Calibration of a surgical microscope with automated zoom lenses using an active optical tracker

BACKGROUND: In this paper, we present a new method for the calibration of a microscope and its registration using an active optical tracker. METHODS: Practically, both operations are done simultaneously by moving an active optical marker within the field of view of the two devices. The IR LEDs composing the marker are first segmented from the microscope images. By knowing their corresponding three-dimensional (3D) position in the optical tracker reference system, it is possible to find the transformation matrix between the referential of the two devices. Registration and calibration parameters can be extracted directly from that transformation. In addition, since the zoom and focus can be modified by the surgeon during the operation, we propose a spline based method to update the camera model to the new setup. RESULTS: The proposed technique is currently being used in an augmented reality system for image-guided surgery in the fields of ear, nose and throat (ENT) and craniomaxillofacial surgeries. CONCLUSIONS: The results have proved to be accurate and the technique is a fast, dynamic and reliable way to calibrate and register the two devices in an OR environment.

Quality controls for two heel bone ultrasounds used in the Swiss Evaluation of the Methods of Measurement of Osteoporotic Fracture Risk Study

Because of the important morbidity and mortality associated with osteoporosis, it is essential to detect subjects at risk by screening methods, such as bone quantitative ultrasounds (QUSs). Several studies showed that QUS could predict fractures. None, however, compared prospectively different QUS devices, and few data of quality controls (QCs) have been published. The Swiss Evaluation of the Methods of Measurement of Osteoporotic Fracture Risk is a prospective multicenter study that compared three QUSs for the assessment of hip fracture risk in a population of 7609 women age >/=70 yr. Because the inclusion phase lasted 20 mo, and because 10 centers participated in this study, QC became a major issue. We therefore developed a QC procedure to assess the stability and precision of the devices, and for their cross-calibration. Our study focuses on the two heel QUSs. The water bath system (Achilles+) had a higher precision than the dry system (Sahara). The QC results were highly dependent on temperature. QUS stability was acceptable, but Sahara must be calibrated regularly. A sufficient homogeneity among all the Sahara devices could be demonstrated, whereas significant differences were found among the Achilles+ devices. For speed of sound, 52% of the differences among the Achilles+ was explained by the water s temperature. However, for broadband ultrasound attenuation, a maximal difference of 23% persisted after adjustment for temperature. Because such differences could influence measurements in vivo, it is crucial to develop standardized phantoms to be used in prospective multicenter studies.

Multiscale methods for shape constraints in deconvolution: Confidence statements for qualitative features

We derive multiscale statistics for deconvolution in order to detect qualitative features of the unknown density. An important example covered within this framework is to test for local monotonicity on all scales simultaneously. We investigate the moderately ill-posed setting, where the Fourier transform of the error density in the deconvolution model is of polynomial decay. For multiscale testing, we consider a calibration, motivated by the modulus of continuity of Brownian motion. We investigate the performance of our results from both the theoretical and simulation based point of view. A major consequence of our work is that the detection of qualitative features of a density in a deconvolution problem is a doable task, although the minimax rates for pointwise estimation are very slow.

Transconvolution and the virtual positron emission tomograph--a new method for cross calibration in quantitative PET∕CT imaging

