A rolling-gliding wear simulator for the investigation of tribological material pairings for application in total knee arthroplasty

Background: Material wear testing is an important technique in the development and evaluation of materials for use in implant for total knee arthroplasty. Since a knee joint induces a complex rolling-gliding movement, standardised material wear testing devices such as Pin-on-Disc or Ring-on-Disc testers are suitable to only a limited extent because they generate pure gliding motion only.Methods: A rolling-gliding wear simulator was thus designed, constructed and implemented, which simulates and reproduces the rolling-gliding movement and loading of the knee joint on specimens of simplified geometry. The technical concept was to run a base-plate, representing the tibia plateau, against a pivoted cylindrical counter-body, representing one femur condyle under an axial load. A rolling movement occurs as a result of the friction and pure gliding is induced by limiting the rotation of the cylindrical counter-body. The set up also enables simplified specimens handling and removal for gravimetrical wear measurements. Long-term wear tests and gravimetrical wear measurements were carried out on the well known material pairings: cobalt chrome-polyethylene, ceramic-polyethylene and ceramic-ceramic, over three million motion cycles to allow material comparisons to be made.Results: The observed differences in wear rates between cobalt-chrome on polyethylene and ceramic on polyethylene pairings were similar to the differences of published data for existing material-pairings. Test results on ceramic-ceramic pairings of different frontal-plane geometry and surface roughness displayed low wear rates and no fracture failures.Conclusions: The presented set up is able to simulate the rolling-gliding movement of the knee joint, is easy to use, and requires a minimum of user intervention or monitoring. It is suitable for long-term testing, and therefore a useful tool for the investigation of new and promising materials which are of interest for application in knee joint replacement implants. © 2010 Richter et al; licensee BioMed Central Ltd.

Oxímetro de pulso com comunicação via Bluetooth

Dissertação (mestrado)—Universidade de Brasília, Faculdade Gama, Programa de Pós-Graduação em Engenharia Biomédica, 2015.

The Effect of Architecture and Shear Stress on Endothelialization of 3D Printed Vascular Networks

Despite significant progress in the field of tissue engineering within the last decade, a number of unsolved problems still remain. One of the most relevant issues is the lack of proper vascularization that limits the size of engineered tissues to smaller than clinically relevant dimensions. In particular, the growth of engineered tissue in vitro within bioreactors is plagued with this challenge. Specifically, the tubular perfusion system bioreactor has been used for large scale bone constructs; however these engineered constructs lack inherent vasculature and quickly develop a hypoxic core, where no nutrient exchange can occur, thus leading to cell death. Through the use of 3D printed vascular templates in conjunction with a tubular perfusion system bioreactor, we attempt to create an endothelial cell monolayer on 3D scaffolds that could potentially serve as the foundation of inherent vasculature within these engineered bone grafts.

Exploração de escalonamentos óptimos na gestão de exames médicos

Uma das áreas de aplicação da optimização é a Engenharia Biomédica, pois a optimização intervém no estudo de próteses e implantes, na reconstrução tomográfica, na mecânica experimental, entre outras aplicações. Este projecto tem como principal objectivo a criação de um novo programa de marcação de exames médicos a fim de minimizar o tempo de espera na realização dos mesmos. É efectuada uma breve referência à teoria da optimização bem como à optimização linear e não-linear, aos algoritmos genéticos, que foram usados para a realização deste trabalho. É também apresentado um caso de estudo, formulado como um problema de optimização não linear com restrições. Com este estudo verificou-se que o escalonamento de exames médicos nunca poderá ser optimizado a 100por cento devido à quantidade de variáveis existentes, sendo que algumas delas não são passíveis de prever com antecedência.

