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Year: 2023

Three-Dimensional Printed Hydroxyapatite Bone Substitutes Designed by a Novel
Periodic Minimal Surface Algorithm Are Highly Osteoconductive
Maevskaia, Ekaterina ; Khera, Nupur ; Ghayor, Chafik ; Bhattacharya, Indranil ; Guerrero, Julien ; Nicholls,
Flora ; Waldvogel, Christian ; Bärtschi, Ralph ; Fritschi, Lea ; Salamon, Dániel ; Özcan, Mutlu ; Malgaroli, Patrick; Seiler, Daniel ; de Wild, Michael ; Weber, Franz E

DOI: https://doi.org/10.1089/3dp.2022.0134

Posted at the Zurich Open Repository and Archive, University of Zurich
ZORA URL: https://doi.org/10.5167/uzh-223913
Journal Article
Published Version

The following work is licensed under a Creative Commons: Attribution-NonCommercial 4.0 International (CC
BY-NC 4.0) License.
Originally published at:
Maevskaia, Ekaterina; Khera, Nupur; Ghayor, Chafik; Bhattacharya, Indranil; Guerrero, Julien; Nicholls, Flora;
Waldvogel, Christian; Bärtschi, Ralph; Fritschi, Lea; Salamon, Dániel; Özcan, Mutlu; Malgaroli, Patrick; Seiler,
Daniel; de Wild, Michael; Weber, Franz E (2023). Three-Dimensional Printed Hydroxyapatite Bone Substitutes
Designed by a Novel Periodic Minimal Surface Algorithm Are Highly Osteoconductive. 3D Printing and Additive
Manufacturing, 10(5):905-916.
DOI: https://doi.org/10.1089/3dp.2022.0134

3D PRINTING AND ADDITIVE MANUFACTURING
Volume 00, Number 00, 2022
Mary Ann Liebert, Inc.
DOI: 10.1089/3dp.2022.0134

Open camera or QR reader andscan code to access this article
and other resources online.

Three-Dimensional Printed Hydroxyapatite Bone
Substitutes Designed by a Novel Periodic Minimal Surface
Algorithm Are Highly Osteoconductive
Ekaterina Maevskaia,1 Nupur Khera,1 Chafik Ghayor,1 Indranil Bhattacharya,1 Julien Guerrero,1Flora Nicholls,2 Christian Waldvogel,3 Ralph Bärtschi,3 Lea Fritschi,3 Dániel Salamon,3 Mutlu Özcan,4Patrick Malgaroli,5 Daniel Seiler,5 Michael de Wild,5 and Franz E. Weber1,6

Abstract

Autologous bone remains the gold standard bone substitute in clinical practice. Therefore, the microarchitectureof newly developed synthetic bone substitutes, which reflects the spatial distribution of materials in the scaffold,aims to recapitulate the natural bone microarchitecture. However, the natural bone microarchitecture is optimized to obtain a mechanically stable, lightweight structure adapted to the biomechanical loading situation. In
the context of synthetic bone substitutes, the application of a Triply Periodic Minimum Surface (TPMS)
algorithm can yield stable lightweight microarchitectures that, despite their demanding architectural complexity, can be produced by additive manufacturing. In this study, we applied the TPMS derivative Adaptive
Density Minimal Surfaces (ADMS) algorithm to produce scaffolds from hydroxyapatite (HA) using alithography-based layer-by-layer methodology and compared them with an established highly osteoconductive
lattice microarchitecture. We characterized them for compression strength, osteoconductivity, and bone regeneration. The in vivo results, based on a rabbit calvaria defect model, showed that bony ingrowth into ADMS
constructs as a measure of osteoconduction depended on minimal constriction as it limited the maximum
apparent pore diameter in these scaffolds to 1.53 mm. Osteoconduction decreased significantly at a diameter of
1.76 mm. The most suitable ADMS microarchitecture was as osteoconductive as a highly osteoconductive
orthogonal lattice microarchitecture in noncritical- and critical-size calvarial defects. However, the compression
strength and microarchitectural integrity in vivo were significantly higher for scaffolds with their microarchitecture based on the ADMS algorithm when compared with high-connectivity lattice microarchitectures.
Therefore, bone substitutes with high osteoconductivity can be designed with the advantages of the ADMSbased microarchitectures. As TPMS and ADMS microarchitectures are true lightweight structures optimized forhigh mechanical stability with a minimal amount of material, such microarchitectures appear most suitable forbone substitutes used in clinical settings to treat bone defects in weight-bearing and non-weight-bearing sites.
Keywords: triply periodic minimal surface, TPMS, adaptive density minimal surfaces, ADMS, hydroxyapatite,
osteoconduction, microarchitecture, bone substitute, additive manufacturing, 3D printing, ceramics, titanium
1

Oral Biotechnology & Bioengineering, Center of Dental Medicine, University of Zurich, Zurich, Switzerland.
Central Biological Laboratory, University Hospital Zurich, Zurich, Switzerland.
3
Spherene, Zurich, Switzerland.
4
Center of Dental Medicine, Division of Dental Biomaterials, Clinic for Reconstructive Dentistry, University of Zurich, Zurich, Switzerland.
5Institute for Medical Engineering and Medical Informatics IM2, School of Life Sciences, University of Applied Sciences Northwestern
Switzerland, FHNW, Muttenz, Switzerland.
6
CABMM, Center for Applied Biotechnology and Molecular Medicine, University of Zurich, Zurich, Switzerland.
Opposite page: Adaptive periodic minimal surface (ADMS) microarchitecture printed in hydroxyapatite. Image Credit: Franz E. Weber.
2ª Ekaterina Maevskaia et al., 2022; Published by Mary Ann Liebert, Inc. This Open Access article is distributed under the terms of theCreative Commons License [CC-BY] (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, andreproduction in any medium, provided the original work is properly cited.

