Improving Laser Powder Bed Fusion Printability of Tungsten Powders Using Simulation-Driven Process Optimization Algorithms.

This study applies numerical and experimental techniques to investigate the effect of process parameters on the density, structure and mechanical properties of pure tungsten specimens fabricated by laser powder bed fusion. A numerical model based on the simplified analysis of a thermal field generated in the powder bed by a moving laser source was used to calculate the melt pool dimensions, predict the density of printed parts and build a cost-effective plan of experiments. Specimens printed using a laser power of 188 W, a scanning speed of 188 mm/s, a hatching space of 80 µm and a layer thickness of 30 µm showed a maximum printed density of 93.2%, an ultimate compression strength of 867 MPa and a maximum strain to failure of ~7.0%, which are in keeping with the standard requirements for tungsten parts obtained using conventional powder metallurgy techniques. Using the optimized printing parameters, selected geometric artifacts were manufactured to characterize the printability limits. A complementary numerical study suggested that decreasing the layer thickness, increasing the laser power, applying hot isostatic pressing and alloying with rhenium are the most promising directions to further improve the physical and mechanical properties of printed tungsten parts.

A Geometric Analysis of Polyethylene Liners Exposed to Acrylic-based Bone Cement.

Background: Acrylic-based bone cement (polymethyl methacrylate [PMMA]) is a material commonly used in orthopaedic surgeries; however, during PMMA polymerization, a highly exothermic reaction occurs. The heat released in polymerization can damage nearby materials including poorly heat-resistant cross-linked polyethylene (XLPE). Both PMMA and XLPE are used in total hip arthroplasty and could interact during femoral stem fixation. We sought to determine if the exothermic polymerization of PMMA could alter the surface characteristics of XLPE acetabular liners. Methods: Six XLPE liners were assigned to one of 4 experimental categories with varying volumes of PMMA applied in a manner that mimicked how the 2 materials would come into contact intraoperatively. Measurements were taken both pre- and post-intervention using a coordinate measuring machine for geometric and gravimetric analysis. Light microscopy was conducted postintervention to examine the surface for damage. Results: Coordinate measuring machine measurements showed minimal gross deformation in all 6 liners, but there were isolated surface deposits in 4 of 6 liners. The average maximal surface deviations, when compared to the control, for liners exposed to 1 cc of cement, 2 cc of cement, or 1 cc of cement with a femoral head implant attached were 26.6 µm, 77.2 µm, and 26.4 µm, respectively. All but one liner showed an increase in volume following intervention when compared to the control. Subtle scratches were identified using light microscopy on all 6 liners. Conclusions: XLPE shows areas of isolated surface deformation in a dose-dependent manner but with minimal gross deformation after interacting with highly exothermic PMMA.

A review of the techno-economic potential and environmental impact analysis through life cycle assessment of parabolic trough collector towards the contribution of sustainable energy.

Parabolic trough collectors (P.T.Cs) are efficient solar energy harvesting devices utilized in various industries, for instance, space heating, solar cooling, solar drying, pasteurization, sterilization, electricity generation, process heat, solar cooking, and many other applications. However, their usage is limited as the high capital and operating costs; according to the International Renewable Energy Agency's 2020 report, the global weighted average levelized cost of electricity (L.C.O.E) for P.T.Cs was 0.185 $/kWh in 2018. This work analyses the economic, technical, and environmental potential of sustainable energy to increase the use of P.T.Cs in different sectors. To study how self-weight, heat loss, and wind velocity affect P.T.C performance, prototype testing, and wind flow analysis were used. Although P.T.Cs outperform in capacity factor, gross-to-net conversion, and annual energy production, improving their overall efficiency is crucial in reducing total energy production costs. Wire coils, discs, and twisted tape-type inserts can enhance their performance by increasing turbulence and heat transfer area. Improving the system's overall efficiency by enhancing the functioning and operation of individual components will also help decrease total energy production costs. The aim is to minimize the L.C.O.E associated with a P.T.C in order to enhance its economic viability for an extended period. When the nanofluid-oriented P.T.C was included in the conventional P.T.C workings, there was a decrease in the L.C.O.E by 1%. Of all the technologies available, ocean, geothermal, and C.S.P parabolic trough plants generate lower amounts of waste and harmful gases, with average emissions of 2.39%, 2.23%, and 2.16%, respectively, throughout their lifespan. For solar-only and non-hybrid thermal energy storage plants, the range of greenhouse gas emissions is between 20 and 34 kgCO2 equivalents per megawatt-hour. Coal, natural gas steam turbines, nuclear power plants, bioenergy, solar PV, geothermal, concentrated solar power, hydropower reservoir, hydropower river, ocean, and wind power plants all release greenhouse gases at rates of 1022, 587.5, 110.5, 633, 111, 48, 41, 82.5, 7.5, 12.5, and 41.5 gCO2-e/kWh, respectively. This information is useful to compare the environmental effect of various energy sources and help us to choose cleaner, more sustainable options for the production of electricity. The ongoing advancements and future scope of P.T.Cs could potentially make them more economically viable for domestic, commercial, and industrial applications.

