Simulated tissue growth for 3D printed scaffolds

Cell-Based Modeling of Tissue Developing in the Scaffold Pores of Varying Cross-Sections

In this work, we present a mathematical model of cell growth in the pores of a perfusion bioreactor through which a nutrient solution is pumped. We have developed a 2-D vertex model that allows us to reproduce the microscopic dynamics of the microenvironment of cells and describe the occupation of the pore space with cells. In this model, each cell is represented by a polygon; the number of vertices and shapes may change over time. The model includes mitotic cell division and intercalation. We study the impact of two factors on cell growth. On the one hand, we consider a channel of variable cross-section, which models a scaffold with a porosity gradient. On the other hand, a cluster of cells grows under the influence of a nutrient solution flow, which establishes a non-uniform distribution of shear stresses in the pore space. We present the results of numerical simulation of the tissue growth in a wavy channel. The model allows us to obtain complete microscopic information that includes the dynamics of intracellular pressure, the local elastic energy, and the characteristics of cell populations. As we showed, in a functional-graded scaffold, the distribution of the shear stresses in the pore space has a complicated structure, which implies the possibility of controlling the growth zones by varying the pore geometry.

Multicellular dynamics on structured surfaces: Stress concentration is a key to controlling complex microtissue morphology on engineered scaffolds

Tissue engineers have utilised a variety of three-dimensional (3D) scaffolds for controlling multicellular dynamics and the resulting tissue microstructures. In particular, cutting-edge microfabrication technologies, such as 3D bioprinting, provide increasingly complex structures. However, unpredictable microtissue detachment from scaffolds, which ruins desired tissue structures, is becoming an evident problem. To overcome this issue, we elucidated the mechanism underlying collective cellular detachment by combining a new computational simulation method with quantitative tissue-culture experiments. We first quantified the stochastic processes of cellular detachment shown by vascular smooth muscle cells on model curved scaffolds and found that microtissue morphologies vary drastically depending on cell contractility, substrate curvature, and cell-substrate adhesion strength. To explore this mechanism, we developed a new particle-based model that explicitly describes stochastic processes of multicellular dynamics, such as adhesion, rupture, and large deformation of microtissues on structured surfaces. Computational simulations using the developed model successfully reproduced characteristic detachment processes observed in experiments. Crucially, simulations revealed that cellular contractility-induced stress is locally concentrated at the cell-substrate interface, subsequently inducing a catastrophic process of collective cellular detachment, which can be suppressed by modulating cell contractility, substrate curvature, and cell-substrate adhesion. These results show that the developed computational method is useful for predicting engineered tissue dynamics as a platform for prediction-guided scaffold design. STATEMENT OF SIGNIFICANCE: Microfabrication technologies aiming to control multicellular dynamics by engineering 3D scaffolds are attracting increasing attention for modelling in cell biology and regenerative medicine. However, obtaining microtissues with the desired 3D structures is made considerably more difficult by microtissue detachments from scaffolds. This study reveals a key mechanism behind this detachment by developing a novel computational method for simulating multicellular dynamics on designed scaffolds. This method enabled us to predict microtissue dynamics on structured surfaces, based on cell mechanics, substrate geometry, and cell-substrate interaction. This study provides a platform for the physics-based design of micro-engineered scaffolds and thus contributes to prediction-guided biomaterials design in the future.

Curvature in Biological Systems: Its Quantification, Emergence, and Implications across the Scales

Surface curvature both emerges from, and influences the behavior of, living objects at length scales ranging from cell membranes to single cells to tissues and organs. The relevance of surface curvature in biology is supported by numerous experimental and theoretical investigations in recent years. In this review, first, a brief introduction to the key ideas of surface curvature in the context of biological systems is given and the challenges that arise when measuring surface curvature are discussed. Giving an overview of the emergence of curvature in biological systems, its significance at different length scales becomes apparent. On the other hand, summarizing current findings also shows that both single cells and entire cell sheets, tissues or organisms respond to curvature by modulating their shape and their migration behavior. Finally, the interplay between the distribution of morphogens or micro-organisms and the emergence of curvature across length scales is addressed with examples demonstrating these key mechanistic principles of morphogenesis. Overall, this review highlights that curved interfaces are not merely a passive by-product of the chemical, biological, and mechanical processes but that curvature acts also as a signal that co-determines these processes.