12
Introduction

Bone is a lightweight composite material because it combines high rigidity and strength relative to its weight. The
overall bone architecture is composed of an outer shell madeof dense tissue known as cortical bone that surrounds cancellous bone and a network of the interconnected plate- androd-like struts called trabeculae (*50–300 lm in thickness).1
According to Wolff́s law,2 healthy bone will constantly adjust to the locally applied load with constant bone turnover.
Therefore, due to this remodeling, trabeculae in cancellous
bone are preferentially aligned in the direction of the biomechanical stresses generated by physical activity. In theevent of a bony defect, when autologous bone is transplanted
to bridge it, the trabecular network of this transplant represents a porous microarchitecture where osteoconduction canoccur.
Osteoconduction is defined as the ingrowth of sprouting
capillaries, perivascular tissue, and osteoprogenitor cells
from a bony bed into the three-dimensional (3D) structure ofa porous implant (adapted from Cornell and Lane3,4) used asa guiding cue to bridge a defect in bony tissue.5 In bone tissue
engineering, as a combination of scaffolds, cells, and growth
factors,6 osteoconduction is heavily dependent on the scaffold microarchitecture.5 Porosity was the focus of scaffold
development during the advent of the bone tissue engineering
era.7 However, the main methodology depends on watersoluble porogens in the size of the preferred pore dimension.8
After curing the scaffold material, the porogens were leachedout, leaving behind a stochastic pore distribution and poresystem.9 The pore size in such a scaffold is generally approximated by the diameter of the largest sphere that can be
fitted into the pore system based on ground sections.10 The
constriction or bottleneck of such a pore system is the diameter of the sphere that can be fitted to the smallest connection in the pore system.
The recent production revolution of layer-by-layer 3D
printing technology facilitates the realization of the demanding, predefined pore systems such that the microarchitectures, pore dimensions, and constrictions in bone
substitutes are defined and designed beforehand and are
ideally optimized for osteoconduction and bone regeneration.11–13 The most widely used 3D printing technology isbased on extruding filaments by melting the material,14 asolution/slurry/gel filament,15,16 or fused deposition.17,18
Since filament-based 3D printing constrains possible variations in microarchitectures, more demanding microarchitectures can only be realized by stereolithography,
selective laser sintering,19 or 3D printing on a powder bed.20
One complex microarchitecture family with the potential to
become a standard in bone tissue engineering is based on
triply periodic minimum surface (TPMS) algorithms.21–23
These algorithms describe lightweight microarchitecturesassociated with high strength.
The TPMS algorithms evolved from the mathematicalproblem of finding the surface that formed the smallest area
for a given perimeter. This problem for a surface formed
between four points located on one of the four sides of atetrahedron was solved by Schwarz in 189024 and led to thediamond (D) and primitive (P) surfaces. In 1970, Schoen
introduced the gyroid (G) surface, another minimal surface25
with the property that the mean curvature vanishes at every

MAEVSKAIA ET AL.

location on the surface and becomes zero. The common
features of all TPMS surfaces include their periodicity in three
independent directions (hence ‘‘triply periodic minimal surface’’), extending infinitely, devoid of self-intersections, andpartitioning the space into two independent labyrinths.22 Afterthe G-surface was identified at the interface between the inorganic crystalline and organic amorphous matter in theechinoderm plates,26 the D-, P-, and G-surfaces were recognized in all the kingdoms of living organisms.22 For example,
in plants grown in the dark, the lamellar structure of chloroplasts adopts P-surface topology and symmetry.27
During the skin barrier formation in humans, a ‘‘TPMSlike lamellar membrane’’ transition occurs inside the tubuloreticular cisternal membrane system of upper granularcells.28 Although the trabecular structure of the bone where
the support structures bear predefined loads resembles agothic cathedral,29 the similarity between the TPMS and theoverall bone structure is based on the common lightweightcharacteristics and not on an algorithm (TPMS or adaptive
density minimal surfaces [ADMS]). This notion is supportedby the finding that unlike the basic element of TPMS structures, the mean curvature of any point on the surface of thecancellous bone diverts from zero and is found to be negative,
demonstrating that their surfaces are hyperbolic on average.30
In bone microarchitecture, ‘‘minimal surface’’ is associated with lightweight and high-strength characteristics
combined with low mass. Moreover, the average curvature ofany point on the surface is zero, leading to a uniform stress
distribution under load and high strength. Owing to thiscombination, TPMS microarchitectures appear attractive fordesigning bone substitutes. Some reports of their use in bone
tissue engineering have already been published.31–34 However, reports of in vivo applications of TPMS structures inbone substitutes are still scarce and lack direct comparisons
to highly osteoconductive microarchitectures.21,35
In TPMS structures, structural thickness and orientation
distribution are constant, leading to a directional dependencyof the mechanical properties.36 Low anisotropy would bedesirable for bone substitutes to be placed at any site.
Therefore, we applied the novel ADMS microarchitecture
characterized by a lack of spikes in the distribution of theorientation of their surface and an equal mechanical performance in all directions, which can be adjusted to satisfy agiven load case. Similar to TPMS structures, ADMS are
doubly curved at each point, such that the mean curvature iszero at every point. The main objective of this project was toproduce bone substitutes from hydroxyapatite (HA) by
lithography-based 3D printing with ADMS structures ofthree different pore system constrictions and a reference
ADMS structure from titanium (Ti) by Selective Laser
Melting (SLM) to identify the most osteoconductive ADMSbased microarchitecture and compare it in vivo to a highly
osteoconductive, well-interconnected lattice microarchitecturethat is already well documented.37
Materials and Methods
Implant production

