Patent Application
20100221347
1. Technical Field
This document provides materials and methods related to tissue scaffolds for use in replacing or augmenting various tissues in the body. For example, flexible tissue scaffolds with controlled pore geometry and methods of enhancing solute transport using rhythmic compression (e.g., 1.0 Hz) of tissue scaffolds are provided.
2. Background Information
Prostheses are devices that are used to support or replace a body part lost by trauma, disease, or defect. Improved prostheses are required to meet the needs of the aging population.
Recently, there has been a shift from replacing lost body parts to regenerating damaged organs or tissues. Tissue engineering techniques have the potential to create tissues and organs de novo, using cells integrated into a three-dimensional scaffold.
This document provides materials and methods related to tissue scaffolds for use in replacing or augmenting various tissues in the body. For example, flexible tissue scaffolds with varying pore geometry and methods of rhythmically compressing tissue scaffolds to increase solute transport within the scaffold are provided. In tissue engineering, scaffolds can provide a three-dimensional template for cells. The cells can attach to and grow onto the surface of the pores in a tissue scaffold. The pores can simultaneously allow for supply of nutrients and oxygen to the attached cells, and removal of metabolic waste from the cells. In some cases, the materials and methods described herein can be used to increase solute convection deep into a tissue scaffold and provide an enhanced environment for cell survival at increased depths (i.e. >>1 mm) before ingrowth of microvessels into a tissue scaffold. For example, tissue scaffolds configured to work to increase solute transport in response to an applied force (e.g., a compressive or expansive force). In some cases, a tissue scaffold can be configured to provide a net unidirectional fluid flow, which can be modulated by compression frequency. The methods and materials described herein can be used in designing tissue scaffolds with appropriate porosity, pore connectivity, elasticity and compliance, flow characteristics, strength and durability as required by the application of a tissue scaffold.
In general, one aspect of this document features a method for supporting tissue growth within a mammal. The method can comprise, or consist essentially of, implanting a tissue scaffold into a location in the mammal. The location can provide a compressive or expansive force to the tissue scaffold. The force can be generated from a natural body movement or body function. The mammal can be a human. The tissue scaffold can include a population of cells. The cells can be selected from among stem cells, preadipocytes, glia, fibroblasts, myocytes, and osteocytes. The location can be selected from among the heart, intestines, vasculature, knee, hip, or jaw. The force can be applied cyclically. The frequency of the force can be equal to or greater than about 1.0 Hz. The force can enhance solute transport within the tissue scaffold. The body function can comprise, or consist essentially of, beating of the mammal's heart, pulsation of the mammal's arteries, or peristaltic motion of the mammal's intestines. The body movement can comprise, or consist essentially of, exercise, walking, running, or chewing.
In another aspect, this document features a method for supporting tissue growth within a mammal. The method can comprise, or consist essentially of, implanting a tissue scaffold that is responsive to external stimulation into a mammal. The external stimulation can provide a compressive or expansive force to the tissue scaffold. The tissue scaffold can be responsive to electrical current stimulation. The tissue scaffold can include magnetic particles and be responsive to magnetic field stimulation. The tissue scaffold can include a population of cells. The cells can be selected from among stem cells, islet cells, preadipocytes, glia, fibroblasts, myocytes, and osteocytes. The method can include stimulating the tissue scaffold. The frequency of the stimulation can be equal to or greater than about 1.0 Hz. The stimulation can enhance solute transport within the tissue scaffold. The mammal can be a human.
In another aspect, this document features a method for supporting tissue growth within a mammal. The method can comprise, or consist essentially of, implanting a tissue scaffold into a location in the mammal that is accessible to externally applied massage. The massage can provide a compressive or expansive force to the tissue scaffold. The mammal can be a human. The tissue scaffold can include a population of cells. The cells can be selected from among stem cells, preadipocytes, glia, fibroblasts, myocytes, and osteocytes. The location can be selected from among the limbs, skin, gums, and jaw. The massage can be performed by a mechanical massage device. The frequency of the force provided by the massage can be equal to or greater than about 1.0 Hz. The massage can enhance solute transport within the tissue scaffold. The method can include massaging the location.
In another aspect, this document features a method for supporting tissue growth within a mammal. The method comprises, or consists essentially of, implanting a tissue scaffold into a location in the mammal, wherein the location provides a compressive or expansive force to the tissue scaffold, wherein the force is generated from a natural body movement or body function, and wherein the tissue scaffold comprises concentric layers. The mammal can be a human. The tissue scaffold can comprise a population of cells. The tissue scaffold can comprise microspheres. The microspheres can be selected from the group consisting of solid microspheres, porous microspheres, and degradable microspheres. The tissue scaffold can comprise a porous geometry for solute transport. The location can be selected from the group consisting of the heart, intestines, vasculature, knee, hip, and jaw. The force can be applied cyclically. The frequency of the force can be equal to or greater than about 1.0 Hz. The force can enhance solute transport within the tissue scaffold. The body function can comprise beating of the mammal's heart or pulsation of the mammal's arteries.
In another aspect, this document features a method for supporting tissue growth within a mammal. The method comprises, or consists essentially of, injecting an injectable tissue scaffold material into a location in the mammal, wherein the location is substantially free from a compressive or expansive force, wherein the injectable tissue scaffold material forms a porous geometry for solute transport. The injectable tissue scaffold can comprise microspheres. The microspheres can be selected from the group consisting of solid microspheres, porous microspheres, and degradable microspheres. The location can be within a vertebral body.
Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. Although methods and materials similar or equivalent to those described herein can be used to practice the invention, suitable methods and materials are described below. All publications, patent applications, patents, and other references mentioned herein are incorporated by reference in their entirety. In case of conflict, the present specification, including definitions, will control. In addition, the materials, methods, and examples are illustrative only and not intended to be limiting.
The details of one or more embodiments of the invention are set forth in the accompanying drawings and the description below. Other features, objects, and advantages of the invention will be apparent from the description and drawings, and from the claims.
This document provides materials and methods related to tissue scaffolds for use in replacing or augmenting various tissues in the body. For example, flexible tissue scaffolds with controlled pore geometry and methods of enhancing solute transport using rhythmic compression (e.g., 1.0 Hz) of tissue scaffolds are provided.
A tissue scaffold can be an artificial structure capable of supporting three-dimensional tissue formation. Any appropriate mechanically deformable material can be used as a tissue scaffold (e.g., a variety of natural, synthetic, and biosynthetic polymers). In some cases, a tissue scaffold can comprise a biodegradable, crosslinkable, and/or biocompatible polymer (e.g., Poly(esters) based on polylactide (PLA), polyglycolide (PGA), polycaprolactone (PCL), and their copolymers).
Any appropriate cross-linking agent can be used to form chemical links between molecule chains to form a three-dimensional tissue scaffold. For example, crosslinked PPF and PCLF have distinct characteristics resulting from different densities of crosslinkable moieties on the polymer backbones. Crosslinked PPF can have an average tensile modulus E=1.3 GPa while crosslinked PCLF can have an average tensile modulus E=2.1 MPa. Material properties, particularly mechanical properties, can be modulated through varying the composition of polymer components of the scaffold materials. PPF/PCLF blends with PPF weight composition of about 25% and PCLF composition of about 75% can be used to manufacture deformable scaffolds as described herein.