Facet Connectivity-Based Estimation Algorithm for Manufacturability of Supportless Parts Fabricated via LPBF.

Recent advances in additive manufacturing have provided more freedom in the design of metal parts; hence, the prototyping of fluid machines featuring extremely complex geometries has been investigated extensively. The fabrication of fluid machines via additive manufacturing requires significant attention to part stability; however, studies that predict regions with a high risk of collapse are few. Therefore, a novel algorithm that can detect collapse regions precisely is proposed herein. The algorithm reflects the support span over the faceted surface via propagation and invalidates overestimated collapse regions based on the overhang angle. A heat exchanger model with an extremely complex internal space is adopted to validate the algorithm. Three samples from the model are extracted and their prototypes are fabricated via laser powder bed fusion. The results yielded by the fabricated samples and algorithm with respect to the sample domain are compared. Regions of visible collapse identified on the surface of the fabricated samples are predicted precisely by the algorithm. Thus, the supporting span reflected by the algorithm provides an extremely precise prediction of collapse.

Transformation of acoustic information to sensory decision variables in the parietal cortex.

The process by which sensory evidence contributes to perceptual choices requires an understanding of its transformation into decision variables. Here, we address this issue by evaluating the neural representation of acoustic information in the auditory cortex-recipient parietal cortex, while gerbils either performed a two-alternative forced-choice auditory discrimination task or while they passively listened to identical acoustic stimuli. During task engagement, stimulus identity decoding performance from simultaneously recorded parietal neurons significantly correlated with psychometric sensitivity. In contrast, decoding performance during passive listening was significantly reduced. Principal component and geometric analyses revealed the emergence of low-dimensional encoding of linearly separable manifolds with respect to stimulus identity and decision, but only during task engagement. These findings confirm that the parietal cortex mediates a transition of acoustic representations into decision-related variables. Finally, using a clustering analysis, we identified three functionally distinct subpopulations of neurons that each encoded task-relevant information during separate temporal segments of a trial. Taken together, our findings demonstrate how parietal cortex neurons integrate and transform encoded auditory information to guide sound-driven perceptual decisions.

Tibial tubercle osteotomy: effect of different osteotomy planes on contact surface area and tubercle anteriorization.

In 1983, Fulkerson introduced a technique of tibial tubercle osteotomy performed according to an inclined plane with respect to frontal plane. Due to obliquity of the osteotomy plane, this procedure allows both anterior and medial transfer of the tibial tubercle. The purpose of the study was to investigate the influence of the different degrees of the oblique plane of osteotomy on anterior displacement and the contact surface area of tibial tubercle. Synthetic bones were used for the study. An osteotomy of the tibial tubercle (TT) was performed in each specimen. Specifically, 3 different degrees of osteotomy planes relative to the reference frontal plane were examined: 20°, 30° and 40°. On each sample, tibial tubercle medial transposition of 5 mm, 10 mm and 15 mm was performed. Anterior displacement was measured with a caliper. Further, the bone contact surface was calculated for each sample and each transposition. Finally, the measured data were statistically compared with a geometric model. At 5 mm of medial TT transposition, the anterior displacement (AD) was 0.1 mm when the osteotomy was performed at 20°. It increased of 1.5 mm and 2.7 mm, respectively at 30° and 40°. At 15 mm of TT transposition, the AD was 3.4 mm at 20°, 7.6 mm at 30° and 10.0 mm at 40°. Concerning the amount of medialization, it was observed a decrease in the overall contact surface passing from 5 to 15 mm of TT transposition. In addition, regarding the oblique plane of the osteotomy, it was observed an increase in the contact surface area passing from 20° to 40°. The main result of the present study is that the amount of anteriorization and medialization of the tibial tubercle could be predicted by the degrees of oblique plane of osteotomy. An increase in medialization significantly reduces the contact surface area at low degrees of osteotomy plane, potentially increasing the risk of non-union.