Integration of virus-like particle macromolecular bioreceptors in electrochemical biosensors

Rapid, sensitive and selective detection of chemical hazards and biological pathogens has shown growing importance in the fields of homeland security, public safety and personal health. In the past two decades, efforts have been focusing on performing point-of-care chemical and biological detections using miniaturized biosensors. These sensors convert target molecule binding events into measurable electrical signals for quantifying target molecule concentration. However, the low receptor density and the use of complex surface chemistry in receptors immobilization on transducers are common bottlenecks in the current biosensor development, adding to the cost, complexity and time. This dissertation presents the development of selective macromolecular Tobacco mosaic virus-like particle (TMV VLP) biosensing receptor, and the microsystem integration of VLPs in microfabricated electrochemical biosensors for rapid and performance-enhanced chemical and biological sensing. Two constructs of VLPs carrying different receptor peptides targeting at 2,4,6-trinitrotoluene (TNT) explosive or anti-FLAG antibody are successfully bioengineered. The VLP-based TNT electrochemical sensor utilizes unique diffusion modulation method enabled by biological binding between target TNT and receptor VLP. The method avoids the influence from any interfering species and environmental background signals, making it extremely suitable for directly quantifying the TNT level in a sample. It is also a rapid method that does not need any sensor surface functionalization process. For antibody sensing, the VLPs carrying both antibody binding peptides and cysteine residues are assembled onto the gold electrodes of an impedance microsensor. With two-phase immunoassays, the VLP-based impedance sensor is able to quantify antibody concentrations down to 9.1 ng/mL. A capillary microfluidics and impedance sensor integrated microsystem is developed to further accelerate the process of VLP assembly on sensors and improve the sensitivity. Open channel capillary micropumps and stop-valves facilitate localized and evaporation-assisted VLP assembly on sensor electrodes within 6 minutes. The VLP-functionalized impedance sensor is capable of label-free sensing of antibodies with the detection limit of 8.8 ng/mL within 5 minutes after sensor functionalization, demonstrating great potential of VLP-based sensors for rapid and on-demand chemical and biological sensing.

MICROFLUIDIC ASSAY PERFORMANCE ENHANCEMENT USING POROUS VOLUMETRIC DETECTION ELEMENTS FOR IMPEDEMETRIC AND OPTICAL SENSING

Microfluidic technologies have great potential to help create automated, cost-effective, portable devices for rapid point of care (POC) diagnostics in diverse patient settings. Unfortunately commercialization is currently constrained by the materials, reagents, and instrumentation required and detection element performance. While most microfluidic studies utilize planar detection elements, this dissertation demonstrates the utility of porous volumetric detection elements to improve detection sensitivity and reduce assay times. Impedemetric immunoassays were performed utilizing silver enhanced gold nanoparticle immunoconjugates (AuIgGs) and porous polymer monolith or silica bead bed detection elements within a thermoplastic microchannel. For a direct assay with 10 µm spaced electrodes the detection limit was 0.13 fM AuIgG with a 3 log dynamic range. The same assay was performed with electrode spacing of 15, 40, and 100 µm with no significant difference between configurations. For a sandwich assay the detection limit was10 ng/mL with a 4 log dynamic range. While most impedemetric assays rely on expensive high resolution electrodes to enhance planar senor performance, this study demonstrates the employment of porous volumetric detection elements to achieve similar performance using lower resolution electrodes and shorter incubation times. Optical immunoassays were performed using porous volumetric capture elements perfused with refractive index matching solutions to limit light scattering and enhance signal. First, fluorescence signal enhancement was demonstrated with a porous polymer monolith within a silica capillary. Next, transmission enhancement of a direct assay was demonstrated by infusing aqueous sucrose solutions through silica bead beds with captured silver enhanced AuIgGs yielding a detection limit of 0.1 ng/mL and a 5 log dynamic range. Finally, ex situ functionalized porous silica monolith segments were integrated into thermoplastic channels for a reflectance based sandwich assay yielding a detection limit of 1 ng/mL and a 5 log dynamic range. The simple techniques for optical signal enhancement and ex situ element integration enable development of sensitive, multiplexed microfluidic sensors. Collectively the demonstrated experiments validate the use of porous volumetric detection elements to enhance impedemetric and optical microfluidic assays. The techniques rely on commercial reagents, materials compatible with manufacturing, and measurement instrumentation adaptable to POC diagnostics.

Effects of Load History on Ovine Spinal Range of Motion

Loading of spinal motion segment units alters biomechanical properties by modifying flexibility and range of motion. This study utilizes angular displacement due to an applied bending moment to assess biomechanical function during high-magnitude and prolonged compressive loading of ovine lumbar motion segments. High compressive loads, representative of physiological lifestyle and occupational behaviors, appear to limit fluid recovery of the intervertebral disc, thereby modifying spinal flexibility and increasing spinal instability. Intermittent extensions, or backwards bending movements, may provide a protective effect against the load-induced spinal instability. This study contributes a greater understanding of the effects of load history on the function and health of the lumbar spine. Findings may inform future efforts investigating adjustments in spinal posture to preserve or promote the recovery of lumbar spinal biomechanics.