HA-based scaffolds were produced with HA slurry LithaBone HA 400 (Lithoz, Vienna, Austria) using a CeraFab7500 from Lithoz, as previously reported.38 The ADMS
scaffolds were characterized by a minimum constriction of

ADMS ARE OSTEOCONDUCTIVE

0.5, 0.8, or 1.1 mm and a wall thickness of 0.2 mm. As acontrol, we used a lattice microarchitecture known for highosteoconductivity with struts of 0.3 mm at a distance of
0.8 mm.37 The maximum dwelling time was set to 1300C toproduce mechanically stable osteoconductive implants.38
Spherene AG (Zurich, Switzerland) provided standard triangular language (STL) files describing the micro- andmacroarchitecture of the scaffolds. The ADMS and lattice
microarchitecture filled a 6.0-mm-diameter and 4.5-mm-highcylinder. The overall construct contained two additional rings
as follows: (1) To prevent immersion of the implant into thebone defect beyond 2.5 mm, a solid ring of 1.0 mm thickness
encased the upper 2.0 mm of the cylinders with ADMS or
lattice microarchitecture. (2) The design included a solid ringwith an outer diameter of 6.0 mm, a height of 0.5 mm, and
0.3 mm thick was included in the design.
For critical-size defects, the cylinders with the ADMS andlattice microarchitecture were 4.5 mm in height and 15.0 mm
in diameter to stabilize the lower part of the cylinder. The tworings for stabilization and prevention of immersion were
designed according to the scaffolds for noncritical-size defects. A solid ring 1.0 mm thick encased the upper 2.0 mm ofthe cylinders, and a solid ring with an outer diameter of
15.0 mm, a height of 0.5 mm, and 0.3 mm thick stabilized thelower part with ADMS or lattice microarchitecture. Upon
producing the green bodies, the sintered scaffolds weretransferred from the oven to a sterile bench in containers,
packed for transportation into the operation workflow, andused as bone substitute implants without further sterilization.
For the additive manufacturing of the titanium-based
scaffolds, the same STL files of the ADMS models were
imported into Magics software (V21; Materialise) where thesupport structures to the building platform were created using‘‘block type’’ support. Note that no supports were necessary
within the ADMS structures. The manufacturing of thesamples was done using a SLM 250 HL system (by SLM
Solutions GmbH, Lübeck, Germany) with a building platform of 250 · 250 mm2, and with integrated powder reconditioning and sieving unit. The SLM system used acontinuous wave 200 W Ytterbium fiber laser with a wavelength between 1068 and 1095 nm. A layer height of 30 lm
was used to print a commercially pure titanium powder (Tigrade II according to ASTM F67; SLM-Solutions GmbH)with a d50 of 41 – 2 lm (Particle size analysis with Helos/KF+ incl. RODOS/ + VIBRI particle size distribution analysis
set up by SympaTec GmbH, Clausthal-Zellerfeld, Germany).
The printing laser parameters were set to 100 W nominal
laser power for the outer contour at a scanning speed of
550 mm/s and 175 W for the inner contour with a scanningspeed of 833 mm/s. After the SLM process, the parts were
carefully detached manually from the building platform. The
downward facing support structures were then broken off at
perforated support breaking points.
Implant characterization and microcomputed
tomography scanning

Wall thickness and maximal diameter of the twodimensional (2D)-sphere fitting in the microarchitecture were
measured on the ground sections using image analysis software(Image-Pro Plus; Media Cybernetic, Silver Springs, MD).
Microcomputed tomography (microCT) scanning of the scaf-

3

folds was performed with a SKYSCAN 1272 (Bruker, Kontich,
Belgium) with the following settings: voltage 90 kV (0.5 mm
Al +0.038 mm Cu filter), current 111 lA, pixel size 10.9 lm,
and rotation step 0.2. The reconstruction was performed using
NRecon software. The analysis of the scaffold morphology(volume, porosity, and surface area) determined from threesamples of each microarchitecture was performed using the
CTAn software. Bruker supplied all software required for thereconstruction and analysis. The region of interest was a cylinder with an ADMS or lattice structure without the outer rings.
Compression strength measurements