Effects of surface patterning and topography on the cellular functions of tissue engineered scaffolds with special reference to 3D bioprinting

The extracellular matrix (ECM) of the tissue organ exhibits a topography from the nano to micrometer range, and the design of scaffolds has been inspired by the host environment. Modern bioprinting aims to replicate the host tissue environment to mimic the native physiological functions. A detailed discussion on the topographical features controlling cell attachment, proliferation, migration, differentiation, and the effect of geometrical design on the wettability and mechanical properties of the scaffold are presented in this review. Moreover, geometrical pattern-mediated stiffness and pore arrangement variations for guiding cell functions have also been discussed. This review also covers the application of designed patterns, gradients, or topographic modulation on 3D bioprinted structures in fabricating the anisotropic features. Finally, this review accounts for the tissue-specific requirements that can be adopted for topography-motivated enhancement of cellular functions during the fabrication process with a special thrust on bioprinting.

Review on Bioinspired Design of ECM-Mimicking Scaffolds by Computer-Aided Assembly of Cell-Free and Cell Laden Micro-Modules

Tissue engineering needs bioactive drug delivery scaffolds capable of guiding cell biosynthesis and tissue morphogenesis in three dimensions. Several strategies have been developed to design and fabricate ECM-mimicking scaffolds suitable for directing in vitro cell/scaffold interaction, and controlling tissue morphogenesis in vivo. Among these strategies, emerging computer aided design and manufacturing processes, such as modular tissue unit patterning, promise to provide unprecedented control over the generation of biologically and biomechanically competent tissue analogues. This review discusses recent studies and highlights the role of scaffold microstructural properties and their drug release capability in cell fate control and tissue morphogenesis. Furthermore, the work highlights recent advances in the bottom-up fabrication of porous scaffolds and hybrid constructs through the computer-aided assembly of cell-free and/or cell-laden micro-modules. The advantages, current limitations, and future challenges of these strategies are described and discussed.

Effects of Disinfection and Steam Sterilization on the Mechanical Properties of 3D SLA- and DLP-Printed Surgical Guides for Orthodontic Implant Placement

Three-dimensional printed surgical guides increase the precision of orthodontic mini-implant placement. The purpose of this research was to investigate the effects of disinfection and of two types of autoclave sterilization on the mechanical properties of 3D printed surgical guides obtained via the SLA (stereolithography) and DLP (digital light processing) printing methods. A total of 96 standard specimens (48 SLA and 48 DLP) were printed to analyze the tensile and flexural properties of the materials. A total of 80 surgical guide (40 SLA and 40 DLP) specimens from each printing method were classified into four groups: CG (control group); G1, disinfected with 4% Gigasept (Gigasept Instru AF; Schülke & Mayer Gmbh, Norderstedt, Germany); G2, autoclave-sterilized (121 °C); and G3, autoclave-sterilized (134 °C). Significant differences in the maximum compressive load were determined between the groups comprising the DLP-(p < 0.001) and the SLA- (p < 0.001) printed surgical guides. Groups G2 (p = 0.001) and G3 (p = 0.029) showed significant parameter modifications compared with the CG. Disinfection with 4% Gigasept (Gigasept Instru AF; Schülke & Mayer Gmbh, Norderstedt, Germany) is suitable both for SLA- and DLP-printed surgical guides. Heat sterilization at both 121 °C and 134 °C modified the mechanical properties of the surgical guides.

