advances in 3d printing technology have made their applications in biomedical sciences a cost effective option in designing customized solutions . among the different techniques of 3d printing technology , stereolithography
is currently recognized to be one of the most common and accurate rapid prototyping techniques . this remarkable advantage in terms of resolution and precision
a major advantage in such custom designing is the ability to create structures with desired mechanical properties . of interest
are scaffolds with gyroid pore architectures designed by trigonometric equation with modulation of the pore size   and prepared by stereolithography technique using a resin based on poly(trimethylene carbonate ) ( ptmc ) .
ptmc is known as a flexible and amorphous material which can degrade enzymatically by surface erosion .
its excellent properties make it possible to maintain mechanical properties of ptmc over degradation time , as the average molar mass remains constant .
in addition , the remarkable potential of ptmc - based scaffolds prepared by stereolithography in cell adhesion and proliferation was recently demonstrated [ 3 , 16 ] . when designing scaffolds with customized mechanical properties , the characteristics of the bulk material are taken into consideration .
however if the scaffolds have microstructures , any deviation from the bulk properties due to the heat extrusion process can potentially have significant effect on the micro - structural properties .
thus it becomes prudent to verify the mechanical behaviour of the scaffold under mechanical loads with respect to the simulated design .
any such verification process would involve gathering the structural geometry of a printed scaffold product , such as through tomographic imaging techniques [ 9 , 15 ] .
the novel method of characterising deformation for printed constructs is gaining ground and being increasingly used on products of various materials [ 1 , 11 ] .
such methods have not been applied on mathematically designed ptmc constructs to date and this study was designed to address this issue . in this study , ptmc scaffolds with 3 different designs produced by stereolithography were imaged in a ct device with in - situ mechanical deformation .
the scaffolds were designed such that the overall porosity was similar among the scaffolds . employing image based
analysis methods with image registration using triangular surface meshes , the deformation in the microstructure of the scaffolds was calculated and analysed .
the scaffolds were designed in and modelled in rhinoceros 3d ( robert mcneel & assoc . , usa ) and k3dsurf ( freeware ; http://k3dsurf.sourceforge.net ) . from a trigonometric function ( equation 1 ) ,
the software is able to generate cad - file that describes a gyroid surface architecture . 

( 1)cos(x)*sin(y)+cos(y)*sin(z)+cos(z)*sin(x)=c 
  the different scaffolds investigated in this work were designed to have a fixed porosity around 72% , but different pore sizes and surface area .
the features of the investigated scaffolds are described in table  1 . by modulating the value of the constant c in the equation 1 , the pore characteristics such as the volume fraction and the pore size can be modulated . for this work
the value of the constant ( table  1 ) was determined to result in a porosity as close to the target ( 72% ) as possible .
the boundary conditions indicate the periodic repetition of the gyroid channel numbers that are present in the scaffolds . in this case , the scaffolds had a cubic shape as the number of gyroid channels was the same in the x , y and z axes .
briefly , the ring opening polymerization was achieved by reaction mixture of trimethylene carbonate monomer ( 0.98  mol , 100  g ; foryou medical , china ) , with stannous octanoate ( 0.05 wt% ; sigma - aldrich , germany ) as a catalyst and 1,1,1-tris(hydroxymethyl)propane ( tmp ) ( 0.0196  mol , 2.62  g ; sigma - aldrich , germany ) as an initiator , under stirring for 3 days at 130c in argon atmosphere .
proton nuclear magnetic resonance ( h - nmr , 300  mhz ) was used to determine the conversion rate and the number averaged molecular weight ( mn ) of the macromer . the second step of the resin preparation consisted of end - functionalization of the macromer by reactive methacrylate groups .
the reaction was performed in dichloromethane ( 100  ml ) solution by addition of methacrylic anhydride ( 94% ) in excess ( 0.176  mol ; 26  ml ; sigma - aldrich , germany ) at room temperature under argon atmosphere for 5 days .
the resin formulation was prepared by dissolution of the macromer in 30% of propylene carbonate solvent in presence of photo - initiator lucirin tpo - l ( 5 wt% ; basf , germany ) and orasol orange dye ( 0.15 wt% ; ciba specialty chemicals , switzerland ) in order to control the blue light penetration ( 400550  nm ) .
once the resin synthesized , the scaffolds were built using stereolithograph apparatus ( perfactory minimultilens , envisiontec inc .