The comparative compression strength was based on scaffolds designed for noncritical size, 6 mm cylinder defects, enlarged by the Cerafab7500 software by a factor of 1.5, in the x,y, and z directions. The specimens were mounted in the jig of auniversal testing machine (Zwick ROELL Z2.5 MA 18-1-3/7,
Ulm, Germany). The occlusal surface (63.62 mm2) in the direction of the building layers was subjected to compressive
loading at a crosshead speed of 1 mm/minute. The stress–strain
curve was analyzed using a software (TestXpert V11.02; Zwick
ROELL) to determine the maximum compression strength.
Surgical procedure

Osteoconductivity of scaffolds was assessed in vivo by inserting the four 6-mm calvaria defect models (500, 800, and1100 lm ADMS or lattice microarchitecture scaffolds) and theTi-ADMS 800 lm scaffolds into ten adult New Zealand whiterabbits, as reported previously.39 In brief: ‘‘Animals were anesthetized by an injection of 65 mg/kg ketamine and 4 mg/kg
xylazine. During operation, isoflurane/O2 was applied. Afterthe disinfection, a straight incision from the nasal bone tothe midsagittal crest was performed with a scalpel, the soft
tissues reflected, and the periosteum removed. In the area ofthe right and left parietal and frontal bones, four evenly distributed 6-mm diameter craniotomy defects or one central 15mm defect were marked with a trephine bur followed by theuse of round burrs of different diameters starting from 6 to
1 mm to generate a full-thickness calvarial defect without
damaging the dura. Finally, bone debris was removed byflushing the defects with sterile physiological saline solution.’’For the 15-mm critical-size defect, which was used to compare
the most suitable ADMS to the lattice microarchitecture, another 13 animals were operated on as previously described.40
Animals had unrestricted access to drinking water and were
fed a standard laboratory diet. The weights of the animals
ranged from 3.5 to 4.5 kg. The protocol was evaluated andapproved by the local Ethics Committee (Veterinäramt Zürich, Zürich, Switzerland; 065/2018). All procedures wereconducted in accordance with local guidelines. Four weeks
after the operation with the 6-mm, noncritical-size defects and8 weeks after the operation involving the 15-mm critical-size
defects, the rabbits were anesthetized and sacrificed by an
overdose of pentobarbital. The craniums containing the fouror single craniotomy sites were removed and placed in 40%
ethanol. Embedding was performed as previously reported.40
Histomorphometry

A single ground section from the middle of each implant
was evaluated using image analysis software (Image-Pro Plus;

4Media Cybernetic). The area of interest (AOI) was determinedby the 6- or 15-mm defect width and the area fraction of theimplant submerged into the bony defect. The regenerated areain the AOI was determined as the percentage of bone and bone
integrated scaffolds in the AOI (bony area %).
Bone bridging

Osteoconductivity was quantified by the extent of thebony-bridged defects, as previously reported.41 Briefly, bone
tissue was identified by Toluidine Blue staining, and areas in
the AOI were projected onto the x-axis. Next, all stretches ofthe x-axis with bone tissue were summed and related to the 6and 15-mm defect widths, respectively. Bone bridging isgiven as a percentage of the 6- or 15-mm defect width wherebone formation had occurred.
Statistics

The primary analysis unit for in vivo experiments was a defect. Data from 9 to 10 rabbits for the 6-mm defect and 6 to 7
rabbits for the 15-mm defects were analyzed in each group. The
Kruskal–Wallis test followed by pairwise comparison of treatment modalities with the Mann–Whitney test for independent
data (IBM SPSS v.19) were applied. The Jonckheere–Terpstra
test was used to determine statistical significance between
groups of decreasing level of constriction. Statistical significance was set to 0.05 and the p-values are displayed in thegraphs. If not specified, the p-values were determined by the
Mann–Whitney test. Values are represented as mean – standard
deviation in the text or median – lower/upper quartile in thegraphs.
Results
Scaffold production

Scaffolds designed with the ADMS algorithm can be produced by the lithography-based layer-by-layer methodology

MAEVSKAIA ET AL.

or by SLM without a support structure (Fig. 1). After producing the noncritical-size defect scaffolds, the porosity andsurface were determined from a cylinder 4.5 mm in height and
6 mm in diameter filled with the diverse microarchitectures by
microCT and compared with the data encrypted in the STL
file. The data compiled in Table 1 show that the porosity of
HA-printed scaffolds determined by microCT was 3–8%
lower than that encrypted in the STL file. Even more pronounced was the discrepancy between the STL file and printed
scaffold in the surface area because, depending on the microarchitecture, the surface of the STL file in silico was 14–
36% higher than measured in the printed HA-scaffolds by
microCT. Minimum constriction or bottleneck between interconnected pores as preset in the STL file and chosen as theprimary determinant of the three ADMS designs influenced
the apparent 2D maximal sphere diameter reaching its maximum of 1.86 – 0.17 mm in the ADMS 1100 lm design.
The material used for 3D printing and methodology affected
the characteristics of the printed scaffolds, despite an identical
STL file being used to program the printing systems (Table 2).
For the ADMS 800 lm microarchitecture, the minimum andmaximum wall thicknesses were higher if the scaffold was
produced by a lithography-based methodology using a HA/
binder-slurry compared with the production with a selective
laser-melting methodology in a titanium powder bed. Thissignificant increase in wall thickness increased the maximum
diameter of a 2D-sphere fitting into the ground sections with
ADMS 800 lm microarchitecture from 1.51 – 0.16 mm for
HA-scaffolds to 1.76 – 0.12 mm for titanium scaffolds. Therefore, the central determinant of osteoconduction and boneregeneration of ADMS microarchitectures appears to be thediameter of the largest sphere that fits into the pore system.
Mechanical testing of scaffolds