PURPOSE Positron emission tomography (PET)∕computed tomography (CT) measurements on small lesions are impaired by the partial volume effect, which is intrinsically tied to the point spread function of the actual imaging system, including the reconstruction algorithms. The variability resulting from different point spread functions hinders the assessment of quantitative measurements in clinical routine and especially degrades comparability within multicenter trials. To improve quantitative comparability there is a need for methods to match different PET∕CT systems through elimination of this systemic variability. Consequently, a new method was developed and tested that transforms the image of an object as produced by one tomograph to another image of the same object as it would have been seen by a different tomograph. The proposed new method, termed Transconvolution, compensates for differing imaging properties of different tomographs and particularly aims at quantitative comparability of PET∕CT in the context of multicenter trials. METHODS To solve the problem of image normalization, the theory of Transconvolution was mathematically established together with new methods to handle point spread functions of different PET∕CT systems. Knowing the point spread functions of two different imaging systems allows determining a Transconvolution function to convert one image into the other. This function is calculated by convolving one point spread function with the inverse of the other point spread function which, when adhering to certain boundary conditions such as the use of linear acquisition and image reconstruction methods, is a numerically accessible operation. For reliable measurement of such point spread functions characterizing different PET∕CT systems, a dedicated solid-state phantom incorporating (68)Ge∕(68)Ga filled spheres was developed. To iteratively determine and represent such point spread functions, exponential density functions in combination with a Gaussian distribution were introduced. Furthermore, simulation of a virtual PET system provided a standard imaging system with clearly defined properties to which the real PET systems were to be matched. A Hann window served as the modulation transfer function for the virtual PET. The Hann's apodization properties suppressed high spatial frequencies above a certain critical frequency, thereby fulfilling the above-mentioned boundary conditions. The determined point spread functions were subsequently used by the novel Transconvolution algorithm to match different PET∕CT systems onto the virtual PET system. Finally, the theoretically elaborated Transconvolution method was validated transforming phantom images acquired on two different PET systems to nearly identical data sets, as they would be imaged by the virtual PET system. RESULTS The proposed Transconvolution method matched different PET∕CT-systems for an improved and reproducible determination of a normalized activity concentration. The highest difference in measured activity concentration between the two different PET systems of 18.2% was found in spheres of 2 ml volume. Transconvolution reduced this difference down to 1.6%. In addition to reestablishing comparability the new method with its parameterization of point spread functions allowed a full characterization of imaging properties of the examined tomographs. CONCLUSIONS By matching different tomographs to a virtual standardized imaging system, Transconvolution opens a new comprehensive method for cross calibration in quantitative PET imaging. The use of a virtual PET system restores comparability between data sets from different PET systems by exerting a common, reproducible, and defined partial volume effect.

Experimental, theoretical and numerical investigation of the nonlinear micromechanical properties of bone