Deformable scaffolds with programmed flow channel geometries can be fabricated using a solid freeform fabrication (SFF) technique, such as a combination of three-dimensional printing and injection molding as described elsewhere (Lee et al., Tissue Eng, 12: 2801-2811 (2006)). For example, SFF can include designing an injection mold using computer-aided design (CAD) software, three-dimensional printing of the mold, injecting and cross-linking of an elastic (biodegradable/biocompatible) polymer into the mold, and removing the mold material by mechanical, thermal, or chemical treatment without affecting the polymer of interest. The CAD files can be used to generate temporary negative molds, which are injected with a biodegradable polymer to cast a tissue scaffold. In some cases, SFF methods can be used to create synthetic scaffolds featuring interconnected pores and programmed pore geometries. Tissue scaffolds featuring complex pore structures e.g., interconnected channels, tortuous (non-straight) channels, and pores with different shapes can be manufactured using the methods and materials provided herein. In some cases, such complex pore structures can be obtained using solid spheres, porous microspheres, and/or degradable microspheres.
SFF methods can be used to maintain the mechanical strength of a tissue scaffold (e.g., by controlling porosity), and permit mechanical properties (e.g., stiffness, yield limit, etc.) to be tailored for specific applications. For example, SFF methods can be used to fabricate a scaffold capable of acting as a load bearing structure during tissue regrowth (e.g., knee cartilage, vascular, or cardiac tissue). In some cases, scaffold fabrication methods can be automated.
During fabrication, a porous tissue scaffold can be embedded with magnetic particles (e.g., ferromagnetic or paramagnetic particles). For example, scaffolds embedded with magnetic particles can form actuable structures. In some cases, such scaffolds can be deformed remotely by application of a magnetic field. See, e.g., Cox et al., U.S. Pat. Pub. No. 2007/0151202 and Mack et al., J. Mater. Sci., 42: 6139-6147 (2007).
Acellular tissue scaffolds or cell-populated tissue scaffolds can be used with the methods described herein. In some cases, a tissue scaffold can be seeded with a population of cells before implantation. Any appropriate cell type, such as naïve or undifferentiated cell types, can be used to seed a tissue scaffold. For example, a population of cells (e.g., stem cells, cardiomyocytes, myocytes, osteocytes, fibroblasts, glia, or preadipocytes) can be cultured on a tissue scaffold. In some cases, autologous stem cells from any tissue source (e.g., skin, bone, synovium, fat, marrow, or muscle) can be used. Any appropriate method for isolating and collected cells for seeding can be used.
Upon fabrication of a tissue scaffold, the polymer material can be embedded with bioactive molecules, e.g., to be transported into surrounding tissue, or distributed to cells inside a scaffold. Bioactive agents can promote wound healing and/or angiogenesis in and around an implanted tissue scaffold, for example. Appropriate bioactive agents can include polypeptides (e.g., growth factors ((VEGF), transforming growth factor-β (TFG-β), and fibroblast growth factor (FGF)), cytokines, and antibodies), antimicrobial agents (e.g., antibiotics and antifungal agents), analgesic/anti-inflammatory agents (e.g., NSAIDs and steroidal agents), immunomodulators (e.g., cyclosporine and interferon), and/or local anesthetics (e.g., lidocaine and procaine), which can be embedded in the scaffold. See, e.g., Rocha et al., Biomaterials 29: 2884-2890 (2008). In some cases, polypeptides or other signal molecules can be released by cells (e.g., engineered cells) embedded in the scaffold (e.g., gene therapy). See, e.g., El-Ayoubi et al., Tissue Eng, Part A (2008). Transport of embedded agents can be enhanced by cyclical distortion of a tissue scaffold. In some cases, the geometry of tissue scaffold pores can be tailored to yield a specific transport pattern of an embedded agent. Repetitive deformation of a tissue scaffold can augment solute transport as compared to a static tissue scaffold (i.e., a scaffold under conditions of diffusional transport). See e.g., Op Den Buijs et al., “High resolution X-ray imaging of dynamic solute transport in cyclically deformed porous tissue scaffolds,” SPIE Medical Imaging: Physiology, Function and Structure from Medical Images, San Diego, Calif., 2008. For example, a tissue scaffold with one or more pores can be subjected to a cyclically varying load (e.g., rhythmic compressions or other deformations). In some cases, a cyclic load can be the result of intrinsic rhythmic deformation of the surrounding tissue (e.g., beating of the heart, pulsation of arteries, peristaltic motion of the intestines, periodic knee cartilage loading during walking, and muscle contraction/relaxation cycles), or repetitive mechanical forces applied external to a part of the body in close proximity to an implantation site. The mechanical distortion of the tissue surrounding a tissue scaffold can be induced by forms of rehabilitation therapy (e.g., massage therapy, exercise, and/or electrical muscle stimulation). See, e.g., Goats, Br J Sports Med 28: 153-156 (1994) and U.S. Pat. App. Pub. No. 2007/0270917. Cyclic loading can cause a corresponding rhythmic distortion of the pores of a tissue scaffold, resulting in a cyclic motion of fluid present within the scaffold pores.
In some cases, the cyclic fluid flow can enhance the dynamic mixing of components in the surrounding interstitial fluid or blood to bring nutrients closer to the scaffold inlets, and pump waste products outside a tissue scaffold. For example, during the part of the loading cycle in which the pore volume effectively decreases (i.e., during compression or stretching), fluid containing waste products of cells and possibly toxic degradation products of the scaffold material present in the scaffold pores can be squeezed out of the scaffold pores and mixed with the interstitial fluid (or blood) surrounding a tissue scaffold. Upon subsequent recoil of the scaffold to its original shape, ‘fresh’ fluid with no (or a low concentration of) waste products can flow back into the scaffold pore, thereby decreasing the concentration of waste and degradation products in the fluid inside the scaffold pores. During the part of the loading cycle in which the pore volume effectively increases (i.e., during recoil after compression or stretching), interstitial fluid rich in nutrients and oxygen can be transported from the surrounding tissue (or blood) into the scaffold. This fluid can mix with the nutrient- and oxygen-deficient fluid inside the scaffold pores, thereby increasing the concentration of nutrients and oxygen in the fluid inside the scaffold pores.
Solute convection due to rhythmic pore deformation and the resulting cyclic fluid motion can be related to the geometry of the pores. For example, different pore geometries can lead to different effective pore volume changes during the cyclic loading, even when the same amount of deformation is applied. The cross-sectional shape of the pores (e.g., a circular cross-section vs. an elliptical cross-section), the diameter of the pore cross-sectional area, the orientation of cross-sectional asymmetries with respect to the direction of the cyclic strain, and any interconnections between pores, can influence convective solute transport. The pore geometry can be tailored to yield the specific nutrient transport rates and depths, as required by the application of a tissue scaffold.
In symmetric flow channels, such as cylinders with circular or elliptic cross-sections that have constant diameters along the channel, cyclic pumping of a scaffold can induce a bi-directional motion of fluid in the flow channels, thereby enhancing the spreading and mixing of nutrients and waste products as described above. In some cases, a combination of cone-shaped channels and cylindrical or spherical pumping chambers can be created to alter the direction of flow. For example, upon cyclic compression (>1.0 Hz) fluid can be preferentially pumped in one direction, thereby resulting in a frequency-dependent net fluid flow across the scaffold. The unidirectional fluid flow can transport solutes deeper into a tissue scaffolds and/or obtain spatially uniform distribution of solutes. In some cases, unidirectional flow can oppose physiological conditions restricting flow in a tissue scaffold, to pump the nutrients from the source deep into a tissue scaffold (e.g., more than 1.0 mm from the surface of the tissue scaffold).
