Design of a novel procedure for the optimization of the mechanical [620002]

Medical Engineering & Physics
Manuscript Draft

Manuscript Number: MEP -D-18-00109

Title: Design of a novel procedure for the optimization of the mechanical
performances of 3D p rinted scaffolds for bone tissue engineering
combining CAD, Taguchi method and FEA

Article Type: Paper

Section/Category: Regular Issue Paper

Keywords: scaffold design; finite element analysis; bone tissue
engineering; fused deposition modelling

Abstract: Here, we propose an innovative and integrated procedure to
design 3D scaffolds for bone tissue engineering to achieve a high level
of control on scaffold performances before its realization, thus to
increase manufacturing and experimental effic iency. The procedure
requires a combination of CAD draw, finite element analysis (FEA) and
design methodologies of experiments (DOE), firstly to understand the
influence of the design parameters, secondly to control them.
Initially, the most relevant geo metrical parameters of the scaffolds
(fibre and pore dimension, fibre orientation and offset) have been
combined by considering literature data and limitations imposed by the
manufacturing process (Fused Deposition Modelling). At this stage, 36
possible sc affold architectures have been drawn. The porosity of each
scaffold has been calculated by CAD. Then, a generic scaffold material
was considered and its variable parameters combined with the geometrical
ones according to the Taguchi method, i.e. a DOE meth od. The compressive
response of those principal combinations was simulated by FEA, and the
influence of each design parameter on the scaffold compressive behaviour
was clarified.
Following these analyses, a regression model relating scaffold mechanical
performances to geometrical and material parameters has been obtained.
This model has been applied to the practical case of study represented by
a novel composite material made of polycaprolactone and bioactive glass.
Thanks to it, by imposing specific poro sity (50%) and stiffness (0.05
GPa) thresholds suitable for trabecular bone substitutes, 4 of the 36
initial scaffold architectures have been selected. Thanks to this
approach, only those more promising geometries will be realized and
physically tested for advanced indications on compressive strength and
biocompatibility.

Graphical Abstract (for review)

Highlights
 This study aims to reduce time and costs of scaffolds manufacturing and testing
 A novel design procedure is provided to fabricate only the most promising scaffolds
 The novel scaffold design combines for the first time CAD, Taguchi method and FEA
 The proposed design controls scaffold geometry, material, porosity and stiffness
 It is applied to Fused Deposition Modelling of novel PCL/bioactive glass scaffolds
*Highlights (for review)

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Design of a novel procedure for the optimization of the mechanical 1
performances of 3D printed scaffolds for bone tissue engineering 2
combining CAD, Taguchi method and FEA 3
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Author names and affiliations 5
Gregorio Marchiori1, Matteo Berni1,2, Marco Boi1, Michele Bianchi1 6
1Rizzoli Orthopaedic Institute, Laboratory of Nanobiotechnology, Bologna, Italy 7
2Rizzoli Orthopaedic Institute , Laboratory of Biomechanics and Innovation Technology , Italy 8
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Corresponding author 10
Gregorio Marchiori 11
Rizzoli Orthopaedic Institute 12
Via di Barbiano 1/10, Bologna, Italy 13
E-mail: gregorio.marchiori@ior.it 14
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26 *Manuscript
Click here to view linked References

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Abstract 27
Here , we propose an innovative and integrated procedure to design 3D scaffolds for bone tissue 28
engineering to achieve a high level of control on scaffold performances before its realization, thus to 29
increase manufacturing and experimental effic iency. The procedure requires a combination of CAD draw, 30
finite element analysis (FEA) and design methodologies of experiments (DOE) , firstly to understand the 31
influence of the design parameters, secondly to control them . 32
Initially, the most relevant geometrical parameters of the scaffolds ( fibre and pore dimens ion, fibre 33
orientation and offset ) have been combined by considering literature data and limitations imposed by the 34
manufacturing process (Fused Deposition Modelling ). At this stage , 36 possible scaffold architecture s have 35
been drawn . The porosity of each scaffold has been calculated by CAD. Then, a generic scaffold material 36
was considered and its variable parameters combined with the geometrical ones according to the Taguchi 37
method, i.e. a DO E method. The compressive response of th ose principal combinatio ns was simulated by 38
FEA, and the influence of each design parameter on the scaffold compressive behaviour was clarified . 39
Following these analys es, a regression model relat ing scaffold mechanical performances to geometrical and 40
material parameters has been obtained. This model h as been applied to the pra ctical case of study 41
represented by a novel composite material made of polycaprolactone and bioactive glass . Thanks to it, b y 42
imposing specific porosity (50%) and stiffness (0.05 GPa) threshold s suitable for trabecular bone 43
substitutes , 4 of the 36 initial scaffold architecture s have been selected . Thanks to this approach , only those 44
more promising geometries will be realized and physically te sted for advanced indications on compressive 45
strength and bioco mpatibility . 46
47
Highlights 48
 This study aims to reduce time and costs of scaffolds manufacturing and testing 49
 A novel design procedure is provided to fabricate only the most promising scaffolds 50