Aging societies suffer from an increasing incidence of bone fractures. Bone strength depends on the amount of mineral measured by clinical densitometry, but also on the micromechanical properties of the bone hierarchical organization. A good understanding has been reached for elastic properties on several length scales, but up to now there is a lack of reliable postyield data on the lower length scales. In order to be able to describe the behavior of bone at the microscale, an anisotropic elastic-viscoplastic damage model was developed using an eccentric generalized Hill criterion and nonlinear isotropic hardening. The model was implemented as a user subroutine in Abaqus and verified using single element tests. A FE simulation of microindentation in lamellar bone was finally performed show-ing that the new constitutive model can capture the main characteristics of the indentation response of bone. As the generalized Hill criterion is limited to elliptical and cylindrical yield surfaces and the correct shape for bone is not known, a new yield surface was developed that takes any convex quadratic shape. The main advantage is that in the case of material identification the shape of the yield surface does not have to be anticipated but a minimization results in the optimal shape among all convex quadrics. The generality of the formulation was demonstrated by showing its degeneration to classical yield surfaces. Also, existing yield criteria for bone at multiple length scales were converted to the quadric formulation. Then, a computational study to determine the influence of yield surface shape and damage on the in-dentation response of bone using spherical and conical tips was performed. The constitutive model was adapted to the quadric criterion and yield surface shape and critical damage were varied. They were shown to have a major impact on the indentation curves. Their influence on indentation modulus, hardness, their ratio as well as the elastic to total work ratio were found to be very well described by multilinear regressions for both tip shapes. For conical tips, indentation depth was not a significant fac-tor, while for spherical tips damage was insignificant. All inverse methods based on microindentation suffer from a lack of uniqueness of the found material properties in the case of nonlinear material behavior. Therefore, monotonic and cyclic micropillar com-pression tests in a scanning electron microscope allowing a straightforward interpretation comple-mented by microindentation and macroscopic uniaxial compression tests were performed on dry ovine bone to identify modulus, yield stress, plastic deformation, damage accumulation and failure mecha-nisms. While the elastic properties were highly consistent, the postyield deformation and failure mech-anisms differed between the two length scales. A majority of the micropillars showed a ductile behavior with strain hardening until failure by localization in a slip plane, while the macroscopic samples failed in a quasi-brittle fashion with microcracks coalescing into macroscopic failure surfaces. In agreement with a proposed rheological model, these experiments illustrate a transition from a ductile mechanical behavior of bone at the microscale to a quasi-brittle response driven by the growth of preexisting cracks along interfaces or in the vicinity of pores at the macroscale. Subsequently, a study was undertaken to quantify the topological variability of indentations in bone and examine its relationship with mechanical properties. Indentations were performed in dry human and ovine bone in axial and transverse directions and their topography measured by AFM. Statistical shape modeling of the residual imprint allowed to define a mean shape and describe the variability with 21 principal components related to imprint depth, surface curvature and roughness. The indentation profile of bone was highly consistent and free of any pile up. A few of the topological parameters, in particular depth, showed significant correlations to variations in mechanical properties, but the cor-relations were not very strong or consistent. We could thus verify that bone is rather homogeneous in its micromechanical properties and that indentation results are not strongly influenced by small de-viations from the ideal case. As the uniaxial properties measured by micropillar compression are in conflict with the current literature on bone indentation, another dissipative mechanism has to be present. The elastic-viscoplastic damage model was therefore extended to viscoelasticity. The viscoelastic properties were identified from macroscopic experiments, while the quasistatic postelastic properties were extracted from micropillar data. It was found that viscoelasticity governed by macroscale properties has very little influence on the indentation curve and results in a clear underestimation of the creep deformation. Adding viscoplasticity leads to increased creep, but hardness is still highly overestimated. It was possible to obtain a reasonable fit with experimental indentation curves for both Berkovich and spherical indenta-tion when abandoning the assumption of shear strength being governed by an isotropy condition. These results remain to be verified by independent tests probing the micromechanical strength prop-erties in tension and shear. In conclusion, in this thesis several tools were developed to describe the complex behavior of bone on the microscale and experiments were performed to identify its material properties. Micropillar com-pression highlighted a size effect in bone due to the presence of preexisting cracks and pores or inter-faces like cement lines. It was possible to get a reasonable fit between experimental indentation curves using different tips and simulations using the constitutive model and uniaxial properties measured by micropillar compression. Additional experimental work is necessary to identify the exact nature of the size effect and the mechanical role of interfaces in bone. Deciphering the micromechanical behavior of lamellar bone and its evolution with age, disease and treatment and its failure mechanisms on several length scales will help preventing fractures in the elderly in the future.

Combining Monte Carlo methods with coherent wave optics for the simulation of phase-sensitive X-ray imaging

Phase-sensitive X-ray imaging shows a high sensitivity towards electron density variations, making it well suited for imaging of soft tissue matter. However, there are still open questions about the details of the image formation process. Here, a framework for numerical simulations of phase-sensitive X-ray imaging is presented, which takes both particle- and wave-like properties of X-rays into consideration. A split approach is presented where we combine a Monte Carlo method (MC) based sample part with a wave optics simulation based propagation part, leading to a framework that takes both particle- and wave-like properties into account. The framework can be adapted to different phase-sensitive imaging methods and has been validated through comparisons with experiments for grating interferometry and propagation-based imaging. The validation of the framework shows that the combination of wave optics and MC has been successfully implemented and yields good agreement between measurements and simulations. This demonstrates that the physical processes relevant for developing a deeper understanding of scattering in the context of phase-sensitive imaging are modelled in a sufficiently accurate manner. The framework can be used for the simulation of phase-sensitive X-ray imaging, for instance for the simulation of grating interferometry or propagation-based imaging.