Any mammal can have a tissue scaffold implanted for supporting tissue growth using the materials and methods provided herein. For example, a human, mouse, cat, dog, or horse can have a tissue scaffold that supports tissue growth implanted for regeneration or support of a damaged tissue. Any appropriate tissue can be replaced using the methods and materials described herein. Mechanically active tissues that are appropriate for tissue-engineering using deformable scaffolds include blood vessels, cardiac muscle and heart valves, bone and cartilage, tendons and ligaments, nerves, adipose tissue (e.g., for breast augmentation or restoration after mastectomy), and periodontal structures. For example, many tissues (e.g., knee cartilage, tendons, cardiac and vascular tissues) undergo forms of cyclic loading with strains up to about 30% (e.g., about 5-10%, 10-20%, and 20-30%). See, e.g., (Teske et al., Cardiovasc. Ultrasound, 5: 27 (2007); Bingham et al., Rheumatology 47(11):1622-1627 (2008); Liang et al., J. Biomech., 41(14):2906-2911 (2008); and, Stafilidis et al., Eur. J. Appl. Physiol., 94: 317-322 (2005). Strains of these magnitudes can induce significant solute convection in scaffolds used to replace or support such tissues with appropriate pore geometry. In some cases, deformable scaffolds can be appropriate for insulin delivery systems in diabetic patients.
In some cases, a tissue scaffold can be injected into a mammal. For example, a tissue scaffold can be injected in liquid form into an intended location of a mammal. Any appropriate bodily organ or tissue of a mammal can be injected according to the methods and materials described herein. For example, bone can be injected with an injectable tissue scaffold. In some cases, an injectable tissue scaffold can produce scaffolds that have interconnected pores suitable for maintaining viable cells. In some cases, an injectable tissue scaffold can be ultimately replaced by ingrowing tissue.
Any appropriate technique can be used to measure mechanical deformation of a tissue scaffold in vitro or an implanted tissue scaffold in vivo. Mechanical strain induced by compression can be measured in vivo using imaging systems such as ultrasound and magnetic resonance. Three dimensional micro-CT or cryostatic micro-CT as described elsewhere (Kantor et al., Scanning 24: 186-190 (2002)) can be used to image compression-induced deformation of a tissue scaffold in vitro.
Any appropriate technique can be used to quantify fluid flow in a tissue scaffold. The term “enhanced” as used herein with respect to solute transport is any transport that is increased relative to passive transport of a solute (e.g., diffusion) in a biological fluid (e.g., plasma). Enhanced solute transport can have an increased rate and/or increased depth of solute transport (e.g., to scaffold depths>0.1 mm). In some cases, an enhanced level of solute transport can be any detectable level of solute transport.
Measurement of solute transport in vivo can be simulated in an experimental setting in vitro. For example, the rate and depth of solute transport can be measured using a contrast agent to simulate a solute in a biological fluid. In addition to the methods described above, an X-ray system with a spectroscopic X-ray source and a detector can provide information about fluid dynamics in a tissue scaffold in vitro. In some cases, physiologically equivalent compressions (e.g., 1.0 Hz) can be simulated using a compression device to induce deformations in a scaffold in a fluid reservoir and X-ray images collected over time can be analyzed to provide rate and depth of solute transport in a tissue scaffold with and without cyclic compressions.
Solute transport can also be determined by assessing ingrowth of cells and microvessels into deep layers of a tissue scaffold. For example, a tissue scaffolds can be seeded with cells in vitro and imaged (e.g., using fluorescent microscopy) at specific intervals during cell culture (e.g., at T=0, 5, 10, and 20 days). In some cases, a tissue scaffold as described herein can support a population of cells at a greater depth from a scaffold surface and/or for a longer period of time in culture than the same cell-type seeded on a corresponding tissue scaffold that is not subjected to cyclic compressions (e.g., deeper than about 200 μm and/or more than 21 days).
The invention will be further described in the following examples, which do not limit the scope of the invention described in the claims.
An X-ray based imaging method to quantify solute transport induced by mechanical compression at 20 μm pixel resolution was developed and applied to flexible biodegradable scaffolds with a controlled pore structure. Using a contrast agent as a surrogate for non-radiopaque nutritional solutes (Jorgensen et al., Am. J. Physiol. Heart Circ. Physiol., 275: H1103-H1114 (1998)), this technique was used to image opaque specimens at micrometer spatial resolution, and collect quantitative information about the local concentration of an X-ray absorbing contrast agent.
Scaffold Material
Polypropylene fumarate (PPF) and polycaprolactone fumarate (PCLF) are biodegradable, crosslinkable, and biocompatible. Peter et al., J. Biomed. Mater. Res., 41: 1-7 (1998); Yaszemski et al., Biomaterials, 17: 2127-2130 (1996); and, Jabbari et al., Biomacromolecules, 6: 2503-2511 (2005). Crosslinked PPF and PCLF have distinct characteristics because of different density of crosslinkable segment on the polymer backbone. Crosslinked PPF is a stiff material with an average tensile modulus E of 1.3 GPa while crosslinked PCLF is a flexible material with E=2.1 MPa. PPF is a promising candidate injectable biomaterial to substitute autologous or allograft bone, especially for load-bearing purposes. PCLF can be used to fabricate single-lumen and multi-channel tubes for guiding axon growth in peripheral nerve repair. Material properties, particularly mechanical properties, can be efficiently modulated through varying the composition of PPF in PPF/PCLF blends. See, e.g., Wang et al., Biomacromolecules, 9(4): 1229-1241 (2008).
PPF with a number-average molecular weight (Mn) of 3460 g/mol and a weight-average molecular weight (Mw) of 7910 g/mol and PCLF with an Mn of 3520 g/mol and an Mw of 6050 g/mol were used to prepare PPF/PCLF blends. One PPF/PCLF blend with PPF weight composition of 25% and PCLF composition of 75% was prepared by first dissolving PPF and PCLF sufficiently in a co-solvent methylene chloride (CH2Cl2) and then evaporating the solvent in a vacuum oven. PPF and PCLF were polymerized in our laboratory (as described in Wang et al., Biomacromolecules, 7: 1976-1982 (2006). The PCLF sample was synthesized using α,ω-telechelic PCL diol with a nominal Mn of 530 g/mol and fumaryl chloride in the presence of potassium carbonate (as described in Wang et al., Biomaterials, 27: 832-841 (2006)).
Scaffold Fabrication
Biodegradable scaffolds with a programmable pore structure were fabricated (as described elsewhere (Lee et al., Tissue Eng, 12: 2801-2811 (2006)). Computer-aided design (CAD) models were created using Solidworks (SolidWorks Corp., Concord, Mass.), meshed into stereolithography (STL) files, and converted to 2D sliced data files with a thickness of 76 μm using the ModelWorks software (Solidscape Corp., Merrimack, N.H.). The 3D phase-change ink jet printer, PatternMaster, was used to create 3D scaffolds by printing PTM files layer-by-layer with a build material (polystyrene) and a support material (wax). After printing, the polystyrene was dissolved by immersing the printed scaffolds into acetone for 30 minutes to obtain wax molds (
Experimental Setup
To manufacture the scaffolds, a CAD-based cubic mold (5.0 mm on the side) with a 1.0 mm channel in the middle was generated. After crosslinking, the polymer slightly shrunk and the final scaffold had dimensions 3.1 mm on a side and the channel diameter was 0.56 mm. The scaffold was glued to the bottom of a fluid reservoir placed underneath the loading platen of a custom-made compression device. The setup was mounted inside a custom-made X-ray scanner (
Projection X-Ray Imaging
The specimens were scanned in a X-ray system consisting of a spectroscopy X-ray source with a molybdenum anode and zirconium foil filter so that the Kalpha emission radiation (17.5 keV) photons predominate in the emitted X-ray spectrum. The specimen's X-ray image was converted into a light image in a Terbium doped fiber optic glass plate and this image was recorded on a Charge Coupled Device (CCD) array, consisting of 1340×1300 pixels with a 20 μm on-a-side pixel resolution. Specimens were placed at 15 mm from the detector and the distance between X-ray source and detector was 485 mm. X-ray exposure time was 5.0 seconds, a scintillator decay time of 0.5 seconds was allowed, and the maximal shutter operation delay was set at 0.2 seconds. The compression device was switched on and off from outside the lead scanner-housing.