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 The novel scaffold design combine s for the first time CAD, Taguchi method and FEA 51
 The proposed design controls scaffold geometry, material, porosity and stiffness 52
 It is applied to Fused Deposition Modelling of novel PCL/bioactive glass scaffolds 53
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Keywords 55
Scaffold design; finite element analysis; bone tissue engineering ; fused deposition modelling 56
57
Abbreviations 58
CAD: Computer Aided Design 59
FEA: Finite Element Analysis 60
DOE: Design Of Experiments 61
FDM: Fused Deposition Modelling 62
PCL: Polycaprolactone 63
64
1. Introduction 65
In bone tissue engineering, 3D printed s caffolds are of particular interest for the regeneration of critical 66
bone defects , thanks to the possibility to properly tailor the geometrical features of constructs by simply 67
modifying the printing parameters [1][2]. 68
Noteworthy , in addition to a suitable biocompatibility and osteoconductivity , scaffolds must fulfil strict 69
criteria in terms of mechanic al requirements and processability t o result effective [1]. As well -known, these 70
criteria are strongly dependen t on scaffold design. In particular , the ability of the scaffold to be 71
osseointegrated has been correlated to its porosity and pore dimension [3][4][5], whereas th e structural 72
integrity of the construct has been closely associa ted to the compressive response [3][6]. 73

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In the attempt to optimize ab initio the mechanical performance of the 3D printed scaffolds, Computer 74
Aided Design ( CAD ), Finite Element Analysis (FEA) and Taguchi method (a DOE method) have been 75
investigated as promising solutions. FEA, with or without CAD, has been already exploited in various studies 76
for the optimization of scaffolds architecture [7][8] and composition [9][10]. The Taguchi method is 77
commonly applied to the design of experiments where the effect of many project parameters on the 78
output of interest is investigated , allowing to achieve the best solution by acting only on a very small subset 79
of all the possible parameters combinations. The eff icacy of the Taguchi method a t a modelling level – 80
preceding the experimental phase – has been already demonstrated [11]. However, concerning scaffolds 81
for bone tissue engineering , the use of Taguchi method has been restricted to the optimization of the 82
manufacturing [12][13] and not to the design of th e scaffold performances prior to fabrication . 83
Here, we present an innovative procedure , combining for the first time CAD, FEA and the Taguchi method 84
for the optimization of scaffold design , with the specific aim of controlling scaffold architecture and 85
com position at the same time . We demonstrate that it is possible to achieve a high level of control over the 86
mechanical performance s of the construct before its realization , limiting the fabricat ion step to only the 87
more promising scaffolds . 88
To demonstrate the efficacy of the proposed procedure , the latter was applied to 3D printed 89
organic/inorganic composite scaffolds realized by the Fused Deposition Modelling (FDM) . As scaffold 90
material , polycaprolactone ( PCL), combined with a bioactive glass with an inno vative formulation [14], was 91
selected, since polymeric matrix embedded with an inorganic phase are of increasing interest in the field of 92
bone tissue engineering , due to the possibility of tailor the mechanical properties of the scaffold as well as 93
its bioactivity by mixing the proper amount of the polymeric component and of the inorganic phase [15]. 94
95
2. Materials and Methods 96
A scheme of the proposed procedure for the optimization of scaffold design is illustrated in Fig. 1, where, 97
briefly, CAD is used for drawing scaffold architectures and calculate their porosities. The Taguchi method is 98

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applied to select the principal combinations of scaffold architecture and generic material. FEA simulates the 99
mechanical performances of those combinations and the results serve to build up a regression model that 100
controls the effect of any c ombination of architecture and material on the scaffold design mechanics. 101
2.1 C omputer Aided Design 102
Computer Aided Design (CAD) was used to draw the scaffold architecture s. These ha ve been defin ed on the 103
base of the geometric parameters described in literature and tuneable by the specific manufacturing 104
technique selected for this study , i.e. 3D printing : fibre diameter (FIBRE ), pore size (PORE ), orientation 105
between successive fibre planes (STEP ), offset between planes with the same fibre orientation (OFFSET ) 106
(Fig. 2). 107
Specifically, 3D printing was applied in the form of Fused Deposition Modelling (FDM), in which a material is 108
fed into an d extruded by a nozzle that forms the part layer by layer. At any deposited layer of the 109
manufacturing process , the printer nozzle moves up by the 80% o f the diameter of the fibre. I n the CAD 110
drawing , this reflected on an interpenetration between subsequent fibre planes of about 20%. The 111
parameters changed following a practical approach , i.e. with values achievable by the 3D printer and 112
anyway common in similar applications (e.g. for PORE see [16]): FIBRE 330-840 μm, PORE 300-450-600 μm, 113
STEP 45-60-90°, OFFSET yes/no. Combining the above parameters, 36 different scaffold architectures 114
resulted . These 36 architectures were drawn on CAD wit h the following aims : 1) to calculate the ir porosity , 115
by relating solid and free volume, and 2) to predispose them for the following mechanical simulation s. 116
The scaffolds were designed as cylinders (Φ = 10 mm, h = 6 mm) . Scaffold porosity is defined as: 117

(Eq. 1) 118
where Vsca is the volume of the CAD scaffold and Vcyl is the total volume of the boundary cylinder [6]. 119
In order to control the scaffold porosity by tuning a single parameter, the expression found in [18] is used : 120

(Eq. 2) 121

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where PO:FI is the control parameter , ratio between pore size (PO) and fibre diameter ( FI), while a and c 122
are fitting constants . Fixing the desired porosity in Eq. 2 it is possible to know the PO:FI needed to obtain it. 123
That is , from a practical point of view with FDM, setting FI (the printer nozzle) , to know the minimum pore 124
size PO to be imposed to the scaffold . 125
Finally , the various CAD drawing s were arranged for the mechanical simulation. Particularly, compression 126
plates have been added to every cylindrical scaffold, on top and bottom face s, to simulate the chosen 127
mechanical test (Fig. 3), i.e. axial compression . 128
2.2 Taguchi method 129
Taguchi method is a design method of experiment s (DOE) [19]. It is used for investigat ing the entire space 130
of the input parameter s evaluating only a subset of their combinatio ns, the principal ones, in general with a 131
remarkable saving both of time and costs , here especially of time treating FEA simulations and not yet 132
physical experiments. 133
First of all, the parameters of which levels will be combined by the Taguchi method to be used as input for 134
FEA on scaffold mechanics have to be defined. The previous CAD phase established the geometrical 135
parameters . Once the scaffold geometry has been defined, the other parameters that ha ve to be treated by 136
the Taguchi method to enter FEA are inherent to the scaffold materia l and mesh (the body discretization 137
which the FE method is based on). In order to define them, the FEA output must be considered. FEA 138
simulation s aimed to identify scaffold CM, which represent s its stiffness in the linea r field of the stress – 139
strain response . Consequently, t he scaffold fibre material can be described as linear elastic, through the 140
Young ’s modulus E and the Poisson ’s coefficient ν. The mesh can be described through the type of 141
element s and their average dimension (SIZE). The chosen type of element s was the linear tetrahedron, 142
because the architectures did not allow an efficie nt meshing using the hexahedron and in order to limit the 143
computational time. Thus, only SIZE eventually varied. Therefore, in addition to geometry, the other 144
potential inputs to the scaffold analysis were E, v and SIZE. In order to establish which of them could be 145
neglected , simplifying the analysis , it was necessary to define the sensitivity of the FEA output (CM) to 146

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them. Accordingly , a “preliminary ” FEA was conducted and consist ed in a sensitivity analysis . FIBRE 330 μm, 147
PORE 600 μm, STEP 90 ° e no OFFSET were considered as reference geometry . Every other input parameter 148
varie d on two levels, low and high ( high = low*10 ). In particular for E, 0.1 ( approximately the minimum 149
value of Young’s modulus of the trabecular bone) and 1 GPa; for v, 0.04 ( close to the maxim al 150
compressibility) and 0.4 ( close to incompressibility); for SIZE , 0.06 (a tenth of the high level) and 0.6 (default 151
value in the FEA program ). They would result in 16 combination s. Thanks to the Taguchi method it i s 152
possible to create a L4 table [20] holding only 4 principal combination s to be simulated (Tab.1) . 153
Once the sensitivity analysis had defined the most affecting parameters on the scaffold CM , Tag uchi 154
method was used to define their principal combination s as inputs to the “final ” FEA, which simulate s and 155
rank s their effects on scaffold CM. Finally, t he results of th ose simulations were exploited to create a model 156
of multiple linear regression relating output CM to the various input s, thus permitting the pre- 157
manufacturing control on the scaffold performa nces objective of this study . 158
2.3 FEA 159
The goal of the mech anical simulations was to verif y the dependence of the compressive modulus (CM) of 160
the scaffold on its geometry and composition material. CM was selected because critical to the success of 161
the implant [21], determining the response of the scaffold before permanent deformation and rupture. 162
The simulation s on the scaffold s were conducted by a FEA program (Abaqus, Simulia) as quasi -static . The 163
geometrical input s were describe above (CAD section ), while the mesh and material inputs came from the 164
sensitivity analysis (Taguchi section ). The simulated test condi tions and the analysis of the stress -strain 165
curve s followed the indications in [22]. In particular , the plates were constrained to vertical movement 166
only ; the superior plate displacement press ed the scaffold with a rate of 0.6 mm/s (10% of deformation per 167
seco nd) while the lower plate was grounded ( Fig. 4). 168
Strain is obtained as the vertical shift divided by the initial thickness of the scaffold , stress as the force read 169
by the load cell divided by the initial cross -section area of the sample. The CM is obtained as the gradient of 170
the linear portion of the stress -strain curve. 171