INTEGRATED THRESHOLD-ACTIVATED FEEDBACK MICROSYSTEM FOR REAL-TIME CHARACTERIZATION, SENSING AND TREATMENT OF BACTERIAL BIOFILMS

Biofilms are the primary cause of clinical bacterial infections and are impervious to typical amounts of antibiotics, necessitating very high doses for treatment. Therefore, it is highly desirable to develop new alternate methods of treatment that can complement or replace existing approaches using significantly lower doses of antibiotics. Current standards for studying biofilms are based on end-point studies that are invasive and destroy the biofilm during characterization. This dissertation presents the development of a novel real-time sensing and treatment technology to aid in the non-invasive characterization, monitoring and treatment of bacterial biofilms. The technology is demonstrated through the use of a high-throughput bifurcation based microfluidic reactor that enables simulation of flow conditions similar to indwelling medical devices. The integrated microsystem developed in this work incorporates the advantages of previous in vitro platforms while attempting to overcome some of their limitations. Biofilm formation is extremely sensitive to various growth parameters that cause large variability in biofilms between repeated experiments. In this work we investigate the use of microfluidic bifurcations for the reduction in biofilm growth variance. The microfluidic flow cell designed here spatially sections a single biofilm into multiple channels using microfluidic flow bifurcation. Biofilms grown in the bifurcated device were evaluated and verified for reduced biofilm growth variance using standard techniques like confocal microscopy. This uniformity in biofilm growth allows for reliable comparison and evaluation of new treatments with integrated controls on a single device. Biofilm partitioning was demonstrated using the bifurcation device by exposing three of the four channels to various treatments. We studied a novel bacterial biofilm treatment independent of traditional antibiotics using only small molecule inhibitors of bacterial quorum sensing (analogs) in combination with low electric fields. Studies using the bifurcation-based microfluidic flow cell integrated with real-time transduction methods and macro-scale end-point testing of the combination treatment showed a significant decrease in biomass compared to the untreated controls and well-known treatments such as antibiotics. To understand the possible mechanism of action of electric field-based treatments, fundamental treatment efficacy studies focusing on the effect of the energy of the applied electrical signal were performed. It was shown that the total energy and not the type of the applied electrical signal affects the effectiveness of the treatment. The linear dependence of the treatment efficacy on the applied electrical energy was also demonstrated. The integrated bifurcation-based microfluidic platform is the first microsystem that enables biofilm growth with reduced variance, as well as continuous real-time threshold-activated feedback monitoring and treatment using low electric fields. The sensors detect biofilm growth by monitoring the change in impedance across the interdigitated electrodes. Using the measured impedance change and user inputs provided through a convenient and simple graphical interface, a custom-built MATLAB control module intelligently switches the system into and out of treatment mode. Using this self-governing microsystem, in situ biofilm treatment based on the principles of the bioelectric effect was demonstrated by exposing two of the channels of the integrated bifurcation device to low doses of antibiotics.

INTEGRATION OF INSTRUMENTATION AND PROCESSING SOFTWARE OF A LASER SPECKLE CONTRAST IMAGING SYSTEM

Laser speckle contrast imaging (LSCI) has the potential to be a powerful tool in medicine, but more research in the field is required so it can be used properly. To help in the progression of Michigan Tech's research in the field, a graphical user interface (GUI) was designed in Matlab to control the instrumentation of the experiments as well as process the raw speckle images into contrast images while they are being acquired. The design of the system was successful and is currently being used by Michigan Tech's Biomedical Engineering department. This thesis describes the development of the LSCI GUI as well as offering a full introduction into the history, theory and applications of LSCI.