Because an exposure time of several seconds was required to generate adequate images, the cyclic compression was intermittently paused after different numbers of compression cycles to allow imaging of the dye distribution. Taking into account the image time as well as time delays caused by the shutter operation, scintillator decay allowance, and turning on and off of the compression apparatus, the delay between subsequent compression intervals was estimated to be no more than 10 seconds.
Image Analysis
For a given spatial coordinate in the image, the transmitted X-ray intensity I is given by:
where I0 is the incident X-ray intensity, μi is the linear attenuation coefficient of material i and xi is the thickness of material i along the X-ray beam. The attenuation was due to the diluted contrast agent in the scaffold channel, the polymer material that the scaffold is made of, and the glycerin in the fluid reservoir. Equation 1 can therefore be written as:
The attenuation due to the NaI (μcontrast agentχchannel) can be calculated by subtracting the baseline attenuation (i.e., without NaI present) from the negative logarithm of the measured intensity. In a region of interest (ROI) containing the channel (obtained by manual segmentation), the average attenuation was calculated. Under the assumption that the attenuation coefficient of the NaI/glycerin solution is approximately linear to the NaI concentration, the average NaI concentration in the scaffold channel was calculated relative to the average concentration right after injection of NaI in the channel.
Projection X-ray images with a pixel-resolution of 20 μm show the removal of the contrast agent NaI from the scaffold channel, as caused by passive removal or removal induced by consecutive cycles of deformation of the scaffold (
The channel boundaries were defined by manual segmentation and the average NaI concentration inside the channel was calculated as the average attenuation due to iodide. The average NaI concentration was normalized with respect to the NaI concentration after injection. Spatial profiles of the fraction of NaI left in the channel after 0, 25, 50, 100 and 300 cycles of compression (
y=A exp(−k1t)+(1−A)exp(−k2t) (3)
This function with two rate constants k1 and k2 could be well fitted to the data (
A delay of 10 seconds was added to each measurement point in the time-curve of the compression-induced transport to account for the imaging time (
In this study, dynamic transport of an X-ray contrast agent inside a cyclically deforming porous scaffold was imaged using high-resolution projection X-ray imaging. The current experiment models the transport of nutrients and/or oxygen inside the pore system of a dynamically compressed tissue scaffold. The X-ray imaging methodology described herein offers a means for the experimental validation of theoretical predictions. Using high-resolution X-ray imaging, the pore geometry and quantify local solute concentrations were visualized. In addition, transient alterations in the concentration profile during mechanical deformation of the scaffold were imaged.
The influence of pore geometry on solute transport in tissue scaffolds during cycles of mechanical compression and release was investigated by means of experimental data and numerical modeling. (
Using the boundary conditions as shown in
To describe the deformation of the scaffold, a dynamic small-strain problem was considered with a linear Hooke's law as constitutive equation. The following equation describing change in momentum for the scaffold material was used:
where σy, σy and σz are the normal stresses, and τxy, τxz and τyz are the shear stresses. Furthermore, ρs is the density of the scaffold material, and us, vs and ws are the displacements of a material point in the deforming scaffold. Small deformations were considered using a linear strain-displacement relationship:
Here εx, εy and εz are the normal strains, and γx,y, γxz and γyz are the engineering shear strains. Assuming linear, isotropic elastic behavior, the relation between stress and strain in the scaffold is described by Hooke's law:
where E is the Young's modulus of the scaffold material and v is the Poisson's ratio of the scaffold material. Fluid pressure and velocity of the fluid phase are described by the Navier-Stokes equations. The continuity equation is given by:
where ρf is the fluid density, and uf, vf and wf are the fluid velocity components. Density differences in time and space could occur due to mixing of the fluid with the X-ray contrast agent. Laminar flow of a Newtonian fluid with viscosity μ was considered. The following momentum balance of the Navier-Stokes equation was used:
where p is the fluid pressure, ρf,0 is the density of the fluid without contrast agent and g is the gravitation constant.
Solute transport was modeled by the scalar convection-diffusion equation:
where C is the concentration of X-ray contrast agent in the fluid and D the diffusion coefficient. The fluid density is dependent on the concentration of contrast agent:
ρf=ρf,0+C (10)
The commercial software ANSYS Workbench 11.0 (Ansys Inc., Canonsburg, Pa.) was used to obtain numerical solutions.
Tissue engineering frequently utilizes porous scaffolds. One use of scaffolds is to cultivate cells on the scaffold in vitro and subsequently implant the construct in vivo. Prior to implantation, bioreactors may be used to perfuse the engineered tissue as to provide cells beyond the diffusion distance with the essential oxygen and nutrients, and to remove toxic waste as a result of cell metabolism and scaffold degradation. Mygind et al., Biomaterials 28: 1036-1047 (2007); Carrier et al., Tissue Eng 8: 175-188 (2002). A functional failure of the implant can occur due to chemotaxis and/or necrosis of cells beyond the diffusion distance. For example, as lack of proper mass transport beyond the diffusional distance after application in vivo can decrease cell density from the periphery to the center of the construct. See, e.g., Karande et al., Ann. Biomed. Eng., 32: 1728-1743 (2004); Ramrattan et al., Tissue Eng., 11: 1212-1223 (2005); and, Silva et al., Biomaterials, 27: 5909-5917 (2006). Where acelluar scaffolds are implanted, infiltration of cells and microvessels into deep layers of the scaffold depends on adequate rate of solute transport. Under static conditions, nutrient transfer is governed by diffusion, i.e. transport driven by a concentration gradient. Diffusive transport is relatively slow (e.g., Fermor et al., Eur. Cell. Mater., 13: 56-65 (2007), reported diffusivities of approximately 2.5·×10−7 cm2/s for uncharged dextrans in the surface zone of cartilage) and generally accounts for supplying cells at a depth of only a few hundred micrometers from the surface within a reasonable time. See, e.g., Brown et al., Biotechnol. Bioeng., 97: 962-975 (2007).
Solute transport induced by mechanical compression in cubic imaging phantoms with a range of selected pore geometries, representing simplified tissue engineering scaffolds was quantified. Deformable, biodegradable specimens with programmable pore cross-sectional shapes were fabricated using a 3D printing and injection molding technique as described in Examples 1 and 2. The imaging phantoms were immersed in fluid, loaded with an X-ray absorbing dye, and mechanically compressed inside a custom-made X-ray micro scanner. The recorded X-ray images were quantitatively analyzed as to the rate and spatial distribution of solute transport in the porous phantoms.
