Design, inverted vat photopolymerization 3D printing, and initial characterization of a miniature force sensor for localized in vivo tissue measurements

Background Tissue healthiness could be assessed by evaluating its viscoelastic properties through localized contact reaction force measurements to obtain quantitative time history information. To evaluate these properties for hard to reach and confined areas of the human body, miniature force sensors with size constraints and appropriate load capabilities are needed. This research article reports on the design, fabrication, integration, characterization, and in vivo experimentation of a uniaxial miniature force sensor on a human forearm. Methods The strain gauge based sensor components were designed to meet dimensional constraints (diameter ≤3.5mm), safety factor (≥3) and performance specifications (maximum applied load, resolution, sensitivity, and accuracy). The sensing element was fabricated using traditional machining. Inverted vat photopolymerization technology was used to prototype complex components on a Form3 printer; micro-component orientation for fabrication challenges were overcome through experimentation. The sensor performance was characterized using dead weights and a LabVIEW based custom developed data acquisition system. The operational performance was evaluated by in vivo measurements on a human forearm; the relaxation data were used to calculate the Voigt model viscoelastic coefficient. Results The three dimensional (3D) printed components exhibited good dimensional accuracy (maximum deviation of 183μm). The assembled sensor exhibited linear behavior (regression coefficient of R2=0.999) and met desired performance specifications of 3.4 safety factor, 1.2N load capacity, 18mN resolution, and 3.13% accuracy. The in vivo experimentally obtained relaxation data were analyzed using the Voigt model yielding a viscoelastic coefficient τ=12.38sec and a curve-fit regression coefficient of R2=0.992. Conclusions This research presented the successful design, use of 3D printing for component fabrication, integration, characterization, and analysis of initial in vivo collected measurements with excellent performance for a miniature force sensor for the assessment of tissue viscoelastic properties. Through this research certain limitations were identified, however the initial sensor performance was promising and encouraging to continue the work to improve the sensor. This micro-force sensor could be used to obtain tissue quantitative data to assess tissue healthiness for medical care over extended time periods.

A Data-Driven Memory-Dependent Modeling Framework for Anomalous Rheology: Application to Urinary Bladder Tissue

We introduce a data-driven fractional modeling framework for complex materials, and particularly bio-tissues. From multi-step relaxation experiments of distinct anatomical locations of porcine urinary bladder, we identify an anomalous relaxation character, with two power-law-like behaviors for short/long long times, and nonlinearity for strains greater than 25%. The first component of our framework is an existence study, to determine admissible fractional viscoelastic models that qualitatively describe linear relaxation. After the linear viscoelastic model is selected, the second stage adds large-strain effects to the framework through a fractional quasi-linear viscoelastic approach for the nonlinear elastic response of the bio-tissue of interest. From single-step relaxation data of the urinary bladder, a fractional Maxwell model captures both short/long-term behaviors with two fractional orders, being the most suitable model for small strains at the first stage. For the second stage, multi-step relaxation data under large strains were employed to calibrate a four-parameter fractional quasi-linear viscoelastic model, that combines a Scott-Blair relaxation function and an exponential instantaneous stress response, to describe the elastin/collagen phases of bladder rheology. Our obtained results demonstrate that the employed fractional quasi-linear model, with a single fractional order in the range α = 0.25–0.30, is suitable for the porcine urinary bladder, producing errors below 2% without need for recalibration over subsequent applied strains. We conclude that fractional models are attractive tools to capture the bladder tissue behavior under small-to-large strains and multiple time scales, therefore being potential alternatives to describe multiple stages of bladder functionality.

Anion reorientations and cation diffusion in a carbon-substituted sodium nido-borate Na-7,9-C2B9H12: 1H and 23Na NMR studies

Polyhydroborate-based salts of lithium and sodium have attracted much recent interest as promising solid-state electrolytes for energy-related applications. A member of this family, sodium dicarba-nido-undecahydroborate Na-7,9-C2B9H12 exhibits superionic conductivity above its order-disorder phase transition temperature, ∼360 K. To investigate the dynamics of the anions and cations in this compound at the microscopic level, we have measured the 1H and 23Na nuclear magnetic resonance (NMR) spectra and spin-lattice relaxation rates over the temperature range of 148–384 K. It has been found that the transition from the low-T ordered to the high-T disordered phase is accompanied by an abrupt, several-orders-of-magnitude acceleration of both the reorientational jump rate of the complex anions and the diffusive jump rate of Na+ cations. These results support the idea that reorientations of large [C2B9H12]− anions can facilitate cation diffusion and, thus, the ionic conductivity. The apparent activation energies for anion reorientations obtained from the 1H spin-lattice relaxation data are 314 meV for the ordered phase and 272 meV for the disordered phase. The activation energies for Na+ diffusive jumps derived from the 23Na spin-lattice relaxation data are 350 and 268 meV for the ordered and disordered phases, respectively.