The Utilization of Classical Spin Monte Carlo Methods to Simulate the Magnetic Behavior of Extended Three-Dimensional Cubic Networks Incorporating M(II) Ions with an S = 5/2 Ground State Spin

The numerical simulations of the magnetic properties of extended three-dimensional networks containing M(II) ions with an S = 5/2 ground-state spin have been carried out within the framework of the isotropic Heisenberg model. Analytical expressions fitting the numerical simulations for the primitive cubic, diamond, together with (10−3) cubic networks have all been derived. With these empirical formulas in hands, we can now extract the interaction between the magnetic ions from the experimental data for these networks. In the case of the primitive cubic network, these expressions are directly compared with those from the high-temperature expansions of the partition function. A fit of the experimental data for three complexes, namely [(N(CH3)4][Mn(N3)] 1, [Mn(CN4)]n 2, and [FeII(bipy)3][MnII2(ox)3] 3, has been carried out. The best fits were those obtained using the following parameters, J = −3.5 cm-1, g = 2.01 (1); J = −8.3 cm-1, g = 1.95 (2); and J = −2.0 cm-1, g = 1.95 (3).

Fully Adaptive Newton--Galerkin Methods for Semilinear Elliptic Partial Differential Equations

In this paper we develop an adaptive procedure for the numerical solution of general, semilinear elliptic problems with possible singular perturbations. Our approach combines both prediction-type adaptive Newton methods and a linear adaptive finite element discretization (based on a robust a posteriori error analysis), thereby leading to a fully adaptive Newton–Galerkin scheme. Numerical experiments underline the robustness and reliability of the proposed approach for various examples

Estimation and calibration of the water isotope differential diffusion length in ice core records

Palaeoclimatic information can be retrieved from the diffusion of the stable water isotope signal during firnification of snow. The diffusion length, a measure for the amount of diffusion a layer has experienced, depends on the firn temperature and the accumulation rate. We show that the estimation of the diffusion length using power spectral densities (PSDs) of the record of a single isotope species can be biased by uncertainties in spectral properties of the isotope signal prior to diffusion. By using a second water isotope and calculating the difference in diffusion lengths between the two isotopes, this problem is circumvented. We study the PSD method applied to two isotopes in detail and additionally present a new forward diffusion method for retrieving the differential diffusion length based on the Pearson correlation between the two isotope signals. The two methods are discussed and extensively tested on synthetic data which are generated in a Monte Carlo manner. We show that calibration of the PSD method with this synthetic data is necessary to be able to objectively determine the differential diffusion length. The correlation-based method proves to be a good alternative for the PSD method as it yields precision equal to or somewhat higher than the PSD method. The use of synthetic data also allows us to estimate the accuracy and precision of the two methods and to choose the best sampling strategy to obtain past temperatures with the required precision. In addition to application to synthetic data the two methods are tested on stable-isotope records from the EPICA (European Project for Ice Coring in Antarctica) ice core drilled in Dronning Maud Land, Antarctica, showing that reliable firn temperatures can be reconstructed with a typical uncertainty of 1.5 and 2 °C for the Holocene period and 2 and 2.5 °C for the last glacial period for the correlation and PSD method, respectively.

Computational Comparison of Continuous and Discontinuous Galerkin Time-Stepping Methods for Nonlinear Initial Value Problems

This article centers on the computational performance of the continuous and discontinuous Galerkin time stepping schemes for general first-order initial value problems in R n , with continuous nonlinearities. We briefly review a recent existence result for discrete solutions from [6], and provide a numerical comparison of the two time discretization methods.

Calibration of cosmogenic noble gas production based on ³⁶Cl-³⁶Ar ages. Part 2. The ⁸¹Kr-Kr dating technique