UTILIZING DIELECTROPHORESIS TO DETERMINE THE PHYSIOLOGICAL DIFFERENCES OF EUKARYOTIC CELLS

Type 1 diabetes affects over 108,000 children, and this number is steadily increasing. Current insulin therapies help manage the disease but are not a cure. Over a child’s lifetime they can develop kidney disease, blindness, cardiovascular disease and many other issues due to the complications of type 1 diabetes. This autoimmune disease destroys beta cells located in the pancreas, which are used to regulate glucose levels in the body. Because there is no cure and many children are affected by the disease there is a need for alternative therapeutic options that can lead to a cure. Human mesenchymal stem cells (hMSCs) are an important cell source for stem cell therapeutics due to their differentiation capacity, self-renewal, and trophic activity. hMSCs are readily available in the bone marrow, and act as an internal repair system within the body, and they have been shown to differentiate into insulin producing cells. However, after isolation hMSCs are a heterogeneous cell population, which requires secondary processing. To resolve the heterogeneity issue hMSCs are separated using fluorescent- and magnetic-activate cell sorting with antigen labeling. These techniques are efficient but reduce cell viability after separation due to the cell labeling. Therefore, to make hMSCs more readily available for type 1 diabetes therapeutics, they should be separated without diminishing there functional capabilities. Dielectrophoresis is an alternative separation technique that has the capability to separated hMSCs. This dissertation uses dielectrophoresis to characterize the dielectric properties of hMSCs. The goal is to use hMSCs dielectric signature as a separation criteria rather than the antigen labeling implemented with FACS and MACS. DEP has been used to characterize other cell systems, and is a viable separation technique for hMSCs.

A BACKING DEVICE BASED ON AN EMBEDDED STIFFENER AND RETRACTABLE INSERTION TOOL FOR THIN-FILM COCHLEAR ARRAYS

Intracochlear trauma from surgical insertion of bulky electrode arrays and inadequate pitch perception are areas of concern with current hand-assembled commercial cochlear implants. Parylene thin-film arrays with higher electrode densities and lower profiles are a potential solution, but lack rigidity and hence depend on manually fabricated permanently attached polyethylene terephthalate (PET) tubing based bulky backing devices. As a solution, we investigated a new backing device with two sub-systems. The first sub-system is a thin poly(lactic acid) (PLA) stiffener that will be embedded in the parylene array. The second sub-system is an attaching and detaching mechanism, utilizing a poly(N-vinylpyrrolidone)-block-poly(d,l-lactide) (PVP-b-PDLLA) copolymer-based biodegradable and water soluble adhesive, that will help to retract the PET insertion tool after implantation. As a proof-of-concept of sub-system one, a microfabrication process for patterning PLA stiffeners embedded in parylene has been developed. Conventional hotembossing, mechanical micromachining, and standard cleanroom processes were integrated for patterning fully released and discrete stiffeners coated with parylene. The released embedded stiffeners were thermoformed to demonstrate that imparting perimodiolar shapes to stiffener-embedded arrays will be possible. The developed process when integrated with the array fabrication process will allow fabrication of stiffener-embedded arrays in a single process. As a proof-of-concept of sub-system two, the feasibility of the attaching and detaching mechanism was demonstrated by adhering 1x and 1.5x scale PET tube-based insertion tools and PLA stiffeners embedded in parylene using the copolymer adhesive. The attached devices survived qualitative adhesion tests, thermoforming, and flexing. The viability of the detaching mechanism was tested by aging the assemblies in-vitro in phosphate buffer solution. The average detachment times, 2.6 minutes and 10 minutes for 1x and 1.5x scale devices respectively, were found to be clinically relevant with respect to the reported array insertion times during surgical implantation. Eventually, the stiffener-embedded arrays would not need to be permanently attached to current insertion tools which are left behind after implantation and congest the cochlear scala tympani chamber. Finally, a simulation-based approach for accelerated failure analysis of PLA stiffeners and characterization of PVP-b-PDLLA copolymer adhesive has been explored. The residual functional life of embedded PLA stiffeners exposed to body-fluid and thereby subjected to degradation and erosion has been estimated by simulating PLA stiffeners with different parylene coating failure types and different PLA types for a given parylene coating failure type. For characterizing the PVP-b-PDLLA copolymer adhesive, several formulations of the copolymer adhesive were simulated and compared based on the insertion tool detachment times that were predicted from the dissolution, degradation, and erosion behavior of the simulated adhesive formulations. Results indicate that the simulation-based approaches could be used to reduce the total number of time consuming and expensive in-vitro tests that must be conducted.