Passive Control of Silane Diffusion for Gradient Application of Surface Properties

Liquid lithography represents a robust technique for fabricating three-dimensional (3D) microstructures on a two-dimensional template. Silanization of a surface is often a key step in the liquid lithography process and is used to alter the surface energy of the substrate and, consequently, the shape of the 3D microfeatures produced. In this work, we present a passive technique that allows for the generation of silane gradients along the length of a substrate. The technique relies on a secondary diffusion chamber with a single opening, leading to a directional introduction of silane to the substrate via passive diffusion. The secondary chamber geometry influences the deposited gradient, which is shown to be well captured by Monte Carlo simulations that incorporate the passive diffusion and grafting processes. The technique ultimately allows the user to generate a range of substrate wettabilities on a single chip, enhancing throughput for organ-on-a-chip applications by mimicking the spatial variability of tissue topographies present in vivo.

Simulated tissue growth in tetragonal lattices with mechanical stiffness tuned for bone tissue engineering

Bone tissue engineering approaches have recently begun considering 3D printed lattices as viable scaffold solutions due to their highly tunable geometries and mechanical efficiency. However, scaffold design remains challenging due to the numerous biological and mechanical trade-offs related to lattice geometry. Here, we investigate novel tetragonal unit cell designs by independently adjusting unit cell height and width to find scaffolds with improved tissue growth while maintaining suitable scaffold mechanical properties for bone tissue engineering. Lattice tissue growth behavior is evaluated using a curvature-based growth model while elastic modulus is evaluated with finite element analysis. Computationally efficient modeling approaches are implemented to facilitate bulk analysis of lattice design trade-offs using design maps for biological and mechanical functionalities in relation to unit cell height and width for two contrasting unit cell topologies. Newly designed tetragonal lattices demonstrate higher tissue growth per unit volume and advantageous stiffness in preferred directions compared to cubically symmetric unit cells. When lattice beam diameter is fixed to 200 μm, Tetra and BC-Tetra lattices with elastic moduli of 200 MPa-400 MPa are compared for squashed, cubic, and stretched topologies. Squashed Tetra lattices demonstrated higher growth rates and growth densities compared to symmetrically cubic lattices. BC-Tetra lattices with the same range of elastic moduli show squashed lattices tend to achieve higher growth rates, whereas stretched lattices promote higher growth density. The results suggest tetragonal unit cells provide favorable properties for biological and mechanical tailoring, therefore enabling new strategies for diverse patient needs and applications in regenerative medicine.

Porous Geometry Guided Micro-mechanical Environment Within Scaffolds for Cell Mechanobiology Study in Bone Tissue Engineering

Mechanobiology research is for understanding the role of mechanics in cell physiology and pathology. It will have implications for studying bone physiology and pathology and to guide the strategy for regenerating both the structural and functional features of bone. Mechanobiological studies in vitro apply a dynamic micro-mechanical environment to cells via bioreactors. Porous scaffolds are commonly used for housing the cells in a three-dimensional (3D) culturing environment. Such scaffolds usually have different pore geometries (e.g. with different pore shapes, pore dimensions and porosities). These pore geometries can affect the internal micro-mechanical environment that the cells experience when loaded in the bioreactor. Therefore, to adjust the applied micro-mechanical environment on cells, researchers can tune either the applied load and/or the design of the scaffold pore geometries. This review will provide information on how the micro-mechanical environment (e.g. fluid-induced wall shear stress and mechanical strain) is affected by various scaffold pore geometries within different bioreactors. It shall allow researchers to estimate/quantify the micro-mechanical environment according to the already known pore geometry information, or to find a suitable pore geometry according to the desirable micro-mechanical environment to be applied. Finally, as future work, artificial intelligent - assisted techniques, which can achieve an automatic design of solid porous scaffold geometry for tuning/optimising the micro-mechanical environment are suggested.