The compression strengths of ADMS 500, 800, and 1100 lm
were evaluated and compared with the lattice architecture ofsamples derived from the STL file for scaffolds designed for the

FIG. 1. 3D printing of ADMS structures. ADMS structure during printing in the CeraFab7500 machine (a). ADMS
structure after removal from the machine and attached to the building platform (b). The same ADMS structure after
sintering at 1300C (c). The diameter of the ADMS structure was 23 mm (c). Six and fifteen millimeter scaffolds for animal
testing are shown from the upper and lower sides (d). Scale is provided. Diverse ADMS structures with minimal constriction
diameter as listed (e). Scale is provided. 3D, three-dimensional; ADMS, adaptive density minimal surface.

5

68.71
71.16
78.36
79.40

ADMS 500 lm
ADMS 800 lm
ADMS 1100 lm
Lattice62.78 – 1.87
64.57 – 1.30
71.55 – 1.07
75.58 – 1.20

Porosity
microCT (%)
376.06 – 14.34
388.39 – 43.19
300.58 – 22.28
307.88 – 32.03

Surface area
microCT (mm2)512.40481.90381.97378.60Surface area
STL-file (mm2)
0.50
0.80
1.10
0.80

Minimal constriction
in STL-file (mm)ADMS 800 lm
microarchitecturematerial

Ti, titanium.

HA
Ti

1.53 – 0.12
1.51 – 0.15
1.86 – 0.17
1.07 – 0.04

2D maximal spherediameter fitting inarchitecture (mm)

0.20
0.20

Wall thickness
STL-file (mm)0.25 – 0.03
0.15 – 0.02

Minimal wall
thicknessmeasured (mm)0.31 – 0.06
0.28 – 0.04

Maximal wall
thicknessmeasured (mm)1.51 – 0.16
1.76 – 0.12

2D maximal
sphere diameter
fitting inarchitecture(mm)

82.85 – 18.48
50.94 – 26.07

Bonybridging (%)

65.46 – 42.20
28.53 – 25.60

Bonyregenerated
area (%)

Table 2. Adaptive Density Minimal Surfaces 800 lm Microarchitecture Characteristics and In Vivo Performance Dependent on Production
Methodology and Material (Hydroxyapatite or Titanium)

Comparison between STL file and microCT of HA-based scaffolds.
2D, two-dimensional; ADMS, adaptive density minimal surfaces; HA, hydroxyapatite; microCT, microcomputed tomography; STL, standard triangular language.

Porosity
STL-file(%)

Microarchitecture
in HA

Table 1. Characteristics of Microarchitectures

6

MAEVSKAIA ET AL.

6-mm defect model. To increase the initial stability of thesescaffolds, the STL file of each 6-mm in vivo sample wastransferred to the Cerafab7500 software and scaled up in x, y,
and z-dimensions by a factor of 1.5, printed, and sintered. The
resulting scaffolds (Fig. 2, upper panel) were subjected tocompression analysis. The maximum compression strength of
ADMS 500 lm was 6.34 – 3.20 N/mm2; for ADMS 800 lm
6.54 – 2.11 N/mm2; for ADMS 1100 lm 5.88 – 1.98 N/mm2;
and for orthogonal lattice 2.87 – 0.84 N/mm2 (Fig. 2, lower
panel). The lattice-based scaffold showed a significantly lower
compression strength than all the tested ADMS structures.
Osteoconductivity and bony regeneration capacityof ADMS and lattice-based scaffolds in noncritical-size
defects in vivo

FIG. 2. Compression strength of ADMS and lattice microarchitectures from HA. In the upper panel, all tested scaffold
types are displayed in the same order as in the graph. The graph,in the lower panel visualizes the compression strength of alltested scaffold types, as listed, in a box-blot ranging from the25th (lower quartile) to the 75th (upper quartile) percentile,
with the median displayed as a solid black line and whiskers
extending to the minimum and maximum values. Values outside the box blot are shown individually. HA, hydroxyapatite.