STUDIES OF FUNCTIONALIZED NANOPARTICLES FOR SMART SELF-ASSEMBLY AND AS CONTROLLED DRUG DELIVERY

This dissertation is related to the studies of functionalized nanoparticles for self-assembly and as controlled drug delivery system. The whole topic is composed of two parts. In the first part, the research was conducted to design and synthesize a new type of ionic peptide-functionalized copolymer conjugates for self-assembly into nanoparticle fibers and 3D scaffolds with the ability of multi-drug loading and governing the release rate of each drug for tissue engineering. The self-assembly study confirmed that such peptide-functionalized amphiphilic copolymers underwent different self-assembly behavior. The bigger nanoparticles were more easily assembled into nanoparticle fibers and 3D scaffolds with larger pore size, while the smaller nanoparticle underwent faster self-assembly to form more compact 3D scaffolds with smaller porosity but more stable structure. Controlled release studies confirmed the ability of governing simultaneous release of different model drugs with independent release rate from a same scaffold. Cytotoxicity tests showed that all synthesized peptides, copolymers and peptide-copolymer conjugates were biocompatible with SW-620 cell lines and NIH3T3 cell lines. This new type of self-assembled scaffolds combined the advantages of peptide nanofibers and versatile controlled release of polymeric nanoparticles to achieve simultaneous multi-drug loading and controlled release of each drug, uniform distribution and flexibility of hydrogel scaffolds. The investigations in second part were first to design and synthesize organic biocide-loaded nanoparticles for low-leaching wood preservation using a cost-effective one-pot method to synthesize amphiphilic chitosan-g-PMMA nanoparticles loading with ~25-28 wt.% of the fungicide tebuconazole with particle size of ~100 nm diameter by FESEM. FESEM analysis confirmed efficient penetration of nanoparticles throughout the treated wooden stake with dimension of 19 × 19 × 455 mm^3. Leaching studies showed that biocide introduced into sapwood via nanoparticles leached only ~9% compared with the amount leached from tebuconazole solution-treated control, while soil jar tests showed that the nanoparticle-treated wood blocks were effectively protected from biological decay tested against G. trabeum, a brown rot fungus. Copper oxide nanoparticles with and without polymer stabilizers were also investigated to use as inorganic wood preservatives to clarify the factor affecting copper leaching from treated wood. Copper oxide nanoparticles with uniform diameters of ~10 nm and ~50 nm were prepared, and the leachates from southern pine sapwood treated with these nanoparticles were analyzed. It was found by TEM and EDS analysis that significant numbers of nanoparticles leached from the treated wood. The 50 nm nanoparticles leached slightly less than a soluble copper salt control, but 10 nm nanoparticles leached substantially more than the control. The effect of polymer stabilizers on nanoparticle leaching was also investigated. Results showed that polymer stabilizers increased leaching. The trends showed that nanoparticle size was a major factor in copper leaching.

DESIGN AND APPLICATION OF WIRELESS PASSIVE MAGNETOELASTIC RESONANCE AND MAGNETOHARMONIC FORCE SENSORS

The objective of the work described in this dissertation is the development of new wireless passive force monitoring platforms for applications in the medical field, specifically monitoring lower limb prosthetics. The developed sensors consist of stress sensitive, magnetically soft amorphous metallic glass materials. The first technology is based on magnetoelastic resonance. Specifically, when exposed to an AC excitation field along with a constant DC bias field, the magnetoelastic material mechanically vibrates, and may reaches resonance if the field frequency matches the mechanical resonant frequency of the material. The presented work illustrates that an applied loading pins portions of the strip, effectively decreasing the strip length, which results in an increase in the frequency of the resonance. The developed technology is deployed in a prototype lower limb prosthetic sleeve for monitoring forces experienced by the distal end of the residuum. This work also reports on the development of a magnetoharmonic force sensor comprised of the same material. According to the Villari effect, an applied loading to the material results in a change in the permeability of the magnetic sensor which is visualized as an increase in the higher-order harmonic fields of the material. Specifically, by applying a constant low frequency AC field and sweeping the applied DC biasing field, the higher-order harmonic components of the magnetic response can be visualized. This sensor technology was also instrumented onto a lower limb prosthetic for proof of deployment; however, the magnetoharmonic sensor illustrated complications with sensor positioning and a necessity to tailor the interface mechanics between the sensing material and the surface being monitored. The novelty of these two technologies is in their wireless passive nature which allows for long term monitoring over the life time of a given device. Additionally, the developed technologies are low cost. Recommendations for future works include improving the system for real-time monitoring, useful for data collection outside of a clinical setting.

