation that MD perfusion rate was indeed a factor which causes significant performance difference of the MD probe. Test results gave a p-value 0.193 for probe position and p=0.005 for perfusion rate, meaning that the positioning of the probe and the probes’ positioning relative to each other do not give a significant influence on the FR, whereas the perfusion fluid significantly affects the FR. In conclusion, the FR of the chamber MD system can be controlled accurately via control of the chamber pressure, which is achieved by pressurization injection into the chamber at precise rate. As the chamber MD system in this study is an in vitro system which is designed for mimicking the in vivo MD, the study results of this system can be an indication for the behaviour of in vivo MD. 4.2 Fluid recovery and transmembrane pressure Figure 2 explains the different parameters that affect the FR for an ultra-filtration MD membrane. Series of experiments
(see Table 1 for detailed information) were performed in order to validate the model, Fig 3, and investigate the relationships between the parameters. Fig 4. 4.3 Perfusion flow rate Figure 4(a) presents the results of test set 2, 3, and 4, for which both the MD sample and perfusion fluid used in the test are Ringer’s solution, the only difference between the three tests is the MD perfusion rate Qperfusate. The test sample and perfusion fluid were both Ringer’s solution meaning that there is no osmotic pressure difference were present. Therefore, the only component left to affect the FR was the chamber pressure. The FR is proportional to chamber pressure which is in agreement with a previous study (Siaghy et al. 1999). FR also increased faster with lower MD perfusion flow rate which is in agreement with Eq. 2a where the slope is a representation of the value b/Qperfusate. The ratio of the slope values 14.4: 8.6: 4.8 is a reasonably good representation of 2(1/0.5): 1: 0.5(1/2). According to Eq. 2a and 2b, the intercept, a, is unaffected by Qperfusate, which is the case in Fig. 4(a) with a 95 % confidence. Following the linear model, Eq. 2a, the FR experimental data of each test set was linearly fitted with the chamber pressure, presenting the corresponding linear regression. The
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Fig. 2 The experimental set-up of the pressurized in vitro MD. Four MD probes perform sampling on one side of the chamber, driven by four syringes on a syringe pump; MD sample is in the chamber and can be injected through a port into the chamber at controlled rate, also driven by a syringe on a pump; The port on the right side is connected to a pressure sensor through a section of silica tubing, where the pressure of the trapped air inside the tubing is monitored. A sketch of the pressure system around the membrane, when a MD probe is running test in the in vitro chamber with pressurization condition. Three aspects were presented: (1) the fluid flow inside the MD probe, denoted as the hollow arrows inside the probe with their direction indicating the flow direction; (2) The internal and
external pressure components, denoted as the light weighted solid arrows across the membrane, with the arrow direction indicating the pressure direction. The internal components include Pdynamic′ and Posmotic′ on the upper left. The external components include Pstatic and Posmotic on the lower right. (3) The pressure components comprise the TMP ΔP after summarizing the same contribution. They include ΔPosmotic, Pdynamic′ and Pair. They are denoted as the heavy weighted hollow arrows across the membrane, with the arrow direction indicating the pressure direction, except for the ΔPosmotic and ΔP, the directions are only suggestive. The details on the individual component and explanation on the TMP can be found from the content related from Eqs. 1 to 6
two curves besides each linear fit line marked out a 95 % confidence zone for the experimental data points. In order to find out if the linear fit is the most suitable fit to the experimental data, higher order regressions (quadratic, cubic) were performed on test set 2, 3 and 4. The R2adjvalue
in the regression model is often used to determine which order of regression is the best fit. The criterion is that the order of the best regression model is determined when the R2adj value stops increasing. By comparison of the R2adj R2adj values among the linear, quadratic, cubic regression models of each test set, it