One aim of this study was to determine the osteoconductivity and bone regeneration capacity of the threedifferent ADMS-based scaffolds compared with the highly
osteoconductive lattice-based scaffold at 4 weeks postoperation. Toluidine Blue-stained ground sections from the
middle of each scaffold (Fig. 3a) revealed that bone formation and advancement of mineralized bone tissue into the
ADMS-based scaffold from HA varied with minimal constriction in the scaffold. The lattice microarchitecture performed the best under both measures (Fig. 3a); however, it
was not significantly better than the ADMS 500 lm. The
extent of bone bridging and formation in the defect treated

FIG. 3. Osteoconduction and bone regeneration in ADMS and lattice microarchitectures. Histological sections from the
middle of the noncritical-size defects were treated with ADMS- and lattice-derived scaffolds after 4 weeks of recovery (a).
Scale bars in blue indicate 1000 lm. Original magnifications were 100-fold. Bone appears as grayish purple to purple, and HA
as grayish to black. Histomorphometry results (b, c). Defect bridging (b) and new bone formation (c) decrease significantly in
ADMS microarchitecture with the increase in minimal constriction from 500 to 1100 lm, as evident by the Jonckheere–
Terpstra test results. The lattice microarchitecture yielded the highest values but not significantly higher than with ADMS
500 lm or ADMS 800 lm scaffolds. Values are displayed as box plots ranging from the 25th (lower quartile) to the 75th (upper
quartile) percentile. The median is displayed as a solid black line and whiskers extending to the minimum and maximum
values. Values outside the range of the box blot are shown as individual points. p-Values are provided in the graphs.

ADMS ARE OSTEOCONDUCTIVE

with HA-based scaffolds is illustrated (Fig. 3b, c). Approximately 93.00% – 8.99%, 82.85% – 18.48%, and 62.95%– 19.51% of the middle section was bridged with ADMS 500,
800, and 1100 lm, respectively. In lattice microarchitectures,
bridging was 96.85% – 6.75% complete and significantly
higher than that of ADMS 1100 lm.
In the AOI, the percentage of bony regeneration in the
middle section was 56.90% – 15.90%, 49.86% – 20.90%, and36.65% – 18.47% with ADMS 500, 800, and 1100 lm, respectively. In scaffolds with the lattice microarchitecture, thebony regenerated area covered 64.66% – 15.55% of the AOI
and was significantly higher compared with the ADMS
1100 lm. These results suggest that for ADMS microarchitectures in HA, osteoconductivity and bone regeneration
decrease with an increase in minimal constriction from 500 to1100 lm. Notably, ADMS 800 lm built with Ti performed
significantly worse for bony bridging and regeneration thanthat built with HA (Table 2). To better understand this result,
we switched our viewpoint from the STL-file embedded
minimal constriction in the scaffold to the diameter of thelargest sphere that fits into the pore system based on thehistology derived from our in vivo experiments. For constructs produced in HA, the maximal diameter of the spherewas 1.53 – 0.12 mm for ADMS 500 lm, 1.51 – 0.15 mm for
ADMS 800 lm, 1.86 – 0.17 mm for ADMS 1100 lm, and1.07 – 0.04 mm for the lattice microarchitecture (Table 1).
Since ADMS 500 lm, ADMS 800 lm, and lattice microarchitecture yielded a significantly higher percentage of defect bridging than ADMS 1100 lm, these results suggest that7for high osteoconductivity, the largest sphere that fits into thepore system should not exceed 1.53 mm in diameter (Fig. 3c).
For ADMS 800 lm produced in Ti, the maximal sphere diameter was 1.76 – 0.12 mm and exceeds the maximal diameter for optimal osteoconduction of 1.53 mm. As a result,bony bridging dropped significantly from 82.85 – 18.48 for
ADMS 800 lm in HA to 50.94 – 26.07 for ADMS 800 lm in
Ti and the percentage of bony regenerated area from65.46 – 42.20 to 28.53 – 25.60, respectively (Table 2). These
results support our notion that the central determinant of
osteoconduction and bone regeneration is the diameter of thelargest sphere that fits into the pore system.
Osteoconductivity, bony regeneration capacity,and mechanical strength of ADMS 500 lm
and lattice-based scaffolds in critical-size defects
in vivo

We compared the best-performing ADMS microarchitecture, ADMS 500 lm, and the lattice architecture in a
critical-size bone defect model. The scaffolds (Fig. 1d, rightscaffold) with the ADMS 500 lm microarchitecture and thelattice architecture were designed to span a 15-mm defect in a
rabbit calvarium full-thickness defect model. Healing interms of defect bridging and bone regeneration was evaluatedafter 8 weeks. The histology of the middle section (Fig. 4a)revealed that mineralized bone tissue advanced in ADMS
500 lm constructs to span 65.46% – 29.60% of the defect and71.67% – 15.55% in lattice microarchitectures (Fig. 4b). The

FIG. 4. Osteoconduction and bone regeneration in ADMS 500 lm and lattice microarchitecture in a critical-size defect.
Two histological sections from the middle of the critical-size defects treated with ADMS 500 lm and a lattice-derived
scaffold after 8 weeks of recovery (a). Scale bars in blue indicate 1000 lm. Original magnifications were 100-fold. Boneappears as grayish purple to purple and HA as grayish to black. Histomorphometry results (b, c). No significant difference
could be detected in defect bridging (b) and new bone formation (c) between ADMS 500 lm and the lattice microarchitectures. Values are displayed as box plots ranging from the 25th (lower quartile) to the 75th (upper quartile)
percentile. The median is displayed as a solid black line and whiskers extending to the minimum and maximum values.