Evaluating Directional Dependency of Selective Laser Sintered Patient Specific Biodegradable Devices to Improve Predictive Modeling and Design Verification

Additive manufacturing, or 3D printing, of the bioresorbable polymer [Formula: see text]-polycaprolactone (PCL) is an emerging tissue engineering solution addressing patient specific anatomies. Predictively modeling the mechanical behavior of 3D printed parts comprised of PCL improves the ability to develop patient specific devices that meet design requirements while reducing the testing of extraneous design variants and development time for emergency devices. Predicting mechanical behavior of 3D-printed devices is limited by the variability of effective material moduli that are determined in part by the 3D printing manufacturing process. Powder fusion methods, specifically laser sintering, are known to produce parts with internal porosity ultimately impacting the mechanical performance of printed devices. This study investigates the role of print direction and part size on the material and structural properties of laser sintered PCL parts. Solid PCL cylinders were printed in the XY (perpendicular to laser) and Z direction (parallel to laser), scanned using microcomputed tomography, and mechanically tested under compression. Compositional, structural, and functional properties of the printed parts were evaluated with differential scanning calorimetry, gel permeation chromatography, microcomputed tomography, and mechanical testing. Computational models of printed and scanned cylinders were fit to experimental data to derive effective moduli. Effective moduli were used to predict the mechanical behavior of splints used for emergency repair of severe tracheobronchomalacia. Laser sintering did not cause significant differences in polymer material properties compared to unmanufactured powder. Effective moduli (E_eff) were greater for larger part sizes (p < 0.01) and for parts oriented in the XY direction compared to the Z direction (p < 0.001). These dependencies were congruent with the differences in void volumes associated with the print direction (p < 0.01) and part size (p < 0.01). Finite element models of splint parallel compression tests utilizing the E_eff dependent on print direction and size agreed with experimental closed compression tests of splints. Evaluating the microstructural properties of printed parts and selecting effective moduli for finite element models based on manufacturing parameters allows accurate prediction of device performance. These findings allow testing of a greater number of device design variants in silico to accomodate patient specific anatomies towards providing higher quality parts while lowering overall time and costs of manufacturing and testing.

Application of Computational Method in Designing a Unit Cell of Bone Tissue Engineering Scaffold: A Review

The design of a scaffold of bone tissue engineering plays an important role in ensuring cell viability and cell growth. Therefore, it is a necessity to produce an ideal scaffold by predicting and simulating the properties of the scaffold. Hence, the computational method should be adopted since it has a huge potential to be used in the implementation of the scaffold of bone tissue engineering. To explore the field of computational method in the area of bone tissue engineering, this paper provides an overview of the usage of a computational method in designing a unit cell of bone tissue engineering scaffold. In order to design a unit cell of the scaffold, we discussed two categories of unit cells that can be used to design a feasible scaffold, which are non-parametric and parametric designs. These designs were later described and being categorised into multiple types according to their characteristics, such as circular structures and Triply Periodic Minimal Surface (TPMS) structures. The advantages and disadvantages of these designs were discussed. Moreover, this paper also represents some software that was used in simulating and designing the bone tissue scaffold. The challenges and future work recommendations had also been included in this paper.

Polymer 3D Printing Review: Materials, Process, and Design Strategies for Medical Applications

Polymer 3D printing is an emerging technology with recent research translating towards increased use in industry, particularly in medical fields. Polymer printing is advantageous because it enables printing low-cost functional parts with diverse properties and capabilities. Here, we provide a review of recent research advances for polymer 3D printing by investigating research related to materials, processes, and design strategies for medical applications. Research in materials has led to the development of polymers with advantageous characteristics for mechanics and biocompatibility, with tuning of mechanical properties achieved by altering printing process parameters. Suitable polymer printing processes include extrusion, resin, and powder 3D printing, which enable directed material deposition for the design of advantageous and customized architectures. Design strategies, such as hierarchical distribution of materials, enable balancing of conflicting properties, such as mechanical and biological needs for tissue scaffolds. Further medical applications reviewed include safety equipment, dental implants, and drug delivery systems, with findings suggesting a need for improved design methods to navigate the complex decision space enabled by 3D printing. Further research across these areas will lead to continued improvement of 3D-printed design performance that is essential for advancing frontiers across engineering and medicine.