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2.4 3D-printing of PCL/bioactive glass scaffolds 172
Recently the use of PCL/bioactive glass composites has been proposed [23], being the PCL a medical degree 173
polymer commonly used for tissue engineering [24] whereas the bioactive glass is well known responsible 174
for osteoconductive properties. Therefore, i n order to demonstrate the design procedure, it was applied to 175
a composite of PCL (70% wt.) and a bioactive glass with innovative formulation (30% wt .) [14]. The 176
composite material was realized by mixing PCL pellets and powders of the glass and plotted in scaffolds by 177
a 3D Di scover printer (RegenHU, Switzerland). 5 scaffolds were plotted for experimental testing to validate 178
and develop the design procedure. 179
2.5 Nanoindentation 180
Nanoindentation is useful to characterize the material at a scale proper to scaffold fibre dimensio n [10]. 181
Nanoindentation tests were performed with an instrumented indenter (Nanoindentation Tester NHT2, CSM 182
Instruments) in order to determine the indentation hardness (H IT) and the elastic modulus (E IT) of the 183
scaffold fibre material, accor ding to the Oliver –Pharr method [25]. The loading and unloading time was set 184
to 10 s, with a pause of 60 s between loading and unloading, with a maximum load of 50 mN . 185
Nanoindentation data have been used as input material in the scaffold design model . 186
2.6 Validation and application of the design procedure 187
For the validation of the use of indentation elastic modulus, E IT, in place of E as input of the design model , 188
printed composite scaffolds were tested, again following [22], with a standard compression machine 189
(Instron 4465) . The design model was considered valid when the com pression module of the scaffold (CM) 190
obtained by FEA simulation fell inside the experimental range (mean ± SD ). 191
After FEA validation, the multiple linear regression that relates material, architecture and CM , fitted on the 192
simulation results, served to select the best performing scaffold architectures to be printed in the 193
PCL/ bioactive glass with 70/30 wt%. composition. 194
195

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3. Results 196
3.1 CAD 197
The porosity values obtained by applying Eq. 1 to the different geometrical combinations are listed in Tab.2. 198
The geometrical combination s were pooled by STEP -OFFSET parameters to obtain 6 different groups: 45 °- 199
yes, 45 °-no, 60 °-yes, 60 °-no, 90 °-yes and 90 °-no. At each group corresponded a fitting , by Eq. 2 , that relates 200
porosity with pore:fibre size ratio (PO:FI). Relative fitting parameters a and c are collected in Tab. 3. 201
Thanks to Eq. 2 it was possible to identify the PO:FI which allow ed a particular porosity. For instance i f a 202
60% of porosity ( e. g. suggested in [1]) is chosen, by setting the printer nozzle , that is the fibre diameter FI 203
(330 or 840 µm in this case), the threshold dimension of the pore PO is obtained ( PORE * in Tab. 3). With 204
FIBRE 840 µm , the needed pores would be too large, out of an optimal range , as described in literature 205
[26]. Consequently, only FIBRE 330 µm was taken into account and thus the number of geometrical 206
combination s to be analy sed was reduced from 36 to 18. 207
3.2 Taguchi & FE A 208
The analysis of s ensitivity taked as basis Tab. 1, where every listed combination of input parameters is 209
complete d with the simulation output CM of the corresponding “preliminary ” FEA. For each couple of rows 210
that present s the same level of a parameter, relative average CM was calculated . Thus, a representative CM 211
of the high and low level s for each parameter was obtained. The effect of each parameter was measured as 212
ratio between corresponding high and low CM. For a 10 times variation of the input, the ratio was 8.15 for 213
E, only slightly higher than 1 for ν (1.16) and even closer to 1 for SIZE (1.11) . Thus input SIZE variable 214
resulted almost irrelevant : it was excluded from the following analys es and fixed to the FEA program 215
default value . 216
The list of inputs to “final” FEA has been fulfilled : FIBRE, PORE, OFFSET and STEP were the geometrical 217
inputs, E and ν the fibre material ones. FIBRE was set to 330 µm ( CAD Results paragraph) . PORE, STEP, E and 218
ν varied on t hree levels : 300-450-600 µm for PORE ( CAD Materials and methods paragraph) ; 45°-60°-90° for 219

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STEP ( CAD Materials and methods paragraph) ; 0.05 (trabecu lar bone lower bound in [27])-0.275 (in 220
between value) -0.5 GPa (1 order bigger than the lower bound) for E; 0.1-0.3-0.49 for ν [28]; OFFSET varied 221
on 2 levels, NO (absent) and YES (present) ( CAD Materials and methods paragraph ), defining 2 pools of 222
architectures to be analy sed separately. For each pool , with 4 parameters (STEP , PORE, E, ν) varying on 3 223
levels, 34=81 simulations should be carried out. Thanks to the Taguchi method, they reduced to 9, giving 224
the L9 tables (Tab. 4) [29]. 225
In order to understand the effect of the input parameters on the scaffold CM , Fig. 4 was built up. Starting 226
from Tab. 4, the CM corresponding at the same parameter level were averaged. In this way the various 227
mean CM corresponding to the low, medium and high levels of STEP, PORE, E and ν were obtained. In order 228
to compare the inf luence of those input parameters on output CM , a normalization of the different unit s of 229
measure and of the ranges of variation should occur: input levels and corresponding output CM were 230
normalized respect to their maximum value, expressed as percentage a nd definitely collected in Fig. 4. As 231
example, for E levels and corresponding mean CM, the absolute ranges were 0.05 -0.5 GPa and 0.009 -0.075 232
GPa respectively, in the case without offset . They became the relative ranges 10 -100% and 13 -100%. Same 233
processing was adopted for the other parameters. 234
For each relation between input parameter x and output CM y, a y=mx expression was joined where m is 235
an index of sensitivity. 236
Thanks to Fig. 5 which collects the FEA results in that particular manner, many things can be argued . The 237
most promising architectures have a STEP of 90° without offset and a STEP of 60° with offset . The STEP vs 238
CM relation is strongly proportional between STEP 45° and 60 °, while it is less defined between 60° and 90°, 239
both without and with offset. As expected for PORE vs CM and E vs CM, a higher porosity corresponds to a 240
lower scaffold stiffness , vice versa a higher fibre stiffness corresponds to a higher scaffold stiffne ss with a 241
strongly linear relation ( m closed to 1 in Fig. 5). Thanks to Fig. 4, in particular to gradient m, a different 242
sensitivity to the design parameters is highlighted. Ranking the parameters f rom the most to the least 243
influencing, it was obtained POR E-STEP -E-ν without offset and PORE -E-STEP -ν with offset. But, if for STEP it 244