8bony regenerated area was 46.30% – 21.78% and 33.50%– 6.00% in ADMS 500 lm constructs and lattice microarchitecture, respectively (Fig. 4c). No significant difference
between ADMS 500 lm and lattice constructs was detectedin critical-size cranial defects in rabbits over 8 weeks.
However, the implant integrity of the scaffolds for criticalsize defects was significantly higher with ADMS 500 lm,
where five out of the five implants remained 100% intact after
the 8-week period in the in vivo situation.
The lattice-based scaffolds disintegrated in four out ofseven implants, reflecting the much higher mechanicalstrength of the ADMS-based structure than the lattice architecture (Fig. 2b). The scatter within the lattice structures ismore than three times smaller than within the ADMS structures (Fig. 4c) and may indicate improved predictability ofosteoconductivity.
Discussion

TPMS-based structures are promising microarchitectures
for bone substitutes because they combine lightweight withmechanical strength. However, in vivo results using TPMS
microarchitectures are scarce. In this study, we screened
several ADMS-based microarchitectures, distinguished fromthe TPMS algorithm by an evenly distributed surface orientation and isotropic mechanical properties, for osteoconductivity and bone regeneration in rabbit calvarial defectmodels. In the noncritical-size defect model, an increase inminimal constriction in the ADMS structure was associatedwith an increase in maximum pore size and a significant
decrease in osteoconductivity in terms of defect bridging andbone regeneration. The level of both measurements was not
significantly different between ADMS 500 lm and the highly
osteoconductive lattice architecture.
However, the compression strength of the latter was significantly lower compared with all the tested ADMS structures. The superior mechanical stability of the ADMS 500 lm
was mirrored by the high failure rate of the lattice architecture in critical-size defects. However, both structures performed equally well in the critical-size cranial defect modelin terms of osteoconductivity and bony regeneration.
Lightweight microarchitectures depending on the minimal
surface algorithm are optimal for use as bone substitutes.
Initially, three ADMS microarchitectures were chosen basedon the defined minimal constrictions of 500, 800, and1100 lm. Our results suggest that the central determinant of
osteoconduction and bone regeneration is the diameter of thelargest sphere that fits into the pore system. If the diameter is£1.53 mm, as found in ADMS 500 lm, ADMS 800 lm, andthe lattice microarchitecture (Table 1), osteoconduction issignificantly higher than with ADMS 1100 lm with a
1.83 mm as the largest sphere diameter fitting into the interconnected pore system. Currently, scaffolds based on TPMS–
microarchitectures with pores up to 1.00 mm,42 gyroids with
0.43 mm constrictions, and 0.81 mm pore diameter have beentested.32 Suggestions for an optimal pore size range for boneregeneration could not be drawn from these studies. Published literature on bone regeneration with scaffolds containing pores >1.00 mm is scarce.
In drill hole defects in sheep treated with ceramic scaffolds
with randomly distributed pores of 0.15–1.22 mm in diame-

MAEVSKAIA ET AL.

ter, the pore size did not affect bone healing.43 With uniform
pore diameters in a rabbit defect model, we demonstrated thatthe optimal pore diameter for osteoconduction and bone regeneration was between 0.7 and 1.2 mm. However, diametersof 1.5–1.7 mm disabled osteoconduction and bone regeneration substantially.41 This shift in the optimal pore diameterfrom 1.20 mm for an ordered pore-based microarchitecture to1.53 mm for ADMS microarchitectures might be because, inthe first case, all pores are 1.20 mm in diameter. In contrast,
only a single pore in each section was 1.53 mm in diameter in
ADMS microarchitectures.
Surprisingly, HA-based ADMS 800 lm performed significantly better than the corresponding scaffold made fromtitanium (Table 2). This appears to be because productiondependent minor changes in wall thickness influence thediameter of the maximum sphere fitting into the microarchitecture. A material-dependent influence appears unlikely since titanium and calcium phosphate-based
microarchitectures perform equally well.40 It also suggeststhat the microporosity (interconnected pores in the micrometer range within the sintered material38) of 15% found inthese HA-based scaffolds38 versus a microporosity of 0% in
titanium scaffolds does not affect osteoconductivity. For the
ADMS 800 lm scaffolds made from titanium, the diameter ofthe maximum sphere fitting into the microarchitecture was
1.76 mm, and is significantly higher than the 1.51 mm foundin the HA-based scaffold (Table 2). This result further confines
the maximum pore diameter value in ADMS microarchitectures for optimal osteoconduction and bony regeneration to*1.53–1.76 mm.
Discrepancies between the STL file and printed microarchitecture owing to the production methodology should beconsidered. Moreover, in the ADMS- and TPMS algorithm
used to design the bone substitute microarchitecture, themaximum pore diameter should be set at 1.53 mm to facilitate
optimized osteoconduction and defect healing. The minimal
constriction can be set to 0.50 mm since ADMS 500 and
800 lm performed equally well if made from HA (Fig. 3). In
particular, for powder-bed-based 3D-printing methodologies,
the geometric constrictions should be as wide as possible toenable the efficient release of powder entrapped in the
structure. As ADMS comprises two continuous but independent pore systems, powder removal is possible, and in our
ground sections from ADMS 800 lm in titanium, we did not
find a single pore filled with powder. We did not evaluate thispossibility for the ADMS 500 lm design.
ADMS-based scaffolds showed higher mechanicalstrength than the lattice microarchitecture (Fig. 2) quantitatively in mechanical compression tests and qualitatively in
critical-size defects in in vivo situations, which could partially be explained by the higher porosity according to the
Gibson–Ashby relation.44 These results reflect not only different porosities but also different strength distributions insuch architectures because ADMS, like TPMS structures, aredoubly curved at each point such that the mean curvature iszero at every point. Although lattice architectures can be
adjusted to mechanical needs,45 smooth and continuous
structures such as primitive-TPMSs are less likely to causestress concentration, yielding an overall higher scaffold
strength.46 Moreover, they are optimized for low weight andrequire less material.