Scaffold and Pore Geometry
Scaffolds comprising PPF/PCLF were fabricated as described in Example 1. Cubic injection molds (5.0 mm on a side) were printed, such that imaging phantoms with pores consisting of a single channel through the middle of the specimen were generated. Pores with the following cross-sectional and longitudinal shapes were designed: circular cylinder, elliptic cylinder, and spheroid. Five specimens were generated for each shape. After crosslinking of the polymer in the mold, the final dimensions were slightly altered compared to the original design, presumably due to shrinkage of the polymer. The phantoms were scanned in air (no fluid and/or contrast agent present) with micro-CT at 20 μm voxel resolution using a custom-made X-ray imaging system to determine the dimensions accurately. No swelling or shrinking of the specimens after immersion in fluid was observed.
Experimental Setup
Experiments were carried out at room temperature. The imaging phantoms were glued to the bottom of a fluid reservoir placed underneath the loading platen of a custom-made compression device. The setup was mounted inside a custom-made high-resolution X-ray imager (
where H0 and H are the phantom height at rest and upon maximal compression respectively. The compression rate was set at 1.0 Hz.
Projection X-Ray Imaging Protocol
The specimens were imaged in a custom-made high-resolution X-ray system as described in Example 1. The pixel size in the X-ray image was 20 μm, so that the spatial resolution is approximately 40 μm and, hence, pore diameter differences of ˜500 μm can be resolved. Specimens were placed at 5.5 cm from the detector and the distance between X-ray source and detector was 98.5 cm. X-ray exposure time was 5.0 seconds and a scintillator decay time of 0.5 seconds was allowed for. The compression device was switched on and off from outside the lead-lined scanner-housing. Images of the fluid filled specimens were recorded before and right after injection of the contrast agent. During ‘passive’ experiments (compression turned off), images were recorded after 1, 3, 5 and 10 minutes. During ‘active’ experiments (compression turned on) images were recorded after 5, 10, . . . , 50, 75, 100, 150, 200 and 300 compression cycles, by temporarily pausing the cyclic compression during the imaging time of 5.7 seconds, with the specimen in the uncompressed state. The total imaging time was less than 2 minutes per experiment. The contribution of passive removal was expected to be less than 10% to the total solute transport.
Image Analysis
The transmitted X-ray intensity I at each pixel is given by Equation 1, where I0 is the incident X-ray intensity, μi is the linear attenuation coefficient of material i and xi is the thickness of material i along the X-ray beam illuminating the pixel after passing through the imaging phantom. The total X-ray attenuation is mainly due to the iodine in the channel, the polymer material that the specimen is made of, and the glycerol in the surrounding fluid reservoir. The attenuation due to iodine in the pore was calculated by subtracting the attenuation before contrast agent injection from the attenuation measured with iodine present in the pore. The average attenuation due to iodine was obtained by averaging the attenuation over the entire pore volume. Under the assumption that the attenuation coefficient of the iodine is linearly proportional to the iodine concentration (because the pore dimension remains unchanged in between compressions), the average iodine concentration in the channel was calculated as a fraction of the average iodine concentration calculated immediately after injection.
Statistical Analysis
To compare the results of the image analysis, the remaining fraction of iodine (as measured after 300 seconds of passive removal or after 300 compression cycles at 1.0 Hz) was evaluated with one-way analysis of variance (ANOVA). This fraction was calculated in specimens with different channel shapes and compared with the 0.5 mm circular cylindrical channel by a Tukey-Kramer honestly significant difference test (#: P<0.05). For each channel shape, the effect of passive and deformation-induced transport was compared by a two-tailed t-test (*: P<0.05).
Scaffold Pore Geometry
Representative micro-CT images (20 μm voxel resolution) of the specimens are shown in
Scaffold Compression
On average, the percentage of scaffold compression was 8.6±1.6% of the original specimen height and not significantly different among the different scaffolds as tested by ANOVA. Thus, the scaffold compression amplitude did not depend on the pore shape. For the circular cylindrical channels with different diameters, the percentage of compression of the channel decreased with increasing diameter (Table 2).
#significantly different from 0.5 mm (P < 0.05).
Solute Transport
Projection X-ray images show the removal of the iodine from the scaffold channel, as caused by passive removal or removal induced by consecutive cycles of deformation of the scaffold (
The average iodine concentration inside the channel was calculated relative to the iodine concentration right after injection. This quantitative analysis shows the effect of the pore shape on the removal rate during compression cycles (
To illustrate the spatial distribution of solute transport in the different scaffold types, images recorded right after iodine injection were subtracted from images recorded after 300 compression cycles (
Dynamic transport of an X-ray tracer inside cyclically deformed imaging phantoms with designed pore geometries, mimicking porous tissue scaffolds, was imaged using an X-ray micro imaging technique. These results show that solute transport rates and depths can be significantly influenced by the shape of the pore, its dimension, and the orientation of its cross-section with respect to the direction of the cyclic strain. For example, increasing the diameter of the circular cylindrical channels from 0.5 mm to 1.5 mm slightly decreased the deformation induced solute transport rates, which correlated with the decreased percentage of channel compression of the 1.5 mm channel. The increased passive removal in the 2.0 mm diameter channel as compared to the 0.5 mm channel most likely compensated for this effect. The spheroidal channel showed the slowest transport rates during both passive removal and compression-induced removal. This can be attributed to its relatively large volume compared to its smaller cross-section exposed to the surrounding fluid reservoir. The elliptic cylinder with its major axis perpendicular to the direction of compression was highly collapsible and therefore yielded a high solute transport rate under cyclic compression. In contrast, when its major axis was in parallel with the direction of compression, solute transport was significantly reduced, indicating the strong influence of pore orientation compared to direction of strain.
Limited mass transport currently hinders the development of thick tissue-engineered implants and oxygen (O2) is one of the most important metabolic substrate to be transported to the cells inside the scaffolds to maintain normal cell function. Sensitivity to hypoxia varies among cells: 40% of cells cultured under hypoxia do not survive after ˜5 days for endothelial cells, after ˜12 hours for cardiomyocytes, and after only ˜2 hours for preadipocytes (for adipose tissue engineering). See, e.g., Dore-Duffy et al., Microvasc Res, 57: 75-85 (1999); Mehrhof et al., Circulation, 104: 2088-2094 (2001); and, Patrick et al., Semin. Surg. Oncol., 19: 302-311 (2000). To sustain viable cells inside the scaffolds, O2 transport rate must match rate of O2 consumption (e.g., 1 to 10 nmol O2/min/106 cells as described in Petit et al., Mitochondrion, 5: 154-161 (2005) and Casey et al., Circulation, 102: 3124-3129 (2000). The present results indicate that the time to reach 37% of the initial iodine (as a surrogate for O2) concentration for the elliptic pore compressed along its semi-minor axis was approximately 1 minute (
This is still one to two orders of magnitude lower than cell densities in most human vascularized tissues; however, cyclic strain may induce sufficient temporary convective nutrient transport to maintain viable cells while ingrowth of microvessels proceeds after implantation of the scaffold. Even more, although solute convection dominates transport in these experiments, the diffusion coefficient of O2 in aqueous solution is likely higher as compared to NaI in glycerol due to lower solvent viscosity and lower molecular weight (32 g/mol for O2 vs. 149.9 g/mol for NaI), which could increase the sustainable cell density.
Increased convective transport properties of the scaffold will trade off with its ability to provide temporary mechanical support at the site of implantation. Pores with elliptical cross-section oriented with the semi-minor axis along the strain direction can yield high transport rates, but the effective scaffold stiffness will be lower than when a pore with e.g., a circular cross-section is used. The solid freeform technique used in this study allows the fabrication of scaffolds with programmable pore labyrinths.
Although pore diameters of the imaging phantoms ranged from 370 μm to 1.91 mm, these results can be relevant for pores with smaller dimensions. ‘Optimal’ pore sizes for tissue engineering scaffolds have been suggested to lie between 100 and 500 μm, depending on the cell type. See, e.g., Ikada et al., J. R. Soc. Interface, 3: 589-601 (2006). Bone ingrowth has been demonstrated in scaffolds with pore sizes greater than 1.0 mm as manufactured by SFF or a combination of phase-inversion and particulate extraction as described in Hollister et al., Orthod. Craniofac. Res., 8: 162-173 (2005) and Holy et al., J Biomed Mater Res, A65: 447-453 (2003).
‘Scaffolds’ with simple pores comprised of single straight channels with various shapes were used, whereas more realistic scaffolds would have pore labyrinths comprised of interconnected channels in three dimensions. Using the described scaffold fabrication technique, more complex pore structures can be manufactured.
The results demonstrate that shape, size, and orientation of pores in a tissue scaffold have great effects on solute transport during cyclic mechanical deformation. This has implications for the design of the pore system of thick, deformable implants in which enhanced solute transport rates are desired to facilitate tissue ingrowth. Additionally, pore geometry may be adjusted to achieve ideal release constants in deformable porous drug delivery systems.
Imaging experiments with phantoms representing simple tissue scaffolds were conducted to investigate the influence of pore cross-sectional geometry, flow channel diameter, pore cross-sectional alignment with respect to the main strain direction and the presence of interconnections on the rate of outward transport of a tracer (as a surrogate for waste products). Flexible cubic scaffolds with side dimensions of ˜5 mm were generated with a range of programmed pore geometries using a combined 3D printing and injection molding technique. The scaffolds were cyclically compressed with amplitudes of ˜10-15% of the scaffold height at 1.0 Hz. The (unconfined) compression was applied at the top face of the scaffold while the scaffold was immersed in a fluid reservoir. The pores of the scaffold were loaded with a contrast agent for X-ray or optical contrast, and the removal of the contrast agent as a result of cyclic pumping was quantified. The assumption is made that outward transport (e.g., by waste products) is the opposite of inward transport (e.g., by nutrients and oxygen). These data suggest that scaffold pore geometry can be modified to control the solute transport rate induced by cyclic loading of the scaffold (
Effect of Interconnections Between Pores
Possibility of Directional Flow
Investigations with computational fluid dynamics towards the possibility to induce a net fluid flow through the scaffold upon cyclic compression were performed. The concept consists of a pumping chamber connected to two nozzle-diffuser type channels (
Experiments were conducted to develop a computational model of deformation-induced solute transport in porous tissue scaffolds, which included the pore geometry of the scaffold. This geometry consisted of a cubic scaffold with single channel in the middle of the scaffold, immersed in a fluid reservoir.
X-Ray Experiments
Experiments were described in Op Den Buijs et al., (Tissue Eng Part A 15:1989-99, (2009)). In brief, flexible cubic scaffolds were fabricated from a biodegradable polymer blend (75% polycaprolactone fumarate and 25% polypropylene fumarate) using a combined 3D printing and injection molding technique. Cubic injection molds were printed, such that scaffolds with pores consisting of a single channel through the middle of the specimen could be generated. Pores with the following cross-sectional and longitudinal shapes were designed: circular cylinder, elliptic cylinder and spheroid (5 specimens per shape). After fabrication, the scaffolds were scanned with micro-CT at 20 μm isotropic voxel resolution, to obtain their final dimensions. The imaging phantoms were attached to the bottom of a fluid reservoir placed underneath the loading platen of a custom-made compression device. The specimens were loaded with a solution of the radiopaque solute sodium iodide dissolved in glycerin (31 mg ml−1). The solute distribution was quantified by recording 20 μm pixel-resolution images in an X-ray micro-imaging scanner at selected time points after intervals of dynamic straining with a mean strain of 8.6±1.6% at 1.0 Hz.
One aim of the computational model was to represent the experiment depicted in
Model Equations
The model equations are partial differential equations, describing the physical problem in temporal and 3D spatial dimensions, where t is time and x, y and z are the spatial coordinates.
Scaffold Deformation
To describe the deformation of the scaffold, a dynamic small-strain problem was considered with a linear Hooke's law as constitutive equation. Neglecting external body forces on the scaffold material, the equation describing change in momentum for the scaffold material was given by
where σx, σy and σz are the normal stresses, and τxy, τxz and τyz are the shear stresses. Furthermore, ρs is the density of the scaffold material, and us, vs and ws are the displacements of a material point in the deforming scaffold. Small deformations were considered, and the relation between the strains and the displacements using the linear relationships was described as
Here εx, εy and εz are the normal strains, and γxy, γxz and γy, are the engineering shear strains. Assuming linear, isotropic elastic behavior, the relation between stress and strain in the scaffold was described by Hooke's law:
where E is the Young's modulus and v is the Poisson's ratio of the scaffold material.
Fluid Motion
Fluid pressure and velocity of the fluid phase were described by the Navier-Stokes equations. The continuity equation was given by:
where ρf is the fluid density, and uf, vf and wf are the fluid velocity components. It should be noted that, although the fluid was assumed to be incompressible, density differences in time and space could occur due to mixing of the fluid with the X-ray contrast agent. Furthermore, laminar flow of a Newtonian fluid with viscosity μ was described including a buoyancy source term to model density differences due to mixing with the X-ray absorbing contrast agent, which has a higher density. The momentum balance of the Navier-Stokes equation was given by:
where p is the fluid pressure, pf,0 is the density of the fluid without contrast agent and g is the gravitation constant.
Solute Transport
Finally, solute transport was governed by the scalar convection-diffusion equation:
where C is the concentration of X-ray contrast agent in the fluid and D is the diffusion coefficient. The fluid density was dependent on the concentration of contrast agent (in density units, [g cm−3]):
ρf=ρf,0+C (19)
Model Geometry and Mesh
Consistent with the scaffold geometries obtained by micro-CT, cubic scaffolds with dimensions 4.5×4.5×4.5 mm3 containing single channels in the middle were modeled. Three different type channels were modeled (
To reduce computational time, model symmetry was used. One symmetry plane was in the middle of the scaffold and perpendicular to the channel axis, and one symmetry plane was in the middle of the scaffold and parallel to the channel axis. Hence, only a quarter of the scaffold was modeled. To take into account the fluid surrounding the scaffold, a box was modeled with an interface to the channel domain. The model dimensions of this fluid reservoir were 4.5×2.25×2.25 mm3 (height×width×depth).
Both solid and fluid phases were meshed with tetrahedral elements. In the solid mesh, a refinement towards the fluid-solid interface was included to obtain more accuracy in displacements near the channel wall. The two fluid domains (channel and reservoir) were separately meshed to allow for different initial conditions in these domains. In the reservoir, the elements were increased in size away from the channel into the fluid reservoir. Typical solid and fluid meshes are shown in
Boundary Conditions
An overview of boundary conditions can be found in
where A is the compression amplitude and f is the compression frequency.
The fluid phase (pores and fluid reservoir) was subjected to the following boundary conditions:
Initial Conditions and Model Parameters
At t=0, the scaffold was assumed to be at rest and the fluid pressure and velocity were set to zero in the entire fluid domain. The concentration of solute was set to zero in the fluid reservoir and to C0 inside the channel. Model parameters are summarized in Table 4.
The diffusion coefficient of sodium iodine in glycerol was measured by carefully pouring a layer of the NaI glycerin solution in a vial containing glycerin only. This created a two-layer system, with NaI glycerin at the bottom. The upward diffusion of NaI from the bottom layer into the top layer was imaged using projection X-ray over a time period of 7 hours (
where C/C0 is the NaI concentration relative to the initial concentration in the bottom layer, and x is the absolute position with x0 the position of the two-layer interface. Furthermore, D is the diffusion coefficient, t is the time and erf is the error-function. D was calculated (8.0.10−8 cm2 s−1) using the Levenberg-Marquardt nonlinear least-squares curve fitting algorithm with both x0 and D as adjustable parameters (
Numerical Implementation
The commercial software ANSYS Workbench 11.0 (ANSYS Inc., Canonsburg, Pa.) was used to obtain numerical solutions. In this software, the dynamic solid deformation problem was solved using the Finite Element Method (FEM), whereas the Navier-Stokes and scalar transport equations were solved using the Finite Volume Method (FVM). At each time step, the solid deformation problem was solved first, and the mesh displacement at the fluid-solid interface was then transferred to the fluid solver as a boundary condition in the fluid flow problem. A fixed time step of t=0.025 s was found to be sufficiently small to obtain stable numerical results. Transient simulations were conducted until 100 s (simulation time) during cyclic compression or until 300 s without cyclic compression. The simulations were carried out on a 2.4 GHz AMD Opteron server with 16 GB memory running SUSE Linux 9. Computation time per run was approximately 5 hours.
Results
Passive Removal
Without application of compression, natural convection as a result of gravitation, more so than diffusion, slowly removes some of the denser contrast agent at the openings of the channel into the surrounding fluid reservoir. This effect is captured in the model by including the gravitational term in the momentum equation (Eq. 17).
Compression-Induced Removal
Upon application of 8.6% cyclic compression to the scaffolds at 1.0 Hz, the contrast agent inside the scaffold channel is dispersed into the surrounding fluid reservoir.
The model simulations were quantitatively compared to the experimental data by computing the average iodine concentration inside the pores.
The validated model was used to explore the effect of altering the diffusion coefficient D, the fluid viscosity μ and density ρf, and the maximum solute concentration C0 (Table 5). These simulations were carried out for the scaffold with the 1.0 mm circular pore with a compression of 8.6% at 1.0 Hz. For the diffusion coefficient, values that are typical for physiologically relevant solutes such as albumin, glucose, and oxygen were explored. As expected, higher diffusion coefficients resulted in lower solute concentrations at t=100 s, although this effect was found to be minimal. For the viscosity, we explored a range of values, among which those for plasma and blood. Interestingly, the solute removal did not appear to be sensitive to the viscosity for the range of values simulated. The model also appeared to be insensitive to neglecting the density difference caused by the initial solute concentration C0 as a result of the heavier X-ray tracer, and to reducing the fluid density to a value representative for water (instead of glycerol). Taken together, these simulations increase our confidence that the results obtained under the experimental conditions (using iodine in glycerol) are also relevant for physiological conditions (e.g., involving albumin, glucose or oxygen in water, plasma or blood).
These data demonstrate that a thoroughly validated computational model of fluid and mass transport in cyclically deforming scaffold pores can be developed. In the present study, a fluid-structure interaction model of solute transport in deformable scaffolds with pores of different shapes and dimensions was developed and validated. The model was in agreement with experimentally obtained X-ray imaging data of a contrast agent inside the pores of cyclically deformed biodegradable scaffolds. The significant impact of pore shape and orientation of the pore cross-section with respect to the direction of strain demonstrated that pore geometry is an important factor in a computational model of solute transport in the pores of deformable scaffolds. Considering the increasing use of rapid prototyping technologies to manufacture scaffolds with pre-designed pore architectures (see, e.g., Lu and Mikos, MRS Bull 21:28-32 (1996)), a geometry-based computational model of solute transport can accelerate iterative design processes of scaffolds by rapidly evaluating a number of designs in silica, thereby limiting the costly and time consuming experimental evaluation to only the most promising candidate pore architectures.
Previous models of cyclically compressed porous media that use the biphasic mixture theory generally incorporate the pore geometry into Darcy's permeability constant, which is a statistical average (Mauck et al., J. Biomech. Eng., 125:602-14 (2003); Gardiner et al., Comput. Methods Biomech. Biomed. Engin., 10:265-78 (2007); and Sengers et al., J. Biomech. Eng., 126:82-91 (2004)). Darcy's law can be used to relate the average fluid velocity uf through the scaffold to the pressure difference across the scaffold ΔP via the permeability constant K and the fluid viscosity μ:
The permeability K is a function of the scaffold pore architecture and porosity, and has proven a useful predictor for biological outcomes such as tissue ingrowth. For example, it was shown in cancellous bone grafts implanted in rabbits, that a threshold permeability exists, below which revascularisation and the formation of osteoblasts and fibrous tissues could not be attained (Hui et al., J. Biomech., 29:123-32 (1996)). High scaffold permeability as provided by well interconnected pores is suggested to be essential to provide the space for vascular tissue ingrowth followed by new tissue formation (Li et al., Biomaterials, 28:2810-20, (2007) and Mastrogiacomo et al., Biomaterials, 17:3230-7 (2006)). The use of a lumped parameter for permeability is computationally efficient, especially when dealing with scaffold pore geometries that are difficult to model, which is often the case in hydrogels or scaffolds fabricated using a particulate-leaching or gas-foaming method. However, with the emerging availability of solid freeform fabrication methods it becomes possible to program the scaffold pore geometry with computer-aided design (CAD) software (see, e.g., Hollister, Nat. Mater., 4:518-24 (2005)), such that the scaffold mass transport properties are reproducible and more accurately predictable at the pore level before actual fabrication of the scaffold. These accurate predictions require a thoroughly validated, three-dimensional numerical model of mass transport in the scaffold pores, incorporating the precise pore geometry from the initial CAD data. Such a model will allow for the rapid exploration of transport properties of a wide range of pore architectures before actual fabrication and experimental testing.
The current model contains several simplifications, which were made to reduce computation time and/or because additional parameters were lacking First, the scaffold deformation model pushes the limits of the small strain theory at the ˜10% strain used here. In addition, the scaffold material characteristics were assumed to be linear and isotropic, while a nonlinear stress-strain curve is often observed in polymers. If a more elaborate description of the mechanical behavior of the scaffold is desired, these limitations can be addressed by including large deflection theory and/or a more complex material model. Considering the coupling of solid and fluid, the model assumed one-way coupling, i.e., the pressure of the fluid acting on the scaffold wall was neglected. Two-way coupling, i.e., including the force of the fluid acting on the scaffold material, may need to be included when scaffolds of higher porosity with thinner membranes of scaffold material are modeled. In this case, the fluid pressure and shear stresses may have a significant impact on the scaffold matrix deformation. In this example, scaffolds with single straight pores with various shapes were used, whereas more realistic scaffolds would have pore labyrinths comprised of interconnected channels in three dimensions. However, the modeling approach possesses the capability to describe more complex 3D pore networks, as it is based on the exact geometry of the scaffold design.