Predicting fracture in the proximal humerus using phase field models.

Proximal humerus impacted fractures are of clinical concern in the elderly population. Prediction of such fractures by CT-based finite element methods encounters several major obstacles such as heterogeneous mechanical properties and fracture due to compressive strains. We herein propose to investigate a variation of the phase field method (PFM) embedded into the finite cell method (FCM) to simulate impacted humeral fractures in fresh frozen human humeri. The force-strain response, failure loads and the fracture path are compared to experimental observations for validation purposes. The PFM (by means of the regularization parameter ℓ0) is first calibrated by one experiment and thereafter used for the prediction of the mechanical response of two other human fresh frozen humeri. All humeri are fractured at the surgical neck and strains are monitored by Digital Image Correlation (DIC). Experimental strains in the elastic regime are reproduced with good agreement (R2=0.726), similarly to the validated finite element method (Dahan et al., 2022). The failure pattern and fracture evolution at the surgical neck predicted by the PFM mimic extremely well the experimental observations for all three humeri. The maximum relative error in the computed failure loads is 3.8%. To the best of our knowledge this is the first method that can predict well the experimental compressive failure pattern as well as the force-strain relationship in proximal humerus fractures.

Geometric analysis of pedicle subtraction osteotomy (PSO) for Kyphosis correction: anterior lengthening may occur at the osteotomized body as well as at the discs above and below.

OBJECTIVE: To validate the authors kyphosis correction formula for pedicle subtraction osteotomy (PSO) cases. Additionally, to use the formula to evaluate the safety of PSO by determining if there is anterior lengthening. METHODS: Twenty-two patients with primarily kyphosis corrected by PSO and with clear landmarks on preoperative and postoperative x-rays were selected. Several anatomical lines and angle measurements were utilized as depicted previously in the Vertebral Column Resection formula (see below). Two approximations were calculated: the geometric approximation (G) = (tanG°*2 + 1)*15° and the rough approximation (R) which is about the same amount of actual shortening (x), if parallel length (y) ≥ 40; twice of x, if y < 40. For each patient, the change of segmental kyphosis angle (K°) was measured and compared with G° and R°, and the correlation between each value was analyzed. RESULTS: The absolute Mean ± SE for K - G and K - R was 2.33° ± 0.34 and 6.09° ± 0.58, respectively. K - G is < 3° (p = 0.03). K - R is < 8° (p = 0.001). In other words, K was close to G and R and thus can be predicted by these approximations. Average posterior shortening, anterior shortening, and kyphosis correction at each level were 20.8 ± 2.0 mm, - 3.64 ± 1.5 mm (which equates to anterior lengthening), and 31.05° ± 2.0, respectively. Anterior lengthening occurred in 13 cases (in 4 cases, both at the body as well as at the disc above and below.) The correlation between posterior and anterior shortening was 0.03 (p = 0.88). There were 3 cage insertion cases: 1 had anterior lengthening, while 2 had anterior shortening even with the cage. CONCLUSION: This study validated the geometric and rough approximations originally used in PVCR patients, for PSO patients. Additionally, this study found that anterior lengthening may occur in PSOs usually at the discs, but occasionally at the osteotomized body.

Form Follows Parameter: Algorithmic-Thinking-Oriented Course for Early-stage Architectural Education.

The digital paradigm requires efficient methods of teaching CAAD tools in architecture schools. With the trend of enhancing the design process with parametric methods, linking architecture with other knowledge areas, such as mathematics, is gaining in importance. Equipping future architects with skills in algorithmic thinking is yet another challenge for education. This paper describes the workflow of an early-stage course addressing this challenge, conducted at the Warsaw University of Technology's Faculty of Architecture. The course focuses on the students' ability to construct complex geometric forms in the digital environment by introducing an extensive analytic phase. The students study the geometric foundations of real-world architectural cases and translate them into parametric models. Later, they explore the potential of the generated solutions space. The results compare the course's teaching efficiency with the outcomes of past courses covering similar subjects.