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Fig. 3 Evaluation chart of the chamber pressure capabilities using a Ringer’s−Ringer’s fluid system with a perfusion fluid rate of 1 μL/min and pressurization injection flow rates of 0, 1, 2 and 3 μL/min (test 1 in Table 1). Chamber pressure is plotted as a function of pressurization injection rate. At no pressurization injection rate, the chamber pressure was 1.54±0.28 mmHg (s.e.m) whereas a pressurization injection rate of 3 μL/min resulted in a chamber pressure of 7.16±0.17 mmHg. n=4 for each pressure point
was found that: for perfusion rate as 1, the R2adj R2adj value achieves highest value 0.994 at linear model; for perfusion rate as 2, the R2adj R2adj value achieves highest value 0.999 at linear model; for perfusion rate as 1, the R2adj R2adj value achieves highest value 0.991 at linear model. These suggest that for all three test sets, the linear fit is the best regression model. 4.4 Colloid osmotic pressure inside membrane In Fig. 4(b) the effect of Posmotic was analysed by varying the amount of dextran (1, 3 and 5 %) in the Ringer’s perfusate and keeping the perfusion fluid flow rate (1 μL/min) and sample (Ringer’s solution) unchanged. The three different test set-ups
Fig. 4 a In vitro MD test fluid recovery plotted with chamber air pressure (test 2–4 in Table 1) . Ringer’s solution was used as both sample and perfusate liquid. Three different perfusion flow rates were tested, 0.5 μL/ min (green), 1.0 μL/min (red) and 2.0 μL/min (blue). The grey lines represent the confidence interval of 95 % for each test and the dots represent a measurement which in total were n=72 each for 0.5 μL/min and 1.0 μL/min and n=60 for 2.0 μL/min b In vitro MD test fluid recovery plotted with chamber air pressure. Ringer’s solution was used as sample and the perfusion flow rate was 1.0 μL/min. Three different perfusion fluid compositions, differentiating in the added amount of Dextran T500, were tested, 1 % (w/v) dextran in Ringer’s solution (green), 3 % dextran in Ringer’s solution (red) and 5 % dextran in Ringer’s solution (blue), (test 5–7 in Table 1). The grey lines represent the confidence interval of 95 % for each test and the dots represent a measurement which in total were n= 12 for each test c In vitro MD test fluid recovery plotted with chamber air pressure. Ringer’s solution with added 3 % (w/v) dextran was used as perfusion fluid with a flow rate of 1 μL/min. Three different sample fluid compositions, differentiating in the added amount of dextran, were tested, 1 % dextran in Ringer’s solution (green), 3 % dextran in Ringer’s solution (red) and 5 % dextran in Ringer’s solution (blue), (test 8–10 in Table 1). The grey lines represent the confidence interval of 95 % for each test and the dots represent a measurement which in total were n=24 for each test
correspond to test set no. 5, 6 and 7 in Table 1. As Eq. 2a b suggests, the term a þ Qperfusate ΔPosmotic represents the intercept value, while b/Qperfusate represents the slope value in the linear fit equation. According to this analysis, the contribution of ΔPosmotic to FR is on the intercept value and the contribution should be additive which was the case. The FR at no pressurization injection increased from 76 % when 1 % dextran was added
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compared to 90 % when 3 % dextran was added and finally reaching 99 % when 5 % dextran was added. These results are in agreement with the findings of previous studies (Rosdahl et al. 2000; Marklund et al. 2009). The slopes decreased slightly when more dextran was added to the perfusion fluid which could be explained by increased membrane resistance Rm since all the other parameters of the membrane and outlet tubing (l, L, d, ro and ri) stay unchanged. 4.5 Colloid osmotic pressure outside membrane The effect of different osmotic pressures in the sample was evaluated by adding dextran (1, 3 or 5 %) to the Ringer’s sample in the chamber. Also, dextran in a concentration of 3 % was added to the Ringer’s perfusate that was kept at 1 μL/min flow rate, for all three tests. The three tests’ details are list as test no. 8, 9 and 10 in Table 1. The results are presented in Fig. 4(c) where FR is plotted as a function of chamber pressure. The intercept is clearly decreased with increased amount of dextran in the sample since the increased osmotic pressure outside the membrane caused the decrease on ΔPosmotic.