Effect of Printing Parameters on Dimensional Error, Surface Roughness and Porosity of FFF Printed Parts with Grid Structure

Extrusion printing processes allow for manufacturing complex shapes in a relatively cheap way with low-cost machines. The present study analyzes the effect of printing parameters on dimensional error, roughness, and porosity of printed PLA parts obtained with grid structure. Parts are obtained by means of the fused filament fabrication (FFF) process. Four variables are chosen: Layer height, temperature, speed, and flow rate. A two-level full factorial design with a central point is used to define the experimental tests. Dimensional error and porosity are measured with a profile projector, while roughness is measured with a contact roughness meter. Mathematical regression models are found for each response, and multi-objective optimization is carried out by means of the desirability function. Dimensional error and roughness depend mainly on layer height and flow rate, while porosity depends on layer height and printing speed. Multi-objective optimization shows that recommended values for the variables are layer height 0.05 mm, temperature 195 ºC, speed 50 mm/min, and flow rate 0.93, when dimensional error and roughness are to be minimized, and porosity requires a target value of 60%. The present study will help to select appropriate printing parameters for printing porous structures such as those found in prostheses, by means of extrusion processes.

Numerical-experimental analysis of the permeability-porosity relationship in triply periodic minimal surfaces scaffolds

Bone Tissue Engineering has been focusing on improving the current methods for bone repair, being the use of scaffolds presented as an upgrade to traditional surgery techniques. Scaffolds are artificially porous matrices, meant to promote cell seeding and proliferation, being these properties influenced by the permeability of the structure. This work employed experimental pressure drop tests and Computational Fluid Dynamics models to assess permeability (and fluid streamlines) within different triply periodic minimal surfaces scaffold geometries (Schwarz D, Gyroid and Schwarz P). The pressure outputs from the computational analysis presented a good correlation with the experimental results, with R² equal to 0.903; they have also shown that a lower porosity may not mean a lower permeability if the geometry is altered, such as the difference between 60% porous Gyroid scaffolds (8.1*10^-9 mm²) and 70% porous Schwarz D scaffolds (7.1*10^-9 mm²). Fluid streamlines revealed how the Gyroid geometries are the most appropriate design for most bone tissue engineering applications, due to their consistent fluid permeation, followed by Schwarz D. The Schwarz P geometries have shown flat streamlines and significant variation of the permeability with the porosity (an increase of 10% in their porosity lead to an increase in the permeability from 5.1*10^-9 mm² to 11.7*10^-9 mm²), which would imply a poor environment for cell seeding and proliferation.

Cell proliferation and migration explain pore bridging dynamics in 3D printed scaffolds of different pore size

Tissue growth in bioscaffolds is influenced significantly by pore geometry, but how this geometric dependence emerges from dynamic cellular processes such as cell proliferation and cell migration remains poorly understood. Here we investigate the influence of pore size on the time required to bridge pores in thin 3D-printed scaffolds. Experimentally, new tissue infills the pores continually from their perimeter under strong curvature control, which leads the tissue front to round off with time. Despite the varied shapes assumed by the tissue during this evolution, we find that time to bridge a pore simply increases linearly with the overall pore size. To disentangle the biological influence of cell behaviour and the mechanistic influence of geometry in this experimental observation, we propose a simple reaction-diffusion model of tissue growth based on Porous-Fisher invasion of cells into the pores. First, this model provides a good qualitative representation of the evolution of the tissue; new tissue in the model grows at an effective rate that depends on the local curvature of the tissue substrate. Second, the model suggests that a linear dependence of bridging time with pore size arises due to geometric reasons alone, not to differences in cell behaviours across pores of different sizes. Our analysis suggests that tissue growth dynamics in these experimental constructs is dominated by mechanistic crowding effects that influence collective cell proliferation and migration processes, and that can be predicted by simple reaction-diffusion models of cells that have robust, consistent behaviours.