Mechanical properties and fluid permeability of gyroid and diamond lattice structures for intervertebral devices: functional requirements and comparative analysis.

Current intervertebral fusion devices present multiple complication risks such as a lack of fixation, device migration and subsidence. An emerging solution to these problems is the use of additively manufactured lattice structures that are mechanically compliant and permeable to fluids, thus promoting osseointegration and reducing complication risks. Strut-based diamond and sheet-based gyroid lattice configurations having a pore diameter of 750 µm and levels of porosity of 60, 70 and 80% are designed and manufactured from Ti-6Al-4V alloy using laser powder bed fusion. The resulting structures are CT-scanned, compression tested and subjected to fluid permeability evaluation. The stiffness of both structures (1.9-4.8 GPa) is comparable to that of bone, while their mechanical resistance (52-160 MPa) is greater than that of vertebrae (3-6 MPa), thus decreasing the risks of wither bone or implant failure. The fluid permeability (5-57 × 10-9 m2) and surface-to-volume ratios (~3) of both lattice structures are close to those of vertebrae. This study shows that both types of lattice structures can be produced to suit the application specifications within certain limits imposed by physical and equipment-related constraints, providing potential solutions for reducing the complication rate of spinal devices by offering a better fixation through osseointegration.

Initial Clinical Experience With a New Conformable Abdominal Aortic Endograft: Aortic Neck Coverage and Curvature Analysis in Challenging Aortic Necks.

OBJECTIVES: Aim of this work was to investigate precision of deployment and conformability of a new generation GORE EXCLUDER Conformable Endoprosthesis with active control system (CEXC Device, W.L. Gore and Associates, Flagstaff, AZ, USA) by analyzing aortic neck coverage and curvature. METHODS: All consecutive elective patients affected by abdominal aortic aneurysm or aortoiliac aneurysm treated at our institution between November 2018 and June 2019 with the new CEXC Device were enrolled. Validated software was adopted to determine the available apposition surface area into the aortic neck, apposition of the endograft to the aortic wall, shortest apposition length (SAL), shortest distance between the endograft fabric and the lowest renal arteries (SFD) and between the endograft fabric and the contralateral renal artery (CFD). Pointwise centerline curvature was also computed. RESULTS: Twelve patients (10 men, median age 78 years (71.75, 81.0)) with available pre- and postoperative computed tomography angiography (CTA) were included. Technical success was obtained in all the cases. Preoperative median length of the proximal aortic neck was 16.1 mm (10.7, 21.7) and suprarenal (α) and infrarenal (ß) neck angulation were, respectively, 28.9° (15.7°, 47.5°) and 75.0° (66.9°, 81.4°). Postoperative median apposition surface coverage was 79% (69.25%, 90.75%) of the available apposition surface. SFD and CFD were 1.5 mm (0.75, 5.25) and 7 mm (4.5, 21.5), respectively. Average curvature over the infrarenal aorta decreased from 25 m-1 (21.75, 29.0) to 22.5 m-1 (18.75, 24.5) postoperatively (p=0.02). Maximum curvature did not decrease significantly from 64.5 m-1 (54.25, 92.0) to 62 m-1 (41.75, 71.5) (p=0.1). CONCLUSIONS: Our early experience showed that deployment of the CEXC Device is safe and effective for patients with challenging proximal aortic necks. Absence of significant changes between pre- and postoperative proximal aortic neck angulations and curvature confirms the high conformability of this endograft.

Geometric Analysis to Determine Kinking and Shortening of Bridging Stents After Branched Endovascular Aortic Repair.

