Ken Brakke

Designer ‘blueprint’ for vascular trees: morphology evolution of vascular tissue constructs

Organ printing is a variant of the biomedical application of rapid prototyping technology or layer-by-layer additive biofabrication of 3D tissue and organ constructs using self-assembled tissue spheroids as building blocks. Bioengineering of perfusable intraorgan branched vascular trees incorporated into 3D tissue constructs is essential for the survival of bioprinted thick 3D tissues and organs. In order to design the optimal ‘blueprint’ for digital bioprinting of intraorgan branched vascular trees, the coefficients of tissue retraction associated with post-printing vascular tissue spheroid fusion and remodelling must be determined and incorporated into the original CAD. Using living tissue spheroids assembled into ring-like and tube-like vascular tissue constructs, the coefficient of tissue retraction has been experimentally evaluated. It has been shown that the internal diameter of ring-like and the height of tubular-like tissue constructs are significantly reduced during tissue spheroid fusion. During the tissue fusion process, the individual tissue spheroids also change their shape from ball-like to a conus-like form. A simple formula for the calculation of the necessary number of tissue spheroids for biofabrication of ring-like structures of desirable diameter has been deduced. These data provide sufficient information to design optimal CAD for bioprinted branched vascular trees of desirable final geometry and size.

Using symmetry features of the surface evolver to study foams

This paper describes the use of various symmetry features, including periodic boundary conditions, mirror boundaries, and rotational symmetry, in the Evolver. As a test case, we use these features to study foams, in particular the equal-volume foams of Kelvin and Weaire-Phelan. To compute the shape and energy of one of these compound surfaces, it is most efficient to work with only the smallest possible fundamental domain.

The minimax sphere eversion

We consider an eversion of a sphere driven by a gradient flow for elastic bending energy. We start with a halfway model which is an unstable Willmore sphere with 4-fold orientation-reversing rotational symmetry. The regular homotopy is automatically generated by flowing down the gradient of the energy from the halfway model to a round sphere, using the Surface Evolver. This flow is not yet fully understood; however, our numerical simulations give evidence that the resulting eversion is isotopic to one of Morin’s classical sphere eversions. These simulations were presented as real-time interactive animations in the CAVE TM automatic virtual environment at Supercomputing’95, as part of an experiment in distributed, parallel computing and broad-band, asynchronous networking.

Design, physical prototyping and initial characterisation of ‘lockyballs’

Directed tissue self-assembly or bottom-up modular approach in tissue biofabrication is an attractive and potentially superior alternative to a classic top-down solid scaffold-based approach in tissue engineering. For example, rapidly emerging organ printing technology using self-assembling tissue spheroids as building blocks is enabling computer-aided robotic bioprinting of three-dimensional (3D) tissue constructs. However, achieving proper material properties while maintaining desirable geometry and shape of 3D bioprinted tissue engineered constructs using directed tissue self-assembly, is still a challenge. Proponents of directed tissue self-assembly see the solution of this problem in developing methods of accelerated tissue maturation and/or using sacrificial temporal supporting of removable hydrogels. In the meantime, there is a growing consensus that a third strategy based on the integration of a directed tissue self-assembly approach with a conventional solid scaffold-based approach could be a potential optimal solution. We hypothesise that tissue spheroids with ‘velcro®-like’ interlockable solid microscaffolds or simply ‘lockyballs’ could enable the rapid in vivo biofabrication of 3D tissue constructs at desirable material properties and high initial cell density. Recently, biocompatible and biodegradable photo-sensitive biomaterials could be fabricated at nanoscale resolution using two-photon polymerisation (2PP), a development rendering this technique with high potential to fabricate ‘velcro®-like’ interlockable microscaffolds. Here we report design studies, physical prototyping using 2PP and initial functional characterisation of interlockable solid microscaffolds or so-called ‘lockyballs’. 2PP was used as a novel enabling platform technology for rapid bottom-up modular tissue biofabrication of interlockable constructs. The principle of lockable tissue spheroids fabricated using the described lockyballs as solid microscaffolds is characterised by attractive new functionalities such as lockability and tunable material properties of the engineered constructs. It is reasonable to predict that these building blocks create the basis for a development of a clinical in vivo rapid biofabrication approach and form part of recent promising emerging bioprinting technologies.