(since the positive direction of the TM osmotic pressure is defined as towards the inside of membrane) and according to Eq. 2a, the decrease of ΔPosmotic leads to the decrease on the intercept value. Stepwise changes have been seen in the slope value where increased colloid osmotic pressure of the sample decreases the slope value. The reason for this is that first, the viscosity of the dextran solution increases and hence b in Eq. 2b, decreases. Secondly, and more prominently, the overall membrane resistance Rm increases due the concentration polarization of the colloidal dextran molecules. Solutes and colloids (dextran) are transported towards the surface of the membrane from the sample. The solutes pass through the membrane while the large dextran colloids accumulate at the surface. The concentration of the colloids at the surface have been reported to be 20–50 times higher than in the sample solution and therefore form a gel layer that becomes denser with increased chamber pressure and the concentration of colloids (Baker 2004). This gel layer eventually leads to membrane fouling, which is more severe when it comes from the outside for an anisotropic membrane structure with the separation layer facing the inwards and structure layer facing outward, which is the case for our MD membranes. 4.6 Investigation of gel layer formation using human plasma sample A human plasma sample was used in order to further investigate the gel formation phenomena on a MD membrane in a pressurized system, the test details are listed as test no.11 in Table 1. In Fig. 5 the chamber pressure is plotted against FR for test set no. 9 and 11, in order to compare them. For both set of test, Ringer’s solution with 3 % added dextran was used as perfusion fluid with a flow rate of 1 μL/min, only the MD
Fig. 5 In vitro MD test fluid recovery plotted with chamber air pressure. Ringer’s solution with added 3 % (w/v) dextran was used as perfusion fluid with a flow rate of 1 μL/min. Two different sample fluid compositions were tested, 3 % dextran in Ringer’s solution (blue) and human plasma sample (blue), (test 9 and 11 in Table 1). The grey lines represent the confidence interval of 95 % for each test and the dots represent a measurement which in total were n=24 the 3 % dextran sample and n=16 for the plasma sample
sample is different- plasma to 3 % dextran in Ringer’s solution. As can be seen from their linear fit equations, their FR behaviour along with changed pressure, are similar. This may be explained by the similar content natures when comparing plasma to 3 % dextran, as they are similar in viscosity and particle movement. This result clearly shows that the in vitro MD systems with a pressurized biological sample could be simulated by using this chamber. Complex biological events such as different traumatic brain injuries, where the intracranial pressure could rise and fall dramatically, could be mimicked and evaluated by such in-vitro test system. It has been showed that the different pressure parameters greatly influence the fluid recovery for high MWCO MD membranes. In future studies we are going to investigate if small and large molecules are equally sensitive to different pressure conditions.
5 Conclusions An analytical fluid mechanical model was developed to study the TM fluid exchange dependence on the pressure components over a high MWCO MD membrane. It shows that FR has a linear dependence upon the static pressure of the sample, where TM osmotic pressure difference and MD perfusion rate decide the rate of the linear increase of FR with increased static pressure. A novel MD in vitro test system has been developed and evaluated. It holds four large pore MD probes under static pressure set by a precisely controlled sample injection rate into a chamber. The FR of the in vitro MD system can be accurately studied as a function of chamber pressure. The experimental results are consistent with the theoretic model of the TM fluid exchange. This study opens up for the possibility to
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explore large pore MD sampling mechanisms from a new methodological aspect. The in vitro system is designed for modelling in vivo MD in cerebrospinal fluid and studies with biological samples in this system may be good models for in vivo MD. Acknowledgments This research was supported by the Uppsala Berzelii Technology Centre for Neurodiagnostics, funded by the Swedish Governmental Agency for Innovation Systems and the Swedish Research Council Grant number P29797-1. We acknowledge CMA Microdialysis and Pharmacosomos AS for sharing their knowledge and for material support and Visualize your Science for graphical assistance. Conflict of interest The authors declare that they have no conflict of interest
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