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is considered the range 45° -60° alone, the sensitivity rank was PORE -STEP -E-ν, independently from the 245
offset. Definitely, geometry prevailed on material . Without offset (Fig. 5, left), the relation with CM was 246
almost linear for the STEP, E and PORE parameters, but not for ν. For the architectures with offset (Fig. 5, 247
right) instead , not only ν vs CM was a nonlinear relation , but also STEP vs CM . It follows that the application 248
of a linear regression model is particularly critical in the second case. 249
The influence of the geometry resulted important , but while for the PORE parameter the relation with 250
porosity, and thus with CM, is clear (bigger the pore, bigger the porosity, lower the CM) for STEP and 251
OFFSET it needed to be highlighted . Specifically, from CAD and FEA results collected in Tab. 2 and Tab. 4, 252
Fig. 6 and Fig. 7 were built up. 253
In Fig. 6, mean and SD of porosity and CM corresponding to the different levels of STEP were r eported. In 254
the case without offset (Fig. 6, left), the influence of STEP on CM could be explained, in part, by the 255
concomitant effect on porosity (STEP increase: porosity decrease and CM increase) . In the case with offset 256
(Fig. 6, right), the influence of STEP on porosity was vanished by other factors (porosity and CM follow the 257
same trend with STEP). 258
Concerning t he offset , it weakens the stiffness of the architectures ( the NO OFFSET family presented a 259
mean CM of 0.041 GPa, the YES OFFSET group a mean CM of 0.03 GPa), but this cannot be explained 260
uniquely by lower porosities (the NO OFFSET family present ed a mean porosity of 58.67% , the YES OFFSET 261
group a porosity of 58.4 %). At the contrary, the presence of an offset seemed to mitigate the specific 262
influence of porosity. This fact can be showed fitting CM against porosity with : 263
CM = E*(1 -φa) (Eq. 3) 264
were φ is the porosity, divided by 100, a is the fitting exponent and E is the Young’s modulus of the pore 265
free material [26]. Fig. 6 collect ed the various scaffold porosities, while the material, i.e. E, was fixed 266
(PCL/ bioactive glass 70/30 wt.%). The stiffness of the scaffolds without offset was more sensitive to 267
porosity than with offset : the CM decreased faster in the first case, as showed by the fitting exponents in 268
Fig. 7. 269

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Once understood the influence of the design parameters, the second aim is to control it. In Eq. 4 is 270
presented the expression of the multiple linear regression that relates the inputs of the scaffold design 271
(geometry pa rameters STEP and PORE, material parameters E and ν) to its mechanical performances 272
(scaffold stiffness CM) , thus enabling the preliminary, pre-manufacturing , control : 273
CM = a*STEP+b*PORE+c*E+d*ν+e (Eq. 4) 274
Fitting Eq. 4 on the input and output values of the simulations reported in the Taguchi tables (Tab. 4) , the 275
specific coefficients have been obtained (Tab. 5). 276
3.3 3D-printing, nanoindentation and design of PCL/bioactive glass scaffolds 277
5 PCL/bioactive glass scaffolds with composition 70/30 wt%, FIBRE 330 μm, PORE 600 μm, STEP 90° and no 278
OFFSET were printed. Nanoindentation on the fibres resulted in a mean EIT of 0. 77 GPa and in ν 0.3. To 279
validate the FEA simulations on the chosen scaffold architecture , EIT must be reduced from 0. 77 to 0.23 GPa 280
(that is E in Eq.3) , resulting in a simulated CM (0.038 GPa) inside the experi mental range (0.0384 ± 0.0035 281
GPa) of the compressive tests . 282
Once the PCL/bioactive glass 70/30 wt% material model was validated, it was applied to all the analysed 283
scaffold architec tures. They are listed i n Tab.6 , ranked by descending simulation CM and coupled with the 284
corresponding regression (i.e. Eq. 4) CM. 285
In Tab. 6 , specific to PCL/bioactive glass 70/30 wt.% material , generally the STEP and PORE levels follow the 286
order of influence derived from the Taguchi combinations of geometry and generic material (Fig. 4 ). 287
When using Eq. 3 fitted on Tab. 4 only (coefficients of Tab. 5), t he error of the regression model (“Reg” 288
results in Tab. 6) in predicting the performances (“Sim ” results in Tab. 6) was high (see RMS in Tab. 6). If the 289
simulations on the PCL/ bioactive glass 70/30 wt.% material are used for the regression too, new 290
coefficients for the regression model are obtained (Tab. 7). 291