Toward organ printing: Design characteristics, virtual modelling and physical prototyping vascular segments of kidney arterial tree

Organ printing is defined as the layer by layer additive biofabrication of three-dimensional (3D) tissue and organ constructs using tissue spheroids as building blocks. Ultimately, successful bioprinting of human organ constructs is dependent on a ‘built in’ vascular tree to perfuse and maintain the viability of the organ constructs. Thus, the design of the vascular tree is a critically important step in practical implementation of organ printing technology. Bioprinting a vascular tree requires detailed knowledge of the morphometrical, morphological and biomechanical characteristics of the sequentially branched segments of the natural vascular tree as well as insight on post-printing tissue compaction and remodelling. Toward accomplishing this goal, we characterised the morphometrical, morphological and biomechanical characteristics of the initial segments of the natural kidney arterial vascular tree of the porcine kidney. Computer simulation was used to model compaction of tissue engineered tubular vascular segments with different wall thicknesses virtually biofabricated from closely packed and fused uniformly sized vascular tissue spheroids. The number of concentric layers of tissue spheroids required to bioprint tubular vascular segments with desirable wall thickness and diameter was theoretically estimated. Our results demonstrate that vascular segment compaction correlates well with reported experimental data. Finally, physical prototyping of linear and branched tubular constructs using silicon droplets as physical analogues of tissue spheroids was performed. Thus, virtual and physical prototyping provide important insights into the design parameters and demonstrate the principal feasibility of bioprinting a branched vascular tree using vascular tissue spheroids.

Delivery of Human Adipose Stem Cells Spheroids into Lockyballs

Adipose stem cells (ASCs) spheroids show enhanced regenerative effects compared to single cells. Also, spheroids have been recently introduced as building blocks in directed self-assembly strategy. Recent efforts aim to improve long-term cell retention and integration by the use of microencapsulation delivery systems that can rapidly integrate in the implantation site. Interlockable solid synthetic microscaffolds, so called lockyballs, were recently designed with hooks and loops to enhance cell retention and integration at the implantation site as well as to support spheroids aggregation after transplantation. Here we present an efficient methodology for human ASCs spheroids biofabrication and lockyballs cellularization using micro-molded non-adhesive agarose hydrogel. Lockyballs were produced using two-photon polymerization with an estimated mechanical strength. The Young’s modulus was calculated at level 0.1362 +/-0.009 MPa. Interlocking in vitro test demonstrates high level of loading induced interlockability of fabricated lockyballs. Diameter measurements and elongation coefficient calculation revealed that human ASCs spheroids biofabricated in resections of micro-molded non-adhesive hydrogel had a more regular size distribution and shape than spheroids biofabricated in hanging drops. Cellularization of lockyballs using human ASCs spheroids did not alter the level of cells viability (p › 0,999) and gene fold expression for SOX-9 and RUNX2 (p › 0,195). The biofabrication of ASCs spheroids into lockyballs represents an innovative strategy in regenerative medicine, which combines solid scaffold-based and directed self-assembly approaches, fostering opportunities for rapid in situ biofabrication of 3D building-blocks.

Design of vascular tree for organ bioprinting

Abstract Organ printing is a variant of the biomedical application of additive manufacturing (rapid prototyping) technology or layer-by-layer additive biofabrication of 3D tissue and organ constructs using self-assembled tissue spheroids as building blocks. Bioengineering of perfusable intraorgan branched vascular trees incorporated into 3D tissue constructs is essential for the survival of bioprinted thick 3D tissues and organs. In order to design the optimal ‘blueprint’ for digital bioprinting of intraorgan branched vascular trees, the coefficients of tissue retraction associated with post-printing vascular tissue spheroid fusion and remodeling must be determined and incorporated into the original CAD. Using living tissue spheroids assembled into ring-like and tube-like vascular tissue constructs, the coefficient of tissue retraction has been experimentally evaluated. It has been shown that the internal diameter of ring-like and the height of tubular-like tissue constructs are significantly reduced during tissue spheroid fusion. During the tissue fusion process, the individual tissue spheroids also change their shape from ball-like to a conus-like form. A simple formula for the calculation of the necessary number of tissue spheroids for biofabrication of ring-like structures of desirable diameter has been deduced. These data provide sufficient information to design optimal CAD for bioprinted branched vascular trees of different human organs desirable final geometry and size.

C S Smith’s development of a viewpoint

Cyril Smith’s distinguished career in industrial metallurgy was wonderfully transformed into his masterful engagement with the history of science and technology. These two phases were bridged by a piece of research that particularly pleased him, as epitomising his general ideas of form and organisation. It was based on his conception of the 2D soap froth as a prototype for metallic grain growth (and much else). He rightly sensed that it would be an enduring source of understanding of some of the complex effects that he so admired in materials.

Targeting formation in microporous and mesoporous materials

Inorganic, ordered microporous and mesoporous materials have utility in a continuum of applications. However, the formation of these materials relies on different, yet overlapping chemistry. As a consequence the tools at our disposal to study the formation mechanisms have to be carefully selected. The goal of this paper is to illustrate some of these techniques using the mesoporous silica SBA-1 as an example with a view to understanding how both structural and kinetic measurements can be married in such a way to produce a consistent picture of the mechanism of formation.