On the Tortuosity of TPMS Scaffolds for Tissue Engineering

Recently, bone tissue engineering (TE) has seen new developments, with triply periodic minimal surfaces (TPMSs) being used to develop new porosity-controlled scaffolds to interface new tissue growth. The process of choosing the best geometry to a specific application still lacks research, so the goal for this work is to propose a new method of scaffold selection, based on assessing the tortuosity inside these symmetric TPMS-based structures. Additionally, computer fluid dynamic (CFD) simulations were conducted to validate this method. The comparison between tortuosity and CFD outputs suggests that an analysis of the tortuosity could be used as an early indicator of the scaffold’s viability for specific applications, favouring scaffolds with more intricate and curvature-dependent streamlines.

Design framework for mechanically tunable soft biomaterial composites enhanced by modified horseshoe lattice structures

Soft biomaterials have a wide range of applications in many areas. However, one material can only cover a specific range of mechanical performance such as the elastic modulus and stretchability. In order to improve the mechanical performance of soft biomaterials, lattice structures are embedded to reinforce the biomaterials. In this paper, rectangular and triangular lattice structures formed by modified horseshoe microstructures are used because their mechanical properties are tunable and can be tailored precisely to match the desired properties by adjusting four geometrical parameters, the length L, radius R, width w and arc angle θ0. A theoretical design framework for the modified horseshoe lattice structures is developed to predict the dependence of the mechanical behaviors on geometrical parameters. Both experiments and finite element simulations on lattice structures are conducted to validate the theoretical models. Results show that a wide range of design space for the elastic modulus (a few kPa to hundreds of MPa), stretchability (strain up to 180%) and Poisson ratio (ranging from -0.5 to 1.2) can be achieved. Experiments on lattice-hydrogel composites are also conducted to verify the reinforcement effect of lattice structures on the hydrogel. This work provides a theoretical method to predict the mechanical behaviors of the lattice structures and aid the rational design of reinforced biomaterials, which has applications in tissue engineering, drug delivery and intraocular lenses.

Substrate curvature as a cue to guide spatiotemporal cell and tissue organization

Recent evidence clearly shows that cells respond to various physical cues in their environments, guiding many cellular processes and tissue morphogenesis, pathology, and repair. One aspect that is gaining significant traction is the role of local geometry as an extracellular cue. Elucidating how geometry affects cell and tissue behavior is, indeed, crucial to design artificial scaffolds and understand tissue growth and remodeling. Perhaps the most fundamental descriptor of local geometry is surface curvature, and a growing body of evidence confirms that surface curvature affects the spatiotemporal organization of cells and tissues. While well-defined in differential geometry, curvature remains somewhat ambiguously treated in biological studies. Here, we provide a more formal curvature framework, based on the notions of mean and Gaussian curvature, and summarize the available evidence on curvature guidance at the cell and tissue levels. We discuss the involved mechanisms, highlighting the interplay between tensile forces and substrate curvature that forms the foundation of curvature guidance. Moreover, we show that relatively simple computational models, based on some application of curvature flow, are able to capture experimental tissue growth remarkably well. Since curvature guidance principles could be leveraged for tissue regeneration, the implications for geometrical scaffold design are also discussed. Finally, perspectives on future research opportunities are provided.

3D Printed Wavy Scaffolds Enhance Mesenchymal Stem Cell Osteogenesis

There is a growing interest in developing 3D porous scaffolds with tunable architectures for bone tissue engineering. Surface topography has been shown to control stem cell behavior including differentiation. In this study, we printed 3D porous scaffolds with wavy or linear patterns to investigate the effect of wavy scaffold architecture on human mesenchymal stem cell (hMSC) osteogenesis. Five distinct wavy scaffolds were designed using sinusoidal waveforms with varying wavelengths and amplitudes, and orthogonal scaffolds were designed using linear patterns. We found that hMSCs attached to wavy patterns, spread by taking the shape of the curvatures presented by the wavy patterns, exhibited an elongated shape and mature focal adhesion points, and differentiated into the osteogenic lineage. When compared to orthogonal scaffolds, hMSCs on wavy scaffolds showed significantly enhanced osteogenesis, indicated by higher calcium deposition, alkaline phosphatase activity, and osteocalcin staining. This study aids in the development of 3D scaffolds with novel architectures to direct stem osteogenesis for bone tissue engineering.