, usa ) at a pixel resolution of 1616m and a layer thickness of 25m .
the irradiation time for solidifying each layer was fixed at 40  s for a light intensity of 20 mw / cm .
a mechanical compression device was fabricated to be used in conjunction with an xradia high - resolution ct device ( xradia xct400 , zeiss , germany ) ( fig .  1 ) .
the compression of a sample was performed by mechanically moving the top piston with the stationary bottom piston acting as a sample stage .
the top piston assembly ( 80  gms ) was screwed - in until it was resting on the sample and the position was fixed , thus providing an initial static loading force in the range of 0.80.1  n. in keeping with the scope of the study , the applied forces were not monitored .
subsequent to sample loading the pre and post compression tomographic image volumes were obtained . the imaging parameters ( table  2 ) were set similarly for all 3 samples . as the samples were of a single phase material with a low attenuation , filters were not required .
the reconstructed image volumes obtained from the ct device were imported into avizo image processing software ( vsg / fei , mrignac cedex , france ) .
the software is able to directly load the native file format ( txm ) from the xradia device .
thus all global coordinate positions with respect to the sample within the instrument were transferred forward in the analysis procedures .
subsequent to non - local means filtering   to improve the signal to noise ratio , the image volumes were segmented using simple thresholding procedures . as the samples were of a homogenous material exhibiting high contrast with respect to the background ,
morphological methods were used to smooth and fill any speckles in the segmented region ; the closed surface of the labelled volume was subsequently extracted in avizo and simplified , smoothed and cleaned   ( fig .  2 ) .
the triangular surface meshes of the corresponding pre and post compression samples were registered using iterative closest point ( icp ) algorithm with affine transformation .
the deformation of the scaffold under unidirectional compression loads was analysed by tracking the surface points of the pre - compression surface nodes when registered to the post - load scaffold surface .
the samples in this study exhibited geometric structures and were subjected to simple uni - axial deformation .
thus the global registration employed was sufficient for the study purposes to extract deformation values of the sample .
the registration algorithm was iterated until it reached the lowest possible root mean square ( rms ) error value with affine transformations .
subsequent to registration , the vertex positional differences were defined as the deformation at corresponding vertices . as the compression
was applied axially ( -z direction of the global axes ) , the deformation on axial planes was calculated by averaging the deformation of all vertices lying on the plane .
this value succinctly presented the distribution of deformation given in its corresponding 3d visualization . in order to visualize any deviation from an expected linear behaviour ,
the z - component of the deformation vector was subtracted from a linear deformation model .
the model assumes linear deformation along the z - axis starting with the maximum observed z - component deformation on the top surface and 0 on the bottom resting surface .
the remaining x and y - components were combined to visualize any variation within the plane of deformation along a given z - axis location .
the scaffolds were designed in and modelled in rhinoceros 3d ( robert mcneel & assoc . , usa ) and k3dsurf ( freeware ; http://k3dsurf.sourceforge.net ) . from a trigonometric function ( equation 1 ) ,
the software is able to generate cad - file that describes a gyroid surface architecture . 

( 1)cos(x)*sin(y)+cos(y)*sin(z)+cos(z)*sin(x)=c 
  the different scaffolds investigated in this work were designed to have a fixed porosity around 72% , but different pore sizes and surface area .
the features of the investigated scaffolds are described in table  1 . by modulating the value of the constant c in the equation 1 , the pore characteristics such as the volume fraction and the pore size can be modulated . for this work
the value of the constant ( table  1 ) was determined to result in a porosity as close to the target ( 72% ) as possible .
the boundary conditions indicate the periodic repetition of the gyroid channel numbers that are present in the scaffolds . in this case , the scaffolds had a cubic shape as the number of gyroid channels was the same in the x , y and z axes .
briefly , the ring opening polymerization was achieved by reaction mixture of trimethylene carbonate monomer ( 0.98  mol , 100  g ; foryou medical , china ) , with stannous octanoate ( 0.05 wt% ; sigma - aldrich , germany ) as a catalyst and 1,1,1-tris(hydroxymethyl)propane ( tmp ) ( 0.0196  mol , 2.62  g ; sigma - aldrich , germany ) as an initiator , under stirring for 3 days at 130c in argon atmosphere .
proton nuclear magnetic resonance ( h - nmr , 300  mhz ) was used to determine the conversion rate and the number averaged molecular weight ( mn ) of the macromer . the second step of the resin preparation consisted of end - functionalization of the macromer by reactive methacrylate groups .
the reaction was performed in dichloromethane ( 100  ml ) solution by addition of methacrylic anhydride ( 94% ) in excess ( 0.176  mol ; 26  ml ; sigma - aldrich , germany ) at room temperature under argon atmosphere for 5 days .
the resin formulation was prepared by dissolution of the macromer in 30% of propylene carbonate solvent in presence of photo - initiator lucirin tpo - l ( 5 wt% ; basf , germany ) and orasol orange dye ( 0.15 wt% ; ciba specialty chemicals , switzerland ) in order to control the blue light penetration ( 400550  nm ) .
once the resin synthesized , the scaffolds were built using stereolithograph apparatus ( perfactory minimultilens , envisiontec inc .