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The error done by Eq. 4 with the updated coefficients (Tab. 7) decreased from 9.17E -5 to 4.069E -5 GPa and 292
from 6.85E -5 to 2.49E -5 for the NO OFFSET and YES OFFSET sets, respectively. Once the regression ability of 293
Eq. 3 has been improved , it can be applied to control the scaffol d performances. For instance, using the 294
STEP 90° and impos ing a porosity threshold of 60% , a PORE of 462/ 455 μ m is obtained for the NO 295
OFFSET/ YES OFFSET cases, respectively. With the PCL/ bioactive glass 70/30 wt.% , applying E = 0.23 GPa, ν 296
= 0.3 and the specific coefficients to Eq. 3, CM of 0.046 (NO OFFSET) and 0.027 GPa ( YES OFFSET) are 297
obtained, both lower than the trabecular bone threshold (0.05 GPa in [27]). Conversely, if the CM 298
threshold has to be reached, with STEP 90° and material PCL/ bioactive glass 7 0/30 wt.% , PORES of 431 299
and 272 μm have to be imposed, corresponding to porosities of 60% and 50% for the NO OFFSET and YES 300
OFFSET cases, respectively. Finally, it is possible to fix both porosity (60%) and CM (0.05 GPa), thus 301
revealing the E that the fibre material should have: again wit h STEP 90°, it results E = 0.266 GPa (NO 302
OFFSET ) and E = 0.475 GPa (YES OFFSET). 303
304
4. Discussion 305
In this paper, the influence of the design parameters on the mechanic al performances of 3D printed 306
scaffolds has been investigated through a combined CAD/Taguchi/FEA approach (Fig. 1) . Accordingly, a 307
regression model able to control the scaffold mechanics in a pre -manufacturing phase has been proposed. 308
Interestingly, it has been found that the compressive modulus (CM) of the designe d scaffold , determinant 309
to its mechanical performance , is primarily related to its geometry , and specifically to the pores size (PORE) 310
and fibre orientation in subsequent fibres planes (STEP), secondly to the material, i.e. to the fibre elastic 311
modulus (E) rather than to the Poisson’s ratio . By a pplying the proposed method to the investigated 312
geometries and to an innovative PCL/ bioactive glass material with composition 70/30 wt% , the more 313
promising scaffolds can be selected for 3D printing and physical testing , aiming to reach an experimental 314
CM of 0.05 GPa (threshold for trabecular bone [27]) and a porosity of 50 % (threshold for bone [30]). 315
Considering the above constraints, four different architectures emerged as optimal from the mechanical 316

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point of view: two architectures without offset (with STEP 90°: PORE 300 and 450 μm) and two with offset 317
(PORE 300 μm: STEP 60° and 90°) . Architectures with an offset, basically a shift between fibers of 318
corresponding planes, were not discarded, even if so fter, because it could provide a more effective 319
biological response [26]. 320
When lookin g at contingent relationships among the investigated scaffold parameters and CM , a clear and 321
proportional relation was found only between fibre stiffness and scaffold stiffness (Fig. 5). Relation 322
between geometrical parameters and scaffold mechanics result ed less defined, nevertheless the major 323
influence pertained to geometry rather than to material. 324
It is well known from the structural mechanics that architecture has a prominent role in determining the 325
structure’s performances. Also slight variations in the geometrical parameters can affect scaffold porosity 326
and thus mechanics [31]. In this work the effect of those variations will be explained by their potential 327
influence on the “pillars ”, which determine the vertical stiffness of the scaffold (Fig. 2 a,b). 328
Generally , the presence and size of voids strongly decrease structure strengt h [32]. This study confirmed 329
once again that pore size, and thus porosity, is predominant in affecting scaffold mechanics, in this 330
particular context because it decreases the spatial frequency of the vertical pillars. 331
When an offset between corresponding layers of fibres is introduced , the vertical pillars lose their straight 332
orientation in favour of a “zig -zag” one (Fig. 2 b). This definitely decreases the scaffold stiffness , although it 333
mitigates the “negative” influence of porosity on it (Fig. 7 where CM vs porosity decreases slower with 334
offset than without), fact that is “positive” towards biocompatibility because higher porositie s are allowed . 335
Finally, concerning the influence of the fibers orientation, it appeared strong , as just found in [5]. In this 336
work, it can be partially explained by its effect on porosity , but only for the family of scaffolds without 337
offset (Fig. 6). In the case with offset instead, the effec t on vertical pillars could be predominant and the 60° 338
orientation represents the best condition for the “zig -zag” pillar s stiffness (Fig. 5, right ). 339