PURPOSE: To evaluate bridging stent geometry in patients who underwent branched endovascular aortic repair (B-EVAR) and to correlate the outcomes with intrinsic bridging stent characteristics aiming to identify the stent(s) that guarantees the best performance. METHODS: Pre-operative and post-operative computed tomography images of all patients undergoing B-EVAR between September 2016 and April 2019 were retrospectively analyzed. Following geometrical features were measured: target vessel take-off angle (TOA); longitudinal stent shortening; shape index (SI), intended as ratio between minimum and maximum diameter of the lumen cross sections, averaged on three segments: zone 1 (proximal stented zone), zone 2 (intermediate), and zone 3 (distal). RESULTS: Thirty-eight branches (8 right (RRA) and 8 left renal arteries (LRA), 11 superior mesenteric arteries (SMA), 11 celiac trunks (CTR)) were treated. Fluency (Bard Peripheral Vascular), COVERA (Bard Peripheral Vascular), and VBX (WLGore&Assoc) stent-grafts were implanted in 10, 12, and 16 branches, respectively. Pre-operative TOA was more acute in RRA and LRA when compared to CTR and SMA, and straightened in post-operative configuration (109.86 ± 28.65° to 150.27 ± 21.0°; P < 0.001). Comparable values of SI among the stent types were found in zone 1 (P = 0.08), whereas higher SI in VBX group was detected in zones 2 (P < 0.001) and 3 (P < 0.001). The VBX group was also the most affected by stent shortening (11.12 ± 5.65%; P = 0.001). CONCLUSION: Our early experience showed that the VBX stent offers greater stent circularity than the other devices even if a greater shortening has been observed drawing attention with regards to the decision of the nominal stent length.

Shearlets as feature extractor for semantic edge detection: the model-based and data-driven realm.

Semantic edge detection has recently gained a lot of attention as an image-processing task, mainly because of its wide range of real-world applications. This is based on the fact that edges in images contain most of the semantic information. Semantic edge detection involves two tasks, namely pure edge detection and edge classification. Those are in fact fundamentally distinct in terms of the level of abstraction that each task requires. This fact is known as the distracted supervision paradox and limits the possible performance of a supervised model in semantic edge detection. In this work, we will present a novel hybrid method that is based on a combination of the model-based concept of shearlets, which provides probably optimally sparse approximations of a model class of images, and the data-driven method of a suitably designed convolutional neural network. We show that it avoids the distracted supervision paradox and achieves high performance in semantic edge detection. In addition, our approach requires significantly fewer parameters than a pure data-driven approach. Finally, we present several applications such as tomographic reconstruction and show that our approach significantly outperforms former methods, thereby also indicating the value of such hybrid methods for biomedical imaging.

Pharmacophore modeling, design, and synthesis of potent antihypertensives, oxazolo/thiazolo-[3,2-a]-pyrimidin-3(2H)-one, and 1,5-dihydroimidazo-[1,2-a]-pyrimidin-3(2H)-one derivatives: A pilot trial.

An improved pharmacophore model, molecular properties, geometric analyses, and SAR led to synthesize oxazolo/thiazolo-[3,2-a]-pyrimidin-3(2H)-one, and 1,5-dihydroimidazo-[1,2-a]-pyrimidin-3(2H)-one derivatives exhibiting potent anti-hypertensive activity. The 6-ethoxycarbonyl-2,7-dimethyl-5-phenyl-1,5-dihydroimidazo[3,2-a]pyrimidin-3(2H)-one (4g), and 6-ethoxycarbonyl-2,7-dimethyl-5-(3-methyl-phenyl)-1,5-dihydroimidazo[3,2-a]pyrimidin-3(2H)-one (4h) showed significant reduction in mean arterial blood pressure (MABP, mm/Hg) of 79.78%, and 92.95% in 6 and 12 h durations, respectively, at 1.5 mg/kg body-weight dose, while at 3.0 mg/kg body-weight dose, the MABP reduction was achieved at 95.46%, and 92.02%, respectively, in 6 and 12 h durations, as compared to the standard drug, nifedipine.

Investigation of the Average Shape and Principal Variations of the Human Talus Bone Using Statistic Shape Model.

Due to the complexity of articular interconnections and tenuous blood supply to the talus, talus fractures are often associated with complications (e.g., avascular necrosis). Currently, surgically fusing the talus to adjacent bones is widely used as treatment to talus fractures, but this procedure can greatly reduce mobility in the ankle and hindfoot. Alternatively, customized talus implants have shown an overall satisfactory patient feedback but with the limitation of high expenses and time-consuming manufacturing process. In order to circumvent these disadvantages, universal talus implants have been proposed as a potential solution. In our study, we aimed to develop a methodology using Statistical Shape Model (SSM) to simulate the talus, and then evaluate the feasibility of the model to obtain the mean shape needed for universal implant design. In order to achieve this, we registered 98 tali (41 females and 57 males) and used the registered dataset to train our SSM. We used the mean shape derived from the SSM as the basis for our talus implant template, and compared our template with that of previous works. We found that our SSM mean shape talus implant was geometrically similar to implants from other works, which used a different method for the mean shape. This suggests the feasibility of SSM as a method of finding mean shape information for the development of universal implants. A second aim of our study was to investigate if one scalable talus implant can accommodate all patients. In our study, we focused on addressing this from a geometric perspective as there are multiple factors impacting this (e.g., articular surface contact characteristics, implant material properties). Our initial findings are that the first two principal components should be afforded consideration for the geometrical accuracy of talus implant design. Additional factors would need to be further evaluated for their role in informing universal talus implant design.