, usa ) at a pixel resolution of 1616m and a layer thickness of 25m .
the irradiation time for solidifying each layer was fixed at 40  s for a light intensity of 20 mw / cm .
a mechanical compression device was fabricated to be used in conjunction with an xradia high - resolution ct device ( xradia xct400 , zeiss , germany ) ( fig .  1 ) .
the compression of a sample was performed by mechanically moving the top piston with the stationary bottom piston acting as a sample stage .
the top piston assembly ( 80  gms ) was screwed - in until it was resting on the sample and the position was fixed , thus providing an initial static loading force in the range of 0.80.1  n. in keeping with the scope of the study , the applied forces were not monitored .
subsequent to sample loading the pre and post compression tomographic image volumes were obtained . the imaging parameters ( table  2 ) were set similarly for all 3 samples . as the samples were of a single phase material with a low attenuation , filters were not required .
the reconstructed image volumes obtained from the ct device were imported into avizo image processing software ( vsg / fei , mrignac cedex , france ) . the software is able to directly load the native file format ( txm ) from the xradia device .
thus all global coordinate positions with respect to the sample within the instrument were transferred forward in the analysis procedures .
subsequent to non - local means filtering   to improve the signal to noise ratio , the image volumes were segmented using simple thresholding procedures . as the samples were of a homogenous material exhibiting high contrast with respect to the background ,
morphological methods were used to smooth and fill any speckles in the segmented region ; the closed surface of the labelled volume was subsequently extracted in avizo and simplified , smoothed and cleaned   ( fig .  2 ) .
the triangular surface meshes of the corresponding pre and post compression samples were registered using iterative closest point ( icp ) algorithm with affine transformation .
the deformation of the scaffold under unidirectional compression loads was analysed by tracking the surface points of the pre - compression surface nodes when registered to the post - load scaffold surface .
the samples in this study exhibited geometric structures and were subjected to simple uni - axial deformation .
thus the global registration employed was sufficient for the study purposes to extract deformation values of the sample .
the registration algorithm was iterated until it reached the lowest possible root mean square ( rms ) error value with affine transformations .
subsequent to registration , the vertex positional differences were defined as the deformation at corresponding vertices . as the compression
was applied axially ( -z direction of the global axes ) , the deformation on axial planes was calculated by averaging the deformation of all vertices lying on the plane .
this value succinctly presented the distribution of deformation given in its corresponding 3d visualization . in order to visualize any deviation from an expected linear behaviour ,
the z - component of the deformation vector was subtracted from a linear deformation model .
the model assumes linear deformation along the z - axis starting with the maximum observed z - component deformation on the top surface and 0 on the bottom resting surface .
the remaining x and y - components were combined to visualize any variation within the plane of deformation along a given z - axis location .
the maximum deformations applied to the 3 scaffold designs , measured from the images , were : 83812m ( scaffold 1 ) , 65712m ( scaffold 2 ) and 63612m ( scaffold 3 ) .
the segmentation procedure gave good results when viewed visually , in part due to the high contrast and high resolution of the reconstructed images .
the surface mesh representation was limited to 400 k faces , which was deemed adequate to represent the sample features and return acceptable execution times for the various image analysis tasks ( fig . 
the rms errors for each of the samples were in the range of 2535 m ( 23 pixels in image data ) , indicating an acceptable registration given the scope of this study ( fig . 
the direction of deformation and the corresponding magnitudes at each node when plotted over the sample surface mesh showed consistent patterns with no clearly observable anomalies .
an example of this visualization is presented in fig .  4 for scaffold b. for each of the 3 scaffold designs tested , the residual z - component deformations were present ( < 100 m ) that consistently indicated an axis of deformation that is not perfectly aligned with the z - axis .
to aid in grasping an intuitive understanding of the results , deformation magnitudes at mesh nodes were plotted against their axial dimension ( z axis ; direction of applied deformation ) ( fig . 
thus , all nodes located on the same axial plane are indexed on the horizontal axis of the plots , starting from 0 ( sample bottom , resting on stage ) to ( 5000 m ( sample top ) .
the resulting scatter plot was averaged with respect to position along the horizontal axis . the distribution of vertex deformations around the average value ( fig . 