Theoretical investigation of intra- and inter-cellular spatiotemporal calcium patterns in microcirculation

Microcirculatory vessels are lined by endothelial cells (ECs) which are surrounded by a single or multiple layer of smooth muscle cells (SMCs). Spontaneous and agonist induced spatiotemporal calcium (Ca2+) events are generated in ECs and SMCs, and regulated by complex bi-directional signaling between the two layers which ultimately determines the vessel tone. The contractile state of microcirculatory vessels is an important factor in the determination of vascular resistance, blood flow and blood pressure. This dissertation presents theoretical insights into some of the important and currently unresolved phenomena in microvascular tone regulation. Compartmental and continuum models of isolated EC and SMC, coupled EC-SMC and a multi-cellular vessel segment with deterministic and stochastic descriptions of the cellular components were developed, and the intra- and inter-cellular spatiotemporal Ca2+ mobilization was examined.^ Coupled EC-SMC model simulations captured the experimentally observed localized subcellular EC Ca2+ events arising from the opening of EC transient receptor vanilloid 4 (TRPV4) channels and inositol triphosphate receptors (IP3Rs). These localized EC Ca2+ events result in endothelium-derived hyperpolarization (EDH) and Nitric Oxide (NO) production which transmit to the adjacent SMCs to ultimately result in vasodilation. The model examined the effect of heterogeneous distribution of cellular components and channel gating kinetics in determination of the amplitude and spread of the Ca2+ events. The simulations suggested the necessity of co-localization of certain cellular components for modulation of EDH and NO responses. Isolated EC and SMC models captured intracellular Ca2+ wave like activity and predicted the necessity of non-uniform distribution of cellular components for the generation of Ca2+ waves. The simulations also suggested the role of membrane potential dynamics in regulating Ca2+ wave velocity. The multi-cellular vessel segment model examined the underlying mechanisms for the intercellular synchronization of spontaneous oscillatory Ca2+ waves in individual SMC. ^ From local subcellular events to integrated macro-scale behavior at the vessel level, the developed multi-scale models captured basic features of vascular Ca2+ signaling and provide insights for their physiological relevance. The models provide a theoretical framework for assisting investigations on the regulation of vascular tone in health and disease.^

Movement effects on the flow physics and nutrient delivery in engineered valvular tissues

Mechanical conditioning has been shown to promote tissue formation in a wide variety of tissue engineering efforts. However the underlying mechanisms by which external mechanical stimuli regulate cells and tissues are not known. This is particularly relevant in the area of heart valve tissue engineering (HVTE) owing to the intense hemodynamic environments that surround native valves. Some studies suggest that oscillatory shear stress (OSS) caused by steady flow and scaffold flexure play a critical role in engineered tissue formation derived from bone marrow derived stem cells (BMSCs). In addition, scaffold flexure may enhance nutrient (e.g. oxygen, glucose) transport. In this study, we computationally quantified the i) magnitude of fluid-induced shear stresses; ii) the extent of temporal fluid oscillations in the flow field using the oscillatory shear index (OSI) parameter, and iii) glucose and oxygen mass transport profiles. Noting that sample cyclic flexure induces a high degree of oscillatory shear stress (OSS), we incorporated moving boundary computational fluid dynamic simulations of samples housed within a bioreactor to consider the effects of: 1) no flow, no flexure (control group), 2) steady flow-alone, 3) cyclic flexure-alone and 4) combined steady flow and cyclic flexure environments. We also coupled a diffusion and convention mass transport equation to the simulated system. We found that the coexistence of both OSS and appreciable shear stress magnitudes, described by the newly introduced parameter OSI-:τ: explained the high levels of engineered collagen previously observed from combining cyclic flexure and steady flow states. On the other hand, each of these metrics on its own showed no association. This finding suggests that cyclic flexure and steady flow synergistically promote engineered heart valve tissue production via OSS, so long as the oscillations are accompanied by a critical magnitude of shear stress. In addition, our simulations showed that mass transport of glucose and oxygen is enhanced by sample movement at low sample porosities, but did not play a role in highly porous scaffolds. Preliminary in-house in vitro experiments showed that cell proliferation and phenotype is enhanced in OSI-:τ: environments.^