Geo-Measures: A PyMOL plugin for protein structure ensembles analysis.

Although molecular dynamics encompasses several applications, studies focusing on biomolecular systems are central issues of this research area. Such simulations require the generation of trajectory files, which provide a path for the analysis and interpretation of results with biological significance. However, although several programs have been developed in Python language for the analyses of molecular dynamics (MD) trajectories, they usually require some knowledge of programming languages in order to write or run the scripts using command lines, which certainly hinders the access of MD simulations to many scientists with the necessary biological background to interpret their results. To ease the access to Python packages focusing on MD trajectory analyses, we built a user-friendly and easy-to-install graphical PyMOL interface. Geo-Measures integrates the PyMOL functionalities with MDTraj, a powerful library of trajectory analyses, allowing the users to access up to 14 different types of analyses. Two sample cases are reported here to demonstrate the use of Geo-Measures. In the first example, which involves the use a MD trajectory file of hemoglobin from the MoDEL MD bank, we exemplified the analyses of the following variables: root mean square deviation, radius of gyration, free energy landscape and principal component analysis. In the second case, we built a trajectory file for the ecto-5'-nucleotidase using the LiGRO program to study the carbon alpha pincer angles, to define the secondary structure of the proteins and to analyze the Modevectors. This user-friendly graphical PyMOL plugin, which can be used to generate several descriptive analyses for protein structures, is open source and can be downloaded at: https://pymolwiki.org/index.php/Geo_Measures_Plugin.

Geometric Analysis of Type B Aortic Dissections Shows Aortic Remodeling After Intervention Using Multilayer Stents.

Recently, multilayer stents for type B aortic dissections (TBAD) have been proposed to decrease false lumen flow, increase and streamline true lumen flow, and retain branch vessel patency. We aimed to provide a protocol with standardized techniques to investigate aortic remodeling of TBAD by multilayer flow modulators (MFM) in static geometric and hemodynamic analyses. Combining existing literature and new insights, a standardized protocol was designed. Using pre- and postoperative CT scans, geometric models were constructed, lumen dimensions were calculated, computational fluid dynamics (CFD) models were composed, and velocity and pressures were calculated. Sixteen TBAD cases treated with MFM were included for analysis. For each case, aortic remodeling was analyzed using post-processing medical imaging software. After 3D models were created, geometrical anatomical measurements were performed, and meshes for finite element analysis were generated. MFM cases were compared pre- and postoperatively; true lumen volumes increased (p < 0.001), false lumen volumes decreased (p = 0.001), true lumen diameter at the plane of maximum compression (PMC) increased (p < 0.001), and false lumen index decreased (p = 0.008). True lumen flow was streamlined, and the overall fluid velocity and pressures decreased (p < 0.001 and p = 0.006, respectively). This protocol provided a standardized method to evaluate the effects of MFM treatments in TBAD on geometric analyses, PMC, and CFD outcomes.

Art Forms in Nature: radiolaria from Haeckel and Blaschka to 3D nanotomography, quantitative image analysis, evolution, and contemporary art.

The illustrations of the late nineteenth-/twentieth-century scientist/artist Ernst Haeckel, as depicted in his book Art Forms in Nature (originally in German as Kunstformen der Natur, 1898-1904), have been at the intersection of art, biology, and mathematics for over a century. Haeckel's images of radiolaria (microscopic protozoans described as amoeba in glass houses) have influenced various artists for over a century (glass artists Leopold and Rudolph Blaschka; sculptor Henry Moore; architects Rene Binet, Zaha Hadid, Antoni Gaudi, Chris Bosse and Frank Gehry; and designers-filmmakers Charles and Ray Eames). We focus on this history and extend the artistic, biological, and mathematical contributions of this interdisciplinary legacy by going beyond the 3D visual, topological, and geometric analyses of radiolaria to include the nanoscale with graph theory, spatial statistics, and computational geometry. We analyze multiple visualizations of radiolaria generated through Haeckel's images, light microscopy, scanning electron microscopy, micro- and nanotomography, and three-dimensional computer rendering. Mathematical analyses are conducted using the image analysis package "Ka-me: A Voronoi Image Analyzer." Further analyses utilize three-dimensional printing, laser etched crystalline glass art, and sculpture. Open sharing of three-dimensional nanotomography of radiolaria and other protozoa through MorphoSource enables new possibilities for artists, architects, paleontologists, structural morphologists, taxonomists, museum curators, and mathematical biologists. Distinctively, newer models of radiolaria fit into a larger context of productive interdisciplinary collaboration that continues Haeckel's legacy that lay a foundation for new work in biomimetic design and additive manufacturing where artistic and scientific models mutually and robustly generate wonder, beauty, utility, curiosity, insight, environmentalism, theory, and questions.

Geometric analysis of ruptured and nonruptured abdominal aortic aneurysms.

OBJECTIVE: The objective of this study was to use parameters to determine the geometric differences between ruptured abdominal aortic aneurysms (AAAs) and nonruptured AAAs. METHODS: Computed tomography data of 38 ruptured AAAs and 215 electively repaired (nonruptured) AAAs were collected from multiple institutes. We compared the ruptured AAA group and nonruptured AAA group with 1:1 matching by using the Mahalanobis distance, which was calculated using the patient's age, sex, and AAA diameter. We selected the longitudinal AAA image in multiplanar reconstruction view, placed a hypothetical ellipse on the aneurysm's protruded curve, and placed a circle on the portion connecting the aneurysm and the aorta. We then measured the aspect ratio (the vertical diameter divided by the horizontal diameter) and fillet radius (the radius of arc). RESULTS: The aspect ratio was significantly lower in the ruptured group than in the nonruptured group (2.02 ± 0.53 vs 2.60 ± 1.02; P = .002), as was the fillet radius (0.28 ± 0.18 vs 0.81 ± 0.44; P < .001). Receiver operating characteristic analysis revealed that the area under the curve of the aspect ratio was 0.688, and the optimal cutoff point was 2.23, with sensitivity and specificity of 0.55 and 0.76, respectively. The area under the curve of the fillet radius was 0.933, and the optimal cutoff was 0.347, with sensitivity and specificity of 0.97 and 0.87, respectively. CONCLUSIONS: The geometric analysis performed in this study revealed that ruptured AAAs had a smaller fillet radius and smaller aspect ratio than nonruptured AAAs did.

Assessment of geometrical remodelling of the aortic arch after hybrid treatment.

OBJECTIVES: The aim of this study was to measure the morphological remodelling of the ascending aorta, aortic arch and thoracic aorta after aortic arch hybrid treatment including debranching and stent graft implantation. METHODS: Preoperative, 1-month and 1-year follow-up of computed tomography angiography scans of 22 patients were analysed to compute the lumen centreline from the aortic root to the coeliac trunk, and the following measurements were derived: the total centreline length, distance from the aortic root to the left subclavian artery, distance from the left subclavian artery to the distal landing zone. For both pre- and postoperative centrelines, the pointwise curvature was measured at the proximal and the distal landing zones. The mean curvature values of the whole aortic segment and the endografting region of the ascending and the descending aorta were measured. Surface outerline was computed as well, and curvature values at the endograft landing points were extracted. RESULTS: At the 1-month follow-up, centreline length were already significantly increased (382.66 ± 48.69 to 388.1 ± 50.75 mm; P = 0.01). Centreline pointwise curvature increased in the proximal (+29%, P = 0.011) and the distal zones (+63%, P = 0.004). Similarly, pointwise curvature of the outerline significantly increased in the proximal (+77%, P = 0.01) and the distal landing zones (+100%, P = 0.04). The centreline mean curvature increased in the ascending aorta (+7%, P = 0.02) and decreased in the endografting region (-3.3%, P = 0.004). No evidence of a relationship of such a remodelling with the type of endograft and the type of pathology was observed. This remodelling trend was confirmed by the analysis of 1-year computed tomography angiographies. CONCLUSIONS: Hybrid arch repair was associated with a significant elongation of the vessel and a significant increase in the curvature on the ascending aorta and the descending aorta and on the endograft proximal and the distal landing zones.