15
Concerning scaffolds aimed to regenerate bone tissue , several studies combined CAD and FEA [3] [4] [7] [8] 340
[9] [10][18] [33] [34] [35] [36] [37], but with different modalities and purposes . Major similarities can be 341
found in [38], where FEA and a DOE method (not the Taguchi method) were used to analy se the 342
parameters sensitivity and to optimize the compressive modulus of the scaffold design , and it was found 343
that a great influence was related to the geometrical parameters, meanwhile the sensitivity to the fibre 344
elastic modulus and overall to the P oisson’s ratio was minor. Nevertheless , the use of CAD to analyse 345
scaffolds porosities, Taguchi method to select the principal combinations of geometry and material 346
parameters and FEA to simulate their influence on the scaffold performances in a fully pre -manufacturing 347
design represent s an innovative procedure introduced by this study respect to what available in literature . 348
The number of the analysed combinations of scaffold parameters (Tab. 4) was the minimum required to 349
reveal their principal effects on scaffold mechanics. It derived from considering the parameters 350
independent each other . Eventual “cross -talking ” effects were neglected “a priori” , and this may be a 351
limitation of the study. In fact , based on that restricted number of combinations, only the simplest 352
regression model, i.e. the linear one, could be used to relate design input parameters with scaffold 353
performances, although some parameters showed a nonlinear effect (Fig. 5). In light of this, the 354
implemented regression should be used to exclude the less promising material -geometry combinations 355
rather than for a precise control o f the scaffold performanc e. Another limitation involved the scaffold 356
model simulated by FEA : in the model validation, the fibre elastic mo dulus, E, cannot be exactly the 357
experimental indentation elastic modulus, EIT, but it had to be tuned to take into account expected 358
deviations of the realized scaffold from the simulation CAD geometry. For instance, fibres in the scaffold 359
model were considered fully solid, when instead internal unintended micro -pores could be physically 360
present [36]. An investigation of the real scaffold (for instance by SEM, μCT) will help in distinguishing the 361
material and geometry contributions. 362
363
364

16
5. Conclusions 365
Experimental testing provides a repeatable controlled environment for evaluation of mechanics, but it can 366
be costly and time -intensive when considering multiple design iterations and large numbers of specimens 367
[39]. In order to realize and test only the most promising scaffolds towards bone regeneration , an 368
innovati ve pre -processing and pre -testing design procedure , combining in a systematic way CAD, Taguchi 369
method and FEA , was proposed in order to analyse the effect of geometry and mate rial on the compressive 370
behaviour of the scaffold . Specifically, FEA was limited to the initial, linear portion of the scaffold stress – 371
strain response, namely stiffness. Stiffness of the scaffold was influenced primarily by its geometry and 372
secondly by its composition . Based on stiffness and porosity, four scaffold architectures were selected as 373
optimal for the 3D printing of an innovative PCL/ bioactive glass material with composition 70/30 wt.%. 374
Their design parameters and performances will be investigated experimentally, both mechanically and 375
biologically . This design procedure can be tuned to any manufacturing process, scaffold material and target 376
performance. 377
378
Acknowledgments 379
The authors would like to particularly thank Dr. Devis Bellucci for providing the bioactive glass powders, Mr. 380
Mauro Petretta for 3D printing of the composite scaffolds and Dr. Chiara Gualandi for carrying out the 381
compression tests. 382
Competing interests: None declared 383
Funding: None 384
Ethical approval: Not required 385
386
387

17
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490
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493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
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Figures 519
520
Geometry
parameters :
FIBRE: 2 levels
PORE: 3 levels
STEP: 3 levels
OFFSET: 2 levels
CAD
Scaffold
porosities36 scaffold
architectures
Material
parameters :
E: 3 levels
ν: 3 levels9 materials
x
18 architectures
=
162 combinationsTaguchi
18
principal
combinations
CM=
f(Geometry ,
Material)FEA
Compressive
Modulus CM
(stiffness )
Theorical control on 3D printed
scaffolds ’ porosity and stiffness
fortrabecular bone engineering3618
521
Fig. 1. Scaffold design procedure combining Computer Aided Design (CAD), Taguchi method and Finite 522
Element Analysis (FEA) 523
524
525
Fig. 2. Partial Lateral view (a and b) and partial view from above (c) of CAD scaffolds. Geometrical 526
parameters: A is the fibre diameter FIBRE, B is the pore size PORE, C is the OFFSET and D is the STEP. 527
Orange dotted lines state vertical (y direction) pillars. 528

21
529
Fig. 3. CAD drawing of a scaffold before (left) and after (right) the application of compre ssive plates. 530
531
532
Fig. 4. Lateral view highlighting the boundary conditions on the plates (in black) compressing the scaffold 533
(in gray) with FIBRE 330 μm, PORE 300 μm, STEP 60°, no OFFSET. The vertical (y direction) displacement of 534
the superior plate (red arrow) is imposed, while the inferior plate is grounded. 535

22
536
Fig. 5. Average effect on CM of the different levels of STEP, PORE, E and ν for the groups without (NO 537
OFFSET) (left) and with offset (YES OFFSET) (right). Horizontal and vertical coordinates are expressed as % 538
of the maximum value in the ranges, respecti vely, of the parameters and CM. Each marker is accompanied 539
by its parameter level, expressed as absolute value. CM -parameter relations are fitted by a y=mx function, 540
were the gradient m becomes a sensitivity index. 541
542

23
543
Fig. 6. Average and deviation ef fect of the different levels of STEP for the groups without (NO OFFSET) (left) 544
and with offset (YES OFFSET) (rigth) on CM and porosity. 545
546
547
548
Fig. 7. Fitting of Eq. 3 (solid line and expression) on Porosity vs CM (square symbols) for the PCL/bioactive 549
glass 70/30 wt.% scaffolds without offset (NO OFFSET) and with offset (YES OFFSET). 550
551
552
553
554
555

