Objective.This study aims to address the issue of long scan durations required by traditional graphical analysis methods, such as the Logan plot and its variant, the reversible equilibrium (RE) Logan plot, for dynamic PET imaging of tracer kinetics.Approach.We propose a relative RE Logan model that builds on the principles of the Logan plot and its variant to significantly reduce scan time without compromising the accuracy of tracer kinetics analysis. The model is supported by theoretical evidence and experimental validations, including two computer simulations and one clinical data analysis.Main results.The proposed model demonstrates a significant linear relationship between the variablexand the slopeDVTof the RE Logan plot, and the variablex\' and the slopeDVT\'of the relative RE Logan plot. The Pearson correlation coefficients (r) of the linear fitting of thex\' to thexequal 0.9849 in the simulated data and 0.9912 in the clinical data. Similarly, thervalues for the linear fitting ofDVT\'toDVTequal 0.9989 and 0.9988 in the simulated data, and 0.9954 in the clinical data.Significance.These results demonstrate the model\'s capability to maintain strong linear relationships and produce parametric images comparable to the traditional RE Logan plot, but with the considerable advantage of shorter scan durations. This innovation holds significant potential for enhancing the efficiency and feasibility of PET imaging in clinical settings.

BACKGROUND: Disease trajectories have become increasingly relevant within the context of an aging population and the rising prevalence of chronic illnesses. Understanding the temporal progression of diseases is crucial for enhancing patient care, preventive measures, and effective management.
OBJECTIVE: The objective of this study is to propose and validate a novel methodology for trajectory impact analysis and interactive visualization of disease trajectories over a cohort of 71,849 patients.
METHODS: This article introduces an innovative comprehensive approach for analysis and interactive visualization of disease trajectories. First, Risk Increase (RI) index is defined that assesses the impact of the initial disease diagnosis on the development of subsequent illnesses. Secondly, visual graphics methods are used to represent cohort trajectories, ensuring a clear and semantically rich presentation that facilitates easy data interpretation.
RESULTS: The proposed approach is demonstrated over the disease trajectories of a cohort comprising 71,849 patients from Tolosaldea, Spain. The study finds several clinically relevant trajectories in this cohort, such as that after suffering a cerebral ischemic stroke, the probability of suffering dementia increases 10.77 times. The clinical relevance of the study outcomes have been assessed by an in-depth analysis conducted by expert clinicians. The identified disease trajectories are in agreement with the latest advancements in the field.
CONCLUSIONS: The proposed approach for trajectory impact analysis and interactive visualization offers valuable graphs for the comprehensive study of disease trajectories for improved clinical decision-making. The simplicity and interpretability of our methods make them valuable approach for healthcare professionals.

The influence of three main parameters including irradiation time, weight fraction of photocatalysts including multi-walled carbon nanotubes and different amount of TiO2 (MCT#1 and MCT#2) and pH is investigated for the degradation rate of methyl orange (MO). Analysis of variance (ANOVA) and response surface methodology (RSM) have been applied to study the binary and ternary interactions of the main parameters on the degradation rate. The ANOVA results confirm that all of three studied factors have a considerable efficacy on degradation rate of MO at 5% level of probability. Meanwhile, the results show that the degradation rate is enhanced with increasing the weight fraction in range of 0.1 to 0.3%wt and irradiation time in a period of 5 to 35min.The lowest and highest degradation are observed at pH=7 and pH=3, respectively. The normality of residue distribution can be confirmed using graphical analysis. The RSM results reveal that the degradation rate dependency on irradiation time is higher than the weight fraction of photocatalysts.

Investigating the interaction of genotype and environment in multi-environment experiments (MET) is one of the reliable techniques to demonstrate the most stable and compatible cultivars. The main contribution of this study is to evaluate the stability and compatibility of rapeseed cultivars using additive main effects and multiplicative interaction (AMMI) and genotype plus genotype environment interaction (GGE) bi-plot methods for grain yield and oil content. For this purpose, an experiment in a randomized complete block design (RCBD) with three replications was conducted for 10 rapeseed cultivars across 10 environments (five regions in 2 years). Hence, the proposed technique can be used to identify the superior cultivars corresponding to the multivariant properties including yield and oil content. To do so, a case-study analysis was conducted over rapeseed, while more than 96% of the data variance for grain yield and more than 94% of the data variance for oil content were explained based on the AMMI model. According to the AMMI model, it was observed that the \"Zarfam\" and \"Licord\" genotypes were introduced as favorable genotypes for grain yield and oil content, respectively. \"Karaj1\" and \"Sanandaj1\" were selected as the superior environments for yield trait, \"Kashmar2\" for oil content, and \"Licord\" and \"Kashmar2\" were identified as the superior genotypes and environment for oil content, respectively. Graphical GGE bi-plot illustrated that \"Hyola401,\" \"Okapi,\" and \"Sarigol\" for grain yield and \"Option500\" and \"Sunday\" for oil content were identified as stable and high-yield genotypes. \"Sanandaj1\" for grain yield and \"Karaj2\" for oil content were identified as environments with high differentiation and screening power.

Animal models of Parkinson\'s disease are useful to evaluate new treatments and to elucidate the etiology of the disease. Hence, it is necessary to have methods that allow quantification of their effectiveness. [18 F]FDOPA-PET (FDOPA-PET) imaging is outstanding for this purpose because of its capacity to measure changes in the dopaminergic pathway noninvasively and in vivo. Nevertheless, PET acquisition and quantification is time-consuming making it necessary to find faster ways to quantify FDOPA-PET data. This study evaluated Male Wistar rats by FDOPA, before and after being partially injured with 6-OHDA unilaterally. MicroPET scans with a duration of 120 min were acquired and Patlak reference plots were created to estimate the influx constant Kc in the striatum using the full dynamic scan data. Additionally, simple striatal-to-cerebral ratios (SCR) of short static acