Optimal Scaling Approaches for Perfusion MRI with Distorted Arterial Input Function (AIF) in Patients with Ischemic Stroke

Background: Diagnosis and timely treatment of ischemic stroke depends on the fast and accurate quantification of perfusion parameters. Arterial input function (AIF) describes contrast agent concentration over time as it enters the brain through the brain feeding artery. AIF is the central quantity required to estimate perfusion parameters. Inaccurate and distorted AIF, due to partial volume effects (PVE), would lead to inaccurate quantification of perfusion parameters. Methods: Fifteen patients suffering from stroke underwent perfusion MRI imaging at the Tri-Service General Hospital, Taipei. Various degrees of the PVE were induced on the AIF and subsequently corrected using rescaling methods. Results: Rescaled AIFs match the exact reference AIF curve either at peak height or at tail. Inaccurate estimation of CBF values estimated from non-rescaled AIFs increase with increasing PVE. Rescaling of the AIF using all three approaches resulted in reduced deviation of CBF values from the reference CBF values. In most cases, CBF map generated by rescaled AIF approaches show increased CBF and Tmax values on the slices in the left and right hemispheres. Conclusion: Rescaling AIF by VOF approach seems to be a robust and adaptable approach for correction of the PVE-affected multivoxel AIF. Utilizing an AIF scaling approach leads to more reasonable absolute perfusion parameter values, represented by the increased mean CBF/Tmax values and CBF/Tmax images.

Lower-order equivalent nonstandard finite element methods for biharmonic plates

The popular (piecewise) quadratic schemes for the biharmonic equation based on triangles are the nonconforming Morley finite element, the discontinuous Galerkin, the C0 interior penalty, and the WOPSIP schemes. Those methods are modified in their right-hand side and then are quasi-optimal in their respective discrete norms. The smoother JI M is defined for a piecewise smooth input function by a (generalized) Morley interpolation I M followed by a companion operator J. An abstract framework for the error analysis in the energy, weaker and piecewise Sobolev norms for the schemes is outlined and applied to the biharmonic equation. Three errors are also equivalent in some particular discrete norm from [Carstensen, Gallistl, Nataraj: Comparison results of nonstandard P 2 finite element methods for the biharmonic problem, ESAIM Math. Model. Numer. Anal. (2015)] without data oscillations. This paper extends and unifies the work [Veeser, Zanotti: Quasioptimal nonconforming methods for symmetric elliptic problems, SIAM J. Numer. Anal. 56 (2018)] to the discontinuous Galerkin scheme and adds error estimates in weaker and piecewise Sobolev norms.

Method for Tuning the Parameters of Active Force Reducing Building Vibrations—Numerical Tests

The paper formulates a method of active reduction of structure vibrations in the selected resonance zones of the tested object. The method ensures reduction of vibrations of the selected resonance zones by determining the parameters of the active force that meets the desired dynamic properties. The paper presents a method for determining the parameters of the active force by reducing the vibrations of the structure in its resonance zones to a given vibration amplitude. For this purpose, an analytical form was formulated, which will clearly define the dynamic properties of the tested object and the force reducing the vibrations in the form of a mathematical model. The formulated mathematical model is a modified object input function, which in its form takes into account the properties of the active force reducing the vibrations. In such a case, it is possible to use the methods of mechanical synthesis to decompose the modified characteristic function into the parameters of the system and the parameters of the force being sought. In the formulated method, the desired dynamic properties of the system and the vibration reducing force were defined in such a way that the determined parameters of the active force (velocity-dependent function) had an impact on all forms of natural vibrations of the tested system. Based on the formalized method, the force reducing the vibrations of the four-story frame to the desired displacement amplitude was determined. Two cases of determining the active force reducing the vibrations to the desired vibration amplitude of the system by modifying the dynamic characteristics describing the object together with the active force were considered. For both cases, the system’s responses to the oscillation generated by harmonic force of frequencies equal to the first two forms of natural vibrations of the tested system were determined. In order to verify the determined force reducing the vibrations of the object and to create a visualization of the analyzed phenomenon, the building structure dynamics were analyzed with the use of PLM Siemens NX 12 software. The determined force parameters were implemented into the numerical model, in which the tested system was modelled, and the response time waveforms were generated with regard to the considered story. The generated waveforms were compared with the waveforms obtained in the formalized mathematical model for determining the active force reducing the vibrations. The vibrations of the tested numerical model were induced by the kinematic excitation with the maximum amplitude equal to 100 mm, which corresponds to the vibration amplitude during the earthquake with a force equal to level 5 on the Richter scale.

Quantitative Myocardial Perfusion with 2D and 3D Sequences Alternating Every Heartbeat

PurposeTo evaluate a myocardial perfusion acquisition that alternates 2D simultaneous multi-slice (SMS) and 3D stack-of-stars (SoS) acquisitions each heartbeat. MethodsA hybrid saturation recovery radial 2D SMS and a saturation recovery 3D SoS sequence were created for the quantification of myocardial blood flow (MBF). Initial studies were done to study the effects of using only every other beat for the 2D SMS in two subjects, and for the 3D SoS in two subjects. Alternating heartbeat 2D SMS and 3D SoS were then performed in ten dog studies at rest, four dog studies at adenosine stress, and two human resting studies. 2D SMS acquisition acquired three slices and 3D SoS acquired six slices. An arterial input function (AIF) for 2D SMS was obtained using the first 24 rays. For 3D, the AIF was obtained in a 2D slice prior to each 3D SoS readout. Quantitative MBF analysis was performed for 2D SMS and 3D SoS separately, using a two-compartment model. ResultsAcquiring every-other-beat data resulted in 5-20% perfusion changes at rest for both 2D SMS and 3D SoS methods. For alternating acquisitions, 2D SMS and 3D SoS quantitative perfusion values were comparable for both the twelve rest studies (2D SMS: 0.68±0.15 vs 3D: 0.69±0.15 ml/g/min, p=0.85) and the four stress studies (2D SMS: 1.28±0.22 vs 3D: 1.30±0.24 ml/g/min, p=0.66).ConclusionEvery-other-beat acquisition changed estimated perfusion values relatively little for both sequences. 2D SMS and 3D SoS gave similar quantitative perfusion estimates when used in an alternating every-other-heartbeat acquisition. Such an approach allows consideration of more diverse perfusion acquisitions that could have complementary features, although testing in a cardiac disease population is needed.

Short 2-[18F]Fluoro-2-Deoxy-D-Glucose PET Dynamic Acquisition Protocol to Evaluate the Influx Rate Constant by Regional Patlak Graphical Analysis in Patients With Non-Small-Cell Lung Cancer

Purpose: To test a short 2-[18F]Fluoro-2-deoxy-D-glucose (2-[18F]FDG) PET dynamic acquisition protocol to calculate Ki using regional Patlak graphical analysis in patients with non-small-cell lung cancer (NSCLC).Methods: 24 patients with NSCLC who underwent standard dynamic 2-[18F]FDG acquisitions (60 min) were randomly divided into two groups. In group 1 (n = 10), a population-based image-derived input function (pIDIF) was built using a monoexponential trend (10–60 min), and a leave-one-out cross-validation (LOOCV) method was performed to validate the pIDIF model. In group 2 (n = 14), Ki was obtained by standard regional Patlak plot analysis using IDIF (0–60 min) and tissue response (10–60 min) curves from the volume of interests (VOIs) placed on descending thoracic aorta and tumor tissue, respectively. Moreover, with our method, the Patlak analysis was performed to obtain Ki,s using IDIFFitted curve obtained from PET counts (0–10 min) followed by monoexponential coefficients of pIDIF (10–60 min) and tissue response curve obtained from PET counts at 10 min and between 40 and 60 min, simulating two short dynamic acquisitions. Both IDIF and IDIFFitted curves were modeled to assume the value of 2-[18F]FDG plasma activity measured in the venous blood sampling performed at 45 min in each patient. Spearman's rank correlation, coefficient of determination, and Passing–Bablok regression were used for the comparison between Ki and Ki,s. Finally, Ki,s was obtained with our method in a separate group of patients (group 3, n = 8) that perform two short dynamic acquisitions.Results: Population-based image-derived input function (10–60 min) was modeled with a monoexponential curve with the following fitted parameters obtained in group 1: a = 9.684, b = 16.410, and c = 0.068 min−1. The LOOCV error was 0.4%. In patients of group 2, the mean values of Ki and Ki,s were 0.0442 ± 0.0302 and 0.33 ± 0.0298, respectively (R2 = 0.9970). The Passing–Bablok regression for comparison between Ki and Ki,s showed a slope of 0.992 (95% CI: 0.94–1.06) and intercept value of −0.0003 (95% CI: −0.0033–0.0011).Conclusions: Despite several practical limitations, like the need to position the patient twice and to perform two CT scans, our method contemplates two short 2-[18F]FDG dynamic acquisitions, a population-based input function model, and a late venous blood sample to obtain robust and personalized input function and tissue response curves and to provide reliable regional Ki estimation.

Comparison of [18F] NaF PET/CT dynamic analysis methods and a static analysis method including derivation of a semi-population input function for site-specific measurements of bone formation in a population with chronic kidney disease-mineral and bone disorder

Purpose The purpose of this study is to compare dynamic and static whole-body (WB) [18F]NaF PET/CT scan methods used for analysis of bone plasma clearance in patients with chronic kidney disease-mineral and bone disorder (CKD-MBD). Methods Seventeen patients with CKD-MBD underwent a 60-min dynamic scan followed by a 30-min static WB scan. Tracer kinetics in four thoracic vertebrae were analysed using nonlinear regression and Patlak analysis using image-derived arterial input functions. The static WB scan was analysed using a simplified Patlak method requiring only a single data point in combination with a fixed y-intercept value (V0), both obtained using a semi-population function. The semi-population function was constructed by combining a previously derived population input function in combination with data from venous blood samples. Static WB scan analysis data, obtained from the semi-population input functions, was compared with paired data obtained using dynamic input functions. Results Bone plasma clearance (Ki) from Patlak analyses correlated well with nonlinear regression analysis, but Ki results using Patlak analysis were lower than Ki results using nonlinear regression analysis. However, no significant difference was found between Ki obtained by static WB scans and Ki obtained by dynamic scans using nonlinear regression analysis (p = 0.29). Conclusion Bone plasma clearance measured from static WB scans correlates with clearance data measured by dynamic analysis. Static [18F]NaF PET/CT scans can be applied in future studies to measure Ki in patients with CKD-MBD, but the results should not be compared uncritically with results obtained by dynamic scan analysis.

Prediction of Tissue Damage Using a User-Independent Machine Learning Algorithm vs. Tmax Threshold Maps

(1) Background: To test the accuracy of a fully automated stroke tissue estimation algorithm (FASTER) to predict final lesion volumes in an independent dataset in patients with acute stroke; (2) Methods: Tissue-at-risk prediction was performed in 31 stroke patients presenting with a proximal middle cerebral artery occlusion. FDA-cleared perfusion software using the AHA recommendation for the Tmax threshold delay was tested against a prediction algorithm trained on an independent perfusion software using artificial intelligence (FASTER). Following our endovascular strategy to consequently achieve TICI 3 outcome, we compared patients with complete reperfusion (TICI 3) vs. no reperfusion (TICI 0) after mechanical thrombectomy. Final infarct volume was determined on a routine follow-up MRI or CT at 90 days after the stroke; (3) Results: Compared to the reference standard (infarct volume after 90 days), the decision forest algorithm overestimated the final infarct volume in patients without reperfusion. Underestimation was observed if patients were completely reperfused. In cases where the FDA-cleared segmentation was not interpretable due to improper definitions of the arterial input function, the decision forest provided reliable results; (4) Conclusions: The prediction accuracy of automated tissue estimation depends on (i) success of reperfusion, (ii) infarct size, and (iii) software-related factors introduced by the training sample. A principal advantage of machine learning algorithms is their improved robustness to artifacts in comparison to solely threshold-based model-dependent software. Validation on independent datasets remains a crucial condition for clinical implementations of decision support systems in stroke imaging.

A Short Dynamic Scan Method of Measuring Bone Metabolic Flux Using [18F]NaF PET

[18F]NaF PET measurements of bone metabolic flux (Ki) are conventionally obtained with 60-min dynamic scans analysed using the Hawkins model. However, long scan times make this method expensive and uncomfortable for subjects. Therefore, we evaluated and compared measurements of Ki with shorter scan times analysed with fixed values of the Hawkins model rate constants. The scans were acquired in a trial in 30 postmenopausal women, half treated with teriparatide (TPT) and half untreated. Sixty-minute PET-CT scans of both hips were acquired at baseline and week 12 after injection with 180 MBq [18F]NaF. Scans were analysed using the Hawkins model by fitting bone time–activity curves at seven volumes of interest (VOIs) with a semi-population arterial input function. The model was re-run with fixed rate-constants for dynamic scan times from 0–12 min increasing in 4-min steps up to 0–60 min. Using the Hawkins model with fixed rate-constants, Ki measurements with statistical power equivalent or superior to conventionally analysed 60-min dynamic scans were obtained with scan times as short as 12 min.