1、Designation: F2952 14Standard Guide forDetermining the Mean Darcy Permeability Coefficient for aPorous Tissue Scaffold1This standard is issued under the fixed designation F2952; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the y
2、ear of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.1. Scope1.1 This guide describes test methods suitable for determin-ing the mean Darcy permeability coefficient for a porou
3、s tissuescaffold, which is a measure of the rate at which a fluid,typically air or water, flows through it in response to an appliedpressure gradient. This information can be used to optimize thestructure of tissue scaffolds, to develop a consistent manufac-turing process, and for quality assurance
4、purposes.1.2 The method is generally non-destructive and non-contaminating.1.3 The method is not suitable for structures that are easilydeformed or damaged. Some experimentation is usually re-quired to assess the suitability of permeability testing for aparticular material/structure and to optimize
5、the experimentalconditions.1.4 Measures of permeability should not be considered asdefinitive metrics of the structure of porous tissue scaffolds andshould complement measures obtained by other investigativetechniques e.g., scanning electron microscopy, gas flow porom-etry and micro-computer x-ray t
6、omography (ASTM F2450).1.5 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior
7、 to use.2. Referenced Documents2.1 ASTM Standards:2D4525 Test Method for Permeability of Rocks by FlowingAirF2450 Guide for Assessing Microstructure of PolymericScaffolds for Use in Tissue-Engineered Medical ProductsF2603 Guide for Interpreting Images of Polymeric TissueScaffolds2.2 American Petrole
8、um Institute (API) Document:3RP-27 Recommended Practice for Determining Permeabilityof Porous Media3. Terminology3.1 Definitions:3.1.1 tortuosity, nthe ratio of the actual path lengththrough connected pores to the Euclidean distance (shortestlinear distance).4. Significance and Use4.1 This document
9、describes the basic principles that needto be followed to obtain a mean value of the Darcy permeabil-ity coefficient for structures that consist of a series of intercon-nected voids or pores. The coefficient is a measure of thepermeability of the structure to fluid flowing through it that isdriven b
10、y a pressure gradient created across it.4.2 The technique is not sensitive to the presence of closedor blind-end pores (Fig. 1).4.3 Values of the permeability coefficient can be used tocompare the consistency of manufactured samples or to deter-mine what the effect of changing one or more manufactur
11、ingsettings has on permeability. They can also be used to assessthe homogeneity and anisotropy of tissue scaffolds. Variabilityin the permeability coefficient can be also be indicative of:4.3.1 Internal damage within the sample e.g., cracking orpermanent deformation.4.3.2 The presence of large voids
12、, including trapped airbubbles, within the structure.4.3.3 Surface effects such as a skin formed during manu-facture.4.3.4 Variable sample geometry.4.4 This test method is based on the assumption that theflow rate through a given sample subjected to an appliedpressure gradient is constant with time.
13、NOTE 1If a steady state flow condition isnt reached, then this could1This test method is under the jurisdiction of ASTM Committee F04 on Medicaland Surgical Materials and Devices and is the direct responsibility of SubcommitteeF04.42 on Biomaterials and Biomolecules for TEMPs.Current edition approve
14、d March 1, 2014. Published April 2014. DOI: 10.1520/F2952-14.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.