24
Tables 556
Simulation SIZE (mm) E (GPa) ν CM (GPa)
1 0,06 0.1 0.04 0.015
2 0,06 1 0.4 0.141
3 0,6 0.1 0.4 0.018
4 0,6 1 0.04 0.123
557
Tab.1. L4 table for the sensitivity analysis. 558
559
FIBRE 330 μm
PORE 300 μm 450 μm 600 μm
STEP 90° 60° 45° 90° 60° 45° 90° 60° 45°
OFFSET NO SI NO SI NO SI NO SI NO SI NO SI NO SI NO SI NO SI
Porosity 51% 50% 51% 51% 51% 50% 59% 59% 59% 60% 60% 59% 65% 65% 65% 66% 66% 65%
FIBRE 840 μm
PORE 300 μm 450 μm 600 μm
STEP 90° 60° 45° 90° 60° 45° 90° 60° 45°
OFFSET NO SI NO SI NO SI NO SI NO SI NO SI NO SI NO SI NO SI
Porosity 32% 31% 31% 32% 31% 31% 39% 38% 40% 39% 40% 39% 44% 44% 44% 45% 45% 45%
560
Tab. 2. Porosity of the various CAD scaffold architectures. 561
562
563
Group of
scaffolds a c PORE*
if FIBRE 330 μm PORE*
if FIBRE 840 μ m
45°-yes 104.451 -0.835 475 μm 1210 μm
45°-no 105.989 -0.848 452 μm 1151 μm
60°-yes 105.91 -0.838 455 μm 1159 μm
60°-no 105.246 -0.843 462 μm 1176 μm
90°-yes 103.909 -0.856 478 μm 1218 μm
90°-no 104.67 -0.821 475 μm 1209 μm
564
Tab. 3. a and c fitting parameters of Eq. 2, which relates porosity with the ratio between pore and fibre size 565
on the scaffold architectures. As example of the fitting application, PORE* stands for the pore size needed 566
to obtain a porosity of 60%, once fixed the fibre (3D printer nozzle) dimension to 330 or 840 μm. 567
568
569

25
NO OFFSET
Simulation STEP (°) PORE (μm) E (GPa) ν CM (GPa)
1 45 300 0.05 0.1 0.010
2 45 450 0.275 0.3 0.022
3 45 600 0.5 0.49 0.028
4 60 300 0.275 0.49 0.068
5 60 450 0.5 0.1 0.077
6 60 600 0.05 0.3 0.006
7 60 300 0.5 0.3 0.119
8 90 450 0.05 0.49 0.013
9 90 600 0.275 0.1 0.03
YES OFFSET
Simulation STEP (°) PORE (μm) E (GPa) ν CM (GPa)
1 45 300 0.05 0.1 0.008
2 45 450 0.275 0.3 0.020
3 45 600 0.5 0.49 0.025
4 60 300 0.275 0.49 0.075
5 60 450 0.5 0.1 0.044
6 60 600 0.05 0.3 0.002
7 60 300 0.5 0.3 0.085
8 90 450 0.05 0.49 0.005
9 90 600 0.275 0.1 0.010
570
Tab. 4. L9 Taguchi tables for the NO OFFSET and YES OFFSET combinations of FEA simulations. 571
572
a b c d e
NO OFFSET 0.000662 -0.000147 0.144407 -0.006630 0.026816
YES OFFSET 0.000265 -0.000146 0.102963 0.037087 0.039397
573
Tab. 5. Values of the coefficients of Eq. 4 relative to the sets without (NO OFFSET) and with (YES OFFSET) 574
offset, fitted on the rows of Tab.4. 575
576
577
578
579
580

26
581
NO OFFSET CM
Rank PORE ( μm) STEP (°) porosity % 70/30 Sim 70/30 Reg
1 300 90 50.29 0.060 0.072
2 450 90 58.96 0.043 0.054
3 300 60 50.51 0.042 0.048
4 300 45 50.85 0.040 0.036
5 450 60 59.46 0.036 0.030
6 600 60 65.61 0.027 0.011
7 600 90 64.93 0.026 0.036
8 450 45 59.93 0.018 0.017
9 600 45 66.15 0.009 -0.001
RMS (GPa) 9.17E -5
582
583
584
585
586
587
588
589
590
591
Tab. 6. Rank of the scaffold architectures in PCL/bioactive glass 70/30 wt.% by simulation (Sim) CM, coupled 592
with the corresponding multiple regression model (Reg) CM, for the scaffolds without offset (NO OFFSET) 593
and with offset (YES OFFSET). RMS is the Root Mean Square of the differences between simulation and 594
regression CM. 595
596
a b c d e
NO OFFSET 0.000547 -0.000118 0.145251 -0.006713 0.020298
SI OFFSET 0.000133 -0.000127 0.105332 0.036854 0.037375
597
Tab. 7. Values of the coefficients of Eq. 4 relative to the sets without (NO OFFSET) and with (YES OFFSET) 598
offset, fitted on both the rows in the general (Tab. 4) and 70/30 wt% (Tab. 6) Taguchi tables. 599 YES OFFSET CM
Rank PORE (μm) STEP (°) porosity % 70/30 Sim 70/30 Reg
1 300 60 50.84 0.044 0.046
2 300 90 49.84 0.039 0.054
3 300 45 50.15 0.039 0.043
4 450 60 59.80 0.021 0.025
5 450 90 58.81 0.018 0.033
6 450 45 58.95 0.017 0.021
7 600 90 64.97 0.008 0.011
8 600 45 65.00 0.008 -0.001
9 600 60 65.95 0.008 0.003
RMS (GPa) 6.85E -5