Water Dynamics in Whey-Protein-Based Composite Hydrogels by Means of NMR Relaxometry

Whey-protein-isolate-based composite hydrogels with encapsulated black carrot (Daucus carota) extract were prepared by heat-induced gelation. The hydrogels were blended with gum tragacanth, pectin and xanthan gum polysaccharides for modulating their properties. 1H spin-lattice relaxation experiments were performed in a broad frequency range, from 4 kHz to 30 MHz, to obtain insight into the influence of the different polysaccharides and of the presence of black carrot on dynamical properties of water molecules in the hydrogel network. The 1H spin-lattice relaxation data were decomposed into relaxation contributions associated with confined and free water fractions. The population of the confined water fraction and the value of the translation diffusion coefficient of water molecules in the vicinity of the macromolecular network were quantitatively determined on the basis of the relaxation data. Moreover, it was demonstrated that the translation diffusion is highly anisotropic (two-dimensional, 2D).

Insights into Protein Dynamics from ¹⁵N-¹H HSQC

Protein dynamic information is customarily extracted from 15N NMR spin-relaxation experiments. These experiments can only be applied to (small) proteins that can be dissolved to high concentrations. However, most proteins of interest to the biochemical and biomedical community are large and relatively insoluble. These proteins often have functional conformational changes, and it is particularly regretful that these processes cannot be supplemented by dynamical information from NMR. We ask here whether (some) dynamic information can be obtained from the 1H line widths in 15N-1H HSQC spectra. Such spectra are widely available, also for larger proteins. We developed computer programs to predict amide proton line widths from (crystal) structures. We aim to answer the following basic questions: is the 1H linewidth of a HSQC cross peak smaller than average because its 1H nucleus has few dipolar neighbors, or because the resonance is motionally narrowed? Is a broad line broad because of conformational exchange, or because the 1H nucleus resides in a dense proton environment? We calibrate our programs by comparing computational and experimental results for GB1 (58 residues). We deduce that GB1 has low average 1HN order parameters (0.8), in broad agreement with what was found by others from 15N relaxation experiments (Idiyatullin et al., 2003). We apply the program to the BPTI crystal structure and compare the results with a 15N-1H HSQC spectrum of BPTI (56 residues) and identify a cluster of conformationally broadened 1HN resonances that belong to an area, for which millisecond dynamics has been previously reported from 15N relaxation data (Szyperski et al., J. Biomol. NMR 3, 151-164, 1993). We feel that our computational approach is useful to glean insights into the dynamical properties of larger biomolecules for which high-quality 15N relaxation data cannot be recorded.

Bootstrap Aggregation for Model Selection in the Model-free Formalism

The ability to make robust inferences about the dynamics of biological macromolecules using NMR spectroscopy depends heavily on the application of appropriate theoretical models for nuclear spin relaxation. Data analysis for NMR laboratory-frame relaxation experiments typically involves selecting one of several model-free spectral density functions using a bias-corrected fitness test. Here, advances in statistical model selection theory, termed bootstrap aggregation or bagging, are applied to 15N spin relaxation data, developing a multimodel inference solution to the model-free selection problem. The approach is illustrated using data sets recorded at four static magnetic fields for the bZip domain of the S. cerevisiae transcription factor GCN4.

How wide is the window opened by high-resolution relaxometry on the internal dynamics of proteins in solution?

The dynamics of molecules in solution is usually quantified by the determination of timescale-specific amplitudes of motions. High-resolution nuclear magnetic resonance (NMR) relaxometry experiments—where the sample is transferred to low fields for longitudinal (T1) relaxation, and back to high field for detection with residue-specific resolution—seeks to increase the ability to distinguish the contributions from motion on timescales slower than a few nanoseconds. However, tumbling of a molecule in solution masks some of these motions. Therefore, we investigate to what extent relaxometry improves timescale resolution, using the “detector” analysis of dynamics. Here, we demonstrate improvements in the characterization of internal dynamics of methyl-bearing side chains by carbon-13 relaxometry in the small protein ubiquitin. We show that relaxometry data leads to better information about nanosecond motions as compared to high-field relaxation data only. Our calculations show that gains from relaxometry are greater with increasing correlation time of rotational diffusion.

Combined description of polymer PVT and relaxation data using a dynamic “SL-TS2” mean-field lattice model

We develop a combined model to describe the pressure–volume–temperature (PVT) thermodynamics and the α- and β-relaxation time dynamics in glass-forming amorphous materials.