Mathematical Model and Numerical Simulation for Tissue Growth on Bioscaffolds

Tissue growth on bioscaffolds can be controlled using substrate geometry such as substrate curvature. In this study, we present a mathematical model and numerical simulation method for tissue growth on a bioscaffold to investigate the effect of local curvature on tissue growth. The mathematical model is based on the Allen–Cahn (AC) equation, which has been extensively used to model many problems involving motion by mean curvature. By solving the AC equation using the explicit Euler method, the proposed method is simple and fast. Numerical simulations on various geometries are presented to demonstrate the applicability of the proposed framework on tissue growth on a bioscaffold.

Integrated Design Approaches for 3D Printed Tissue Scaffolds: Review and Outlook

Emerging 3D printing technologies are enabling the fabrication of complex scaffold structures for diverse medical applications. 3D printing allows controlled material placement for configuring porous tissue scaffolds with tailored properties for desired mechanical stiffness, nutrient transport, and biological growth. However, tuning tissue scaffold functionality requires navigation of a complex design space with numerous trade-offs that require multidisciplinary assessment. Integrated design approaches that encourage iteration and consideration of diverse processes including design configuration, material selection, and simulation models provide a basis for improving design performance. In this review, recent advances in design, fabrication, and assessment of 3D printed tissue scaffolds are investigated with a focus on bone tissue engineering. Bone healing and fusion are examples that demonstrate the needs of integrated design approaches in leveraging new materials and 3D printing processes for specified clinical applications. Current challenges for integrated design are outlined and emphasize directions where new research may lead to significant improvements in personalized medicine and emerging areas in healthcare.

3D Printing of Porous Scaffolds with Controlled Porosity and Pore Size Values

3D printed scaffolds can be used, for example, in medical applications for simulating body tissues or for manufacturing prostheses. However, it is difficult to print porous structures of specific porosity and pore size values with fused deposition modelling (FDM) technology. The present paper provides a methodology to design porous structures to be printed. First, a model is defined with some theoretical parallel planes, which are bounded within a geometrical figure, for example a disk. Each plane has randomly distributed points on it. Then, the points are joined with lines. Finally, the lines are given a certain volume and the structure is obtained. The porosity of the structure depends on three geometrical variables: the distance between parallel layers, the number of columns on each layer and the radius of the columns. In order to obtain mathematical models to relate the variables with three responses, the porosity, the mean of pore diameter and the variance of pore diameter of the structures, design of experiments with three-level factorial analysis was used. Finally, multiobjective optimization was carried out by means of the desirability function method. In order to favour fixation of the structures by osseointegration, porosity range between 0.5 and 0.75, mean of pore size between 0.1 and 0.3 mm, and variance of pore size between 0.000 and 0.010 mm² were selected. Results showed that the optimal solution consists of a structure with a height between layers of 0.72 mm, 3.65 points per mm² and a radius of 0.15 mm. It was observed that, given fixed height and radius values, the three responses decrease with the number of points per surface unit. The increase of the radius of the columns implies the decrease of the porosity and of the mean of pore size. The decrease of the height between layers leads to a sharper decrease of both the porosity and the mean of pore size. In order to compare calculated and experimental values, scaffolds were printed in polylactic acid (PLA) with FDM technology. Porosity and pore size were measured with X-ray tomography. Average value of measured porosity was 0.594, while calculated porosity was 0.537. Average value of measured mean of pore size was 0.372 mm, while calculated value was 0.434 mm. Average value of variance of pore size was 0.048 mm², higher than the calculated one of 0.008 mm². In addition, both round and elongated pores were observed in the printed structures. The current methodology allows designing structures with different requirements for porosity and pore size. In addition, it can be applied to other responses. It will be very useful in medical applications such as the simulation of body tissues or the manufacture of prostheses.