15、3Available from American Petroleum Institute (API), 1220 L. St., NW,Washington, DC 20005-4070, http:/www.api.org.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1be due to structural damage (i.e., crack formation or the porous structur
16、edeformed as a result of the force being placed upon it by the fluid flowingthrough it). Sample deformation in the form of stretching (bowing) canalso occur for less resilient structures as a result of high fluid flow rates.This topic is discussed in more detail in Section 7.4.5 Care should be taken
17、 to ensure that hydrophobic mate-rials are fully wetted out when using water or other aqueous-based liquids as permeants.4.6 Conventionally, the pressure differential created across asample is measured as a function of both increasing anddecreasing flow rates. An alternative approach, which may bepr
18、actically easier to create, is to apply a range of differentpressure differentials across the sample and measure theresultant flow of fluid through it. The hysteresis that occursduring a complete cycle of increasing flow rate followed by aprogressive decrease in flow rate can provide an excellentmea
19、sure of the behavioural consistency of the matrix. Signifi-cant hysteresis in the measured pressure differential duringincreasing and decreasing flow rates can indicate the existenceof induced damage in the structure, the fact that the material isbehaving viscoelastically or suffering from permanent
20、 plasticdeformation. Some guidance on how to identify which of thesefactors are responsible for hysteresis is provided in Section 7.4.7 It is assumed that Darcys law is valid. This can beestablished by plotting the volume flow through the specimenagainst the differential pressure drop across the spe
21、cimen. Thisplot should be linear for Darcys law to apply and a leastsquares fit to the data should pass through the origin. It is notuncommon for such plots to be non-linear which may indicatethat the structure does not obey Darcys law or that the rangeof pressures applied is too broad. This topic i
22、s further discussedin Section 7.5. Characterisation and the Structural Features of TissueScaffolds5.1 Porous tissue scaffolds are typically manufactured frompolymers and ceramics and consist of a network of connectedvoids through which cells, macromolecules such as growthfactors, and small molecules
23、 such as nutrients and dissolvedgases can move (1).4In most cases, the material used to createthe scaffold will disappear over time, either as a result ofenzyme activity or some other degradation processes (e.g.,hydrolysis). The time-dependent permeability of tissue scaf-folds to dissolved gases and
24、 solutes is critical to their function,particularly for high levels of cell occupancy due to thedemands for oxygen and nutrients as well as the need toremove waste products.5.2 There are many methods available for characterizing thestructural features of scaffolds (ASTM F2450-10), but thesecan be ti
25、me-consuming, expensive to use and can result inpermanent damage or contamination to the scaffold.5.3 Most investigators report some measure of pore size andan estimate of the scaffold porosity (2, 3). However, there aresignificant practical issues associated with these measure-ments. Techniques suc
26、h as mercury porosimetry and gas flowporometry are used to estimate pore size distributions whichtypically differ by an order of magnitude due to differences inthe underlying physics of the techniques (ASTM F2450).Despite the shortfalls of these techniques both can be used toinfer a useful amount of
27、 information regarding the structure ofthe scaffold. Both porosimetry and porometry represent thescaffold structure as a distribution of differently sized parallel-sided pores i.e., the model assumes a simple structure that isequivalent to the more complicated structures usually manu-factured where
28、the pores are not parallel-sided and not ofuniform diameter.5.4 Electron and other microscopies are extensively used toimage scaffolds, but the data that these techniques produce isoften challenging to interpret without some undefinable levelof uncertainty (i.e., quantifying the dimensions of typica
29、llyirregularly shaped and sized structural features). The samearguments apply to tomographic methods such as magneticresonance imaging and micro-computer tomography (CT), forexample, calculations based on the analysis of a series ofscaffold images obtained from a tomographical method such asCT will
30、depend on how well the boundaries of the voids orpores can be defined, on the instrument resolution in the x, y4The boldface numbers in parentheses refer to the list of references at the end ofthis standard.FIG. 1 Schematic of the Different Pores Types Found in Tissue Scaffolds.Fluid Flow through th
31、e Structure is via the Open PoresF2952 142and z planes and the methodology used to obtain dimensionalinformation. Nevertheless, many groups have pursued quanti-tative analysis of pore size distributions in polymeric (3) andbioceramic (4) matrices in recognition of the important corre-lation between
32、this parameter and tissue ingrowth.5.5 The pores in a tissue scaffold typically consist of a seriesof irregularly shaped voids5that can be connected to each otherboth by partial fusion and connecting channels (connects).Through pores provide a path through the scaffold from oneside to the other, (se