5a  c  blue line ) showed an increased spread with increasing magnitudes of applied deformation .
however , for each scaffold design , the spread around the average value on the axial planes remains largely stable along its axial length .
this study demonstrated a novel in - situ imaging and image based deformation analysis procedure for analysing the structural response of ptmc scaffolds under compression .
the results indicate that the different scaffold designs exhibit a linear distribution in deformation throughout the inner structure . for scaffold
a which was subjected to the largest deformation , the structures at the bottom contact face showed a greater spread in the deformation values ( fig . 
this was expected , as with increasing deformations , the individual unattached micro - struts at the boundary deform notably .
these structures at the boundary may not be complete due to their location in the design , leading to variation in deformation response . additionally from the residual z - component and xy - component images ( fig . 
4b and c ) , it is evident that the compressing head was applied at a slightly inclined angle .
this would result in the applied deformation not being strictly perpendicular to the top surface of the sample .
hence the spread around the mean in the deformation plots in this study ( fig . 
5 ) can be explained by two factors  the expected variation in deformation within the xy - plane due to sample incompressibility and the effect of a deformation applied at a small angle to the z - axis instead of being exactly along it .
5b and c ) are also likely due to the incomplete printed structures at the sample boundary .
thus , these outliers and variations can be reasonably explained by the difference in the interconnectivity of the scaffold structure internally and on the boundaries .
when studying the performance of scaffold designs within their prospective biological environment , the size and distribution of pores have a direct bearing on the proliferation of the embedded cells . in a mechano - biological environment
, loads may be transmitted through the material matrix to the embedded cells within the scaffold
. thus it would be reasonable to assume that the structural response of the scaffolds to the loads may also have an influence on cell proliferation [ 5 , 17 ] . with various materials available for 3d printing and the numerous designs implemented
, structural verification of prototypes can be used to optimize the criteria for a selected scaffold design for a particular application .
this optimization may be critical in some cases where the design has to be a trade - off between structural support for tissue regeneration and stimulus for cell differentiation or proliferation .
the methodology described in this study serves in displaying the value in imaging and image analysis based verification of structural response of scaffolds .
the analysis includes registration of the 3d image sets  of non - deformed data to the deformed data .
the registration of data was performed to track the deformation of only the surface of the sample which was segmented from the images and the represented as triangular surface meshes . in combination with high resolution image data ( ( 25 m ) and relatively large sample sizes ( up to 101010  mm , at this resolution ) , it is possible to image deformations at sub - pore resolutions .
various modifications of this algorithm assist in working with or observing the feature set of interest with higher resulting accuracy .
however , this initial study also brings to fore issues that will need to be addressed for accurate characterisation of such printed structures . in this
study the deformation device was a simple fabrication where movement of the piston was performed by a manual screw setup .
this results in loads effecting varied deformation magnitudes in our experiment ( 0.80.1  n ) , hindering direct comparison of scaffold design based on deformations .
this was mitigated in the analysis by calculating these deformations accurately from the high resolution images . in terms of the analysis procedure ,
thus for validation studies , high performance registration methods are called for , which result in residual errors at least lower than the resolution of the imaging ( 25 m in this study ) [ 8 , 10 ] . in the future
, an improved fabrication of the deformation device with force monitoring will be used in a systematic study for scaffold characterisation .
importantly , features reflecting functional performance of scaffolds such as porosity and the corresponding flow characteristics within the structure will need to be studied . however , in its current form , the deformation instrument and the image based analysis provide valuable insight into the mechanical characteristics of the scaffolds . in conclusion ,
ct based imaging with in - situ deformation and subsequent extraction of mechanically relevant features provides a vital tool in validating the design parameters and corroborating the simulated ideal design with the realized product .
 abstract 
 background : advances in rapid - prototyping and 3d printing technologies have enhanced the possibilities in preparing designed architectures for tissue engineering applications . a major advantage in custom designing is the ability to create structures with desired mechanical properties . while the behaviour of a designed scaffold can be simulated using bulk material properties , it is important to verify the behaviour of a printed scaffold at the microstructure level . 
 
 objective : in this study we present an effective method in validating the mechanical behaviour of designed scaffolds using a ct with an in - situ mechanical deformation device . 
 
 methods : the scaffolds were prepared from biodegradable poly(trimethylene carbonate ) ( ptmc ) by stereolithography and images obtained using a high - resolution ct with 12.25m isometric voxels . 
 the data was processed ( filtering , segmentation ) and analysed ( surface generation , registration ) to extract relevant deformation features . 
 
 results : the computed local deformation fields , calculated at sub - pore resolutions , displayed expected linear behaviour within the scaffold along the compressions axis . on planes perpendicular to this axis , the deformations varied by 150 200m . 
 
 conclusions : ct based imaging with in - situ deformation provides a vital tool in validating the design parameters of printed scaffolds . 
 deformation fields obtained from micro - tomographic image volumes can serve to corroborate the simulated ideal design with the realized product . 
Introduction
Material and methods
Scaffolds  design and preparation
Compression device and imaging
Analysis
Results
Discussion