We calibrated the ⁸¹Kr-Kr dating system for ordinary chondrites of different sizes using independent shielding-corrected ³⁶Cl-³⁶Ar ages. Krypton concentrations and isotopic compositions were measured in bulk samples from 14 ordinary chondrites of high petrologic type and the cosmogenic Kr component was obtained by subtracting trapped Kr from phase Q. The thus-determined average cosmogenic ⁷⁸Kr/⁸³Kr, ⁸⁰Kr/⁸³Kr, ⁸²Kr/⁸³Kr, and ⁸4Kr/⁸³Kr ratiC(Lavielle and Marti 1988; Wieler 2002). The cosmogenic ⁷⁸Kr/⁸³Kr ratio is correlated with the cosmogenic 22Ne/21Ne ratio, confirming that ⁷⁸Kr/⁸³Kr is a reliable shielding indicator. Previously, ⁸¹Kr-Kr ages have been determined by assuming the cosmogenic production rate of ⁸¹Kr, P(⁸¹Kr)c, to be 0.95 times the average of the cosmogenic production rates of ⁸⁰Kr and ⁸²Kr; the factor Y = 0.95 therefore accounts for the unequal production of the various Kr isotopes (Marti 1967a). However, Y should be regarded as an empirical adjustment. For samples whose ⁸⁰Kr and ⁸²Kr concentrations may be affected by neutron-capture reactions, the shielding-dependent cosmogenic (⁷⁸Kr/⁸³Kr)c ratio has been used instead to calculate P(⁸¹Kr)/P(⁸³Kr), as for some lunar samples, this ratio has been shown to linearly increase with (⁷⁸Kr/⁸³Kr)c (Marti and Lugmair 1971). However, the ⁸¹Kr-Kr ages of our samples calculated with these methods are on average ~30% higher than their ³⁶Cl-³⁶Ar ages, indicating that most if not all the ⁸¹Kr-Kr ages determined so far are significantly too high. We therefore re-evaluated both methods to determine P(⁸¹Kr)c/P(⁸³Kr)c. Our new Y value of 0.70 ± 0.04 is more than 25% lower than the value of 0.95 used so far. Furthermore, together with literature data, our data indicate that for chondrites, P(⁸¹Kr)c/P(⁸³Kr)c is rather constant at 0.43 ± 0.02, at least for the shielding range covered by our samples ([⁷⁸Kr/⁸³Kr]c = 0.119–0.185; [22Ne/21Ne]c = 1.083–1.144), in contrast to the observations on lunar samples. As expected considering the method used, ⁸¹Kr-Kr ages calculated either directly with this new P(⁸¹Kr)c/P(⁸³Kr)c value or with our new Y value both agree with the corresponding ³⁶Cl-³⁶Ar ages. However, the average deviation of 2% indicates the accuracy of both new ⁸¹Kr-Kr dating methods and the precision of the new dating systems of ~10% is demonstrated by the low scatter in the data. Consequently, this study indicates that the ⁸¹Kr-Kr ages published so far are up to 30% too high.

Design and Implementation of a Laparoscope Calibration Method for Augmented Reality Navigation

Intraoperative laparoscopic calibration remains a challenging task. In this work we present a new method and instrumentation for intraoperative camera calibration. Contrary to conventional calibration methods, the proposed technique allows intraoperative laparoscope calibration from single perspective observations, resulting in a standardized scheme for calibrating in a clinical scenario. Results show an average displacement error of 0.52 ± 0.19 mm, indicating sufficient accuracy for clinical use. Additionally, the proposed method is validated clinically by performing a calibration during the surgery.

COSIMA calibration for the detection and characterization of the cometary solid organic matter

On the orbiter of the Rosetta spacecraft, the Cometary Secondary Ion Mass Analyser (COSIMA) will provide new in situ insights about the chemical composition of cometary grains all along 67P/Churyumov–Gerasimenko (67P/CG) journey until the end of December 2015 nominally. The aim of this paper is to present the pre-calibration which has already been performed as well as the different methods which have been developed in order to facilitate the interpretation of the COSIMA mass spectra and more especially of their organic content. The first step was to establish a mass spectra library in positive and negative ion mode of targeted molecules and to determine the specific features of each compound and chemical family analyzed. As the exact nature of the refractory cometary organic matter is nowadays unknown, this library is obviously not exhaustive. Therefore this library has also been the starting point for the research of indicators, which enable to highlight the presence of compounds containing specific atom or structure. These indicators correspond to the intensity ratio of specific peaks in the mass spectrum. They have allowed us to identify sample containing nitrogen atom, aliphatic chains or those containing polyaromatic hydrocarbons. From these indicators, a preliminary calibration line, from which the N/C ratio could be derived, has also been established. The research of specific mass difference could also be helpful to identify peaks related to quasi-molecular ions in an unknown mass spectrum. The Bayesian Positive Source Separation (BPSS) technique will also be very helpful for data analysis. This work is the starting point for the analysis of the cometary refractory organic matter. Nevertheless, calibration work will continue in order to reach the best possible interpretation of the COSIMA observations.