33、e Fig. 1) and are the primary routes forfluid penetration into the scaffold. The dimensions of a givenpore can be difficult to define due to, for example, merging ofadjacent cavities that result in fenestrations or windowsforming in the void walls. Blind-end and closed-pores, al-though not contribut
34、ing to measures of fluid permeability playan important role in gas diffusion through the structure.6. The Darcy Permeability Coefficient6.1 The Darcy permeability coefficient is a measure of theresistance of a porous material to flow of a fluid through it thatis governed by the dimensions and densit
35、y of open (or through)pores and by the tortuosity of the structure.6.2 In its simplest form, the permeability coefficient, k of thescaffold can be determined by measuring the flow of fluidthrough the material in a given time under a known pressuregradient using Darcys law (5) i.e.,Q 52kAPb2 Pa!L(1)w
36、hich states that the flow rate (Q,(m3/s) through thematerial is directly proportional to the cross-sectional area (A,(m2) and the pressure drop (Pb Pa, (Pa) and inverselyproportional to the viscosity of fluid (, (Pa.s) and the length(L, (m) over which the pressure drop occurs.6.3 The permeability co
37、efficient, k, is then derived from theslope of a linear plot of flow rate versus pressure drop wherethe slope is forced to pass through the origin (see Fig. 2).6.4 The SI units of the coefficient are m2.6.5 Permeability coefficients are routinely used in assessingsoils and other porous materials (AS
38、TM D4525-08 and RP-27)and have also been used to characterise polymeric scaffoldsand hard tissues e.g., cancellous bone (6-9).7. Methodology7.1 Obtaining reliable values for the permeability coefficientinvolves a degree of experimental optimization to ensure that arange of flow rates and pressure di
39、fferentials can be measured.Clearly, it is advantageous to measure a range of flow rates andpressure differentials to improve the reliability of the Darcycoefficient but this can produce non-linear plots for reasons thatare discussed in Section 8. This will require some experimen-tation to optimize
40、the sample geometry and to select the mostappropriate fluid, typically air or water, for a given structure/sample geometry and material type. Sections 7.3 and 7.4describe the features that are required in an experimentalsystem in order to obtain robust estimates of the coefficient.7.2 Reliably deter
41、mining the pressure differential across thescaffold and measuring the flow rate through it are fundamentalaspects of permeability testing. In practice, the sensitivity of5The terminology for scaffold structure is not well defined. The term pore iswidely used to mean a void, a window in a void or a c
42、onduit connecting two or morevoids together.FIG. 2 Example of a Plot of Flow Rate versus Pressure DifferentialF2952 143the apparatus used to measure pressure will limit the magnitudeof the pressure gradient that can be used for a given samplegeometry.7.3 Gas-based Systems:7.3.1 Fig. 3 shows a schema
43、tic representation of apparatusthat can be used to measure the flow of gas, in this casecompressed air, through a disc-like sample mounted in acommercially available filter holder that can be purchased in arange of sizes.7.3.2 The rate of flow through the sample is measured by agas flow meter. These
44、 devices are commercially available fordifferent ranges of flow rate. Care should be taken to ensurethat the flow meter used is appropriate for the flow rates usedto avoid potential measurement inaccuracies. The pressureupstream of the sample, Pb, is measured and used together witha measured value f
45、or atmospheric pressure (Pa) to determinethe pressure gradient (Pb Pa) required by Eq 1.7.4 Liquid-based Systems:7.4.1 Fig. 4 shows an experimental configuration that mea-sures the flow of a liquid, such as water, through a poroustubular scaffold sample. The apparatus consist of a circulatingpump, w
46、hich is used to generate an internal pressure within thecircuit, (Pb). Pais the measured value of atmospheric pressure.The internal pressure that develops within the circuit is verydependent on the permeability of the scaffold and its geometry,but is usually sufficiently high that any changes in pre
47、ssurealong the length of a vertically mounted sample due todifferences in height can be ignored. However, the user isadvised to check that this assumption is valid for the sampleand sample geometry that is being investigated.7.4.2 The water that flows through the walls of the specimenand out through
48、 the overflow is collected at given timeintervals, weighed and converted into a flow rate. The fluidreservoir replenishes the fluid lost from the system via theoverflow.7.4.3 Alternative sample geometries can be used (i.e., a discof material sandwiched between O rings in a commerciallyavailable filt
49、er holder), as used for gas-based systems. In bothcases the practical considerations are the same: how to apply aprogressively increasing pressure gradient without signifi-cantly deforming the sample or letting fluid flow around it.8. Practical Considerations8.1 There are many experimental configurations that can beused to generate the flow rate and pressure differential mea-surements required to determine Darcys permeability coeffi-cient. It is not uncommon to observe a degree of non-linearityin plots of flow rate versus differential pressure, particularlyw