With respect to the fluid model, laminar flow was assumed, which seems a reasonable assumption considering the small pore dimensions. The Reynolds's number (Re) is given by:
where d is the channel diameter. Assuming water as the fluid (pf=1.0·103 kg m−3 and μ=1.0·10−3 Pa s), a fluid velocity of uf=5 mm s−1, and a channel diameter of 1.0 mm, the value for Re=5. This is well below the Reynolds number at which a flow typically transitions to turbulence (Re=2000). Still, turbulence may occur at sharp transitions in the geometry or at higher compression frequencies and amplitudes. Turbulence could increase solute mixing and dispersion, and may be included in the model by e.g., the empirical k-ε model (Versteeg and Malalasekera, An introduction to computational fluid dynamics: the finite volume method, Harlow: Pearson Prentice Hall (2007)). At the scaffold-fluid interface, no-slip wall boundary conditions were assumed. Roughness of the scaffold surface was not taken into account, which may alter the fluid flow in regions near the scaffold wall. The fluid flow at the wall may have an impact on the distribution of solutes near the wall, and hence the nutrient supply of cells attached to the scaffold surface. Additionally, an improved fluid mesh in the model near the scaffold wall may yield a more accurate prediction of fluid shear stress, which in addition to nutrient supply could have an important effect on the proliferation, distribution and differentiation of cells. Despite these limitations, the current model yielded a good quantitative prediction of the average solute transport rate in scaffolds with different pore geometries, and could be further improved if more accurate quantitative information on e.g., scaffold mechanical behavior, turbulence and wall shear stress is desired.
These data demonstrate that cyclic compression can increase solute convection by cyclic fluid motion and subsequent spreading of solutes dissolved in the fluid. The efficiency of the cyclic pumping can be increased by considering the strain direction and manufacturing pores with highly deformable cross-sectional geometries. Thus, careful design and fabrication of deformable porous tissue scaffolds may be a strategy through which solutes can be transported beyond the diffusion limit after implantation of constructs with clinically relevant thicknesses. The proposed computational model will aid such scaffold design.
The following is conducted to design and construct a synthetic arterial conduit suitable for ultimate replacement of a vessel segment by ingrowing tissue. The design of the arterial wall is such that it mimics several of the solute transport features of the natural arterial wall. The natural arterial wall is made up of concentric layers of tissue that have different mechanical properties and it has vasa vasorum, most of which enter and leave via the adventitia. The media has a plexus of capillaries which bring nutrients and wash out metabolic products as well as remove solutes that migrate across the arterial wall due to the pressure gradient across the wall. These features can be fairly well replicated by concentric layers of microspheres made up of scaffold material (see
The following is conducted to design and construct an injectable porous scaffold suitable for ultimate replacement by ingrowing tissue components. The concept of an injectable scaffold is schematically demonstrated in
(1) Solid spheres that bond to each other where they come in contact and thereby form the scaffold. The fluid-filled spaces between them form the pores. These spheres have a random packing for porosity to exceed the approximately 40% of “crystalline” porosity. Preliminary studies show that 50% porosity can be readily achieved.
(2) Porous microspheres instead of solid spheres. Porous microspheres permit increasing the porosity even if the packing of the spheres is “crystalline.”
(3) Degradable microspheres, which when packed flatten somewhat and bond there as they touch, which allows the material in the pores between the spheres to polymerize and become the scaffold.
Microspheres are printed in a crystalline or more contrast-containing fluid in the pores by our CT imaging method. Microspheres are injected into a pliable plastic bag, then the contents of that bag are exposed to vacuum so that the spheres are kept in place by friction due to outside pressure. This bag is then encapsulated in a cast (slightly elastic material) which maintains the external shape and volume of the packed microspheres so that the pores can now be filled with contrast-containing fluid. This specimen is imaged and the pore space visualized both statically and during a cyclic compression sequence. This interim approach temporarily avoids (delays) the immediate need to fully develop the technique of injecting the two components of the injectable scaffold and the need to develop the ‘click’ chemistry aspect of this approach. See, e.g., Evans et al., Chem. Commun., (17):2305-2307 (2009) and Zhang et al., Carbohydrate Polymers 77:583-589 (2009).
For the complete scaffold, the 3D images are subjected to finite element analysis so as to provide an estimate of mechanical properties of the scaffold. The algorithm which finds the path of least resistance to flow is used so that regions of inadequate convective transport can be identified. This information can then be compared to CT-based measurements of contrast transport within the porous structure.
A numerical model is developed which describes solute transport inside the pores of the scaffold wall. The model takes into account the deformation of the scaffold wall and hence of the pores, as a result of the arterial pressure pulse. This deformation influences the fluid and solute transport in the wall.
The deformation of the scaffold is modeled using a dynamic small-strain problem with a linear Hooke's law as constitutive equation, assuming linear, isotropic elastic behavior. Fluid pressure and velocity of the fluid phase in the pores are described by the Navier-Stokes equations, assuming an incompressible Newtonian fluid and laminar flow. Solute transport is modeled by the scalar convection-diffusion equation, where the convection is calculated from the Navier-Stokes equations. However, because the Reynolds numbers will be so low that likely only the Stokes equations will be relevant.
The topography of scaffold/pore system is obtained from the stereolithography files used to print the experimental scaffold, or from meshing the micro-CT images of the scaffolds (material) and their complement (the fluid) in the image processing software Mimics (Materialize, Ann Arbor, Mich.). To reduce computation time, a section (approximately 2 mm thick) of the artificial vessel is modeled. 3D 10-node tetrahedral elements with quadratic displacement behavior are used to mesh the scaffold geometry. The fluid domain is meshed using 3D tetrahedral elements with linear shape functions and integration points at the center of each surface. A convergence study is carried out to investigate the effects of mesh element size and time steps on the solution. Boundary conditions are applied such that the model accounts for the interaction between the fluid and the scaffold material. The fluid velocity at the wall of the scaffold is set equal to the velocity of the scaffold material at their interface. To mimic the arterial pressure wave, a pressure boundary condition in the form of a cosine wave is applied to the material surface on the inside of the arterial vessel.
The software Ansys Workbench is used to obtain numerical solutions. The dynamic solid deformation problem is solved using the Finite Element Method (FEM), and the Navier-Stokes and scalar transport equations will be solved using the Finite Volume Method (FVM). At each time step, the solid deformation problem is solved first, and the calculated displacement at the fluid-solid interface is then transferred to the fluid solver as a boundary condition in the fluid flow problem. The fluid velocity, pressure and solute concentration fields are solved using the CFD solver. The numerical solution procedure is carried out on a Sun server with 8 quad-core processors (2.66 GHz) and 256 GB internal memory, running SUSE Linux Enterprise Server 10. File I/O will be governed by a 10,000 rpm Raid 0 array with a disk space of 1.0 TB.
It is to be understood that while the invention has been described in conjunction with the detailed description thereof, the foregoing description is intended to illustrate and not limit the scope of the invention, which is defined by the scope of the appended claims. Other aspects, advantages, and modifications are within the scope of the following claims.
This application claims priority to U.S. Provisional Application No. 61/153,567, filed Feb. 18, 2009, the contents of which are incorporated by reference in their entirety herein.
This invention was made with government support under EB000305 awarded by the National Institutes of Health. The government has certain rights in the invention.
| Number | Date | Country | |
|---|---|---|---|
| 61153567 | Feb 2009 | US |