ADMS ARE OSTEOCONDUCTIVE

For gyroid-TPMS47 the mechanical properties reportedly
corresponded well to the material density.48 Therefore, as
seen in ADMS 500 lm, the least porous scaffold should exhibit the highest strength. To determine the differences between the three ADMS structures presented in this study,
additional studies with structures optimized for mechanicaltesting are required and will be evaluated in the future. Owing
to the brittle nature of ceramic materials, such studies shouldbe performed using titanium-based scaffolds.
Osteoconduction depends on a currently undefined communication guided by the scaffold between defect margins.5,41
Therefore, it is no surprise that lattice microarchitectures thatare highly transparent in terms of the percentage of materialfree area in the projection through the entire scaffold showhigh osteoconductivity. However, the ADMS 500 lm and
ADMS 800 lm microarchitectures with zero transparency
are statistically indistinguishable from the osteoconductivityof the lattice microarchitectures (Figs. 3 and 4). Transparency
is not a critical limiting factor for osteoconductivity and has
been reported for pore-based microarchitectures.41 Moreover, in lattice architectures, the straight and shortest possible
paths for bone ingrowth aimed at defect bridging are unobstructed, and all possible routes are interconnected. However,
the two paths defined by the two-pore systems are not interconnected in ADMS structures and are neither straight nor
short but instead are slightly curved. Therefore, guiding andcommunication for osteoconduction can occur efficiently incurved microarchitectures and independently in the two
separated channel systems.
One could speculate that for more extended defects,
straight and short bone in-growth patterns, as facilitated inlattice architectures, are superior to curved ones, as found in
ADMS architectures because the maximum reach for a
guiding cue might be limited. Therefore, additional studies
and animal model systems are required to provide a definitive
answer to this question.
Conclusion

Lightweight, high-strength ADMS microarchitectures canbe designed to be highly osteoconductive and, therefore, well
suited for the microarchitecture of bone substitutes. The key
design criterion is the 2D maximal sphere diameter fitting
into the microarchitecture. If high osteoconductivity andoptimal bone regeneration are desired, its value should notexceed 1.53 mm. In combination with a minimal constriction,
a 500 lm ADMS microarchitecture appears well suited forbone substitutes used in clinical settings for load-bearing andnonload-bearing applications.
Institutional Review Board Statement

The procedure involving animals was evaluated and accepted by the local authorities (Veterinäramt Zürich) andprovided with the license 065/2018.
Data Availability Statement

The raw/processed data required to reproduce these findings cannot be shared at this time as the data also form part ofadditional ongoing studies.

9
Acknowledgment

The authors would like to thank Ana Perez for her assistance with histologies.
Authors’ Contributions

Conceptualization: F.E.W.; methodology: E.M., N.K.,
C.G., I.B., J.G., M.O., P.M., D.S., M.W., C.W., R.B., L.F.,
F.N., and F.E.W.; formal analysis: E.M., N.K., C.G., I.B.,
J.G., M.O., C.W., R.B., L.F., D.S., and F.E.W.; investigation:
E.M., N.K., P.M., D.S., M.W., C.G., I.B., J.G., M.O., andF.E.W.; resources: F.E.W.; data curation: C.G., I.B., J.G.,
M.O., and F.E.W.; writing—original draft preparation:
F.E.W.; writing—review and editing: E.M., N.K., C.G., I.B.,
J.G., M.O., P.M., D.S., M.W., C.W., R.B., L.F., F.N., andF.E.W.; visualization: E.M., N.K., C.G., I.B., J.G., andF.E.W.; supervision: F.E.W.; supervision ADMS: C.W.; andfunding acquisition: C.W., D.S., and F.E.W. All authors haveread and agreed to the published version of the article.
Author Disclosure Statement

The ADMS algorithm is patented by Spherene AG where
C.W., R.B., L.F., and D.S. own stocks or stock options.
Otherwise, the authors declare no conflicts of interest.
Funding Information

This research was funded predominantly by the Innosuisse
Project 43760.1 IP-LS and in part by Swiss National Science
Foundation through a grant to F.E.W. (310030_197128).
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11

Address correspondence to:Franz E. Weber
Oral Biotechnology & Bioengineering
Center of Dental Medicine
University of Zurich
Plattenstr. 118032 Zurich
Switzerland
E-mail: franz.weber@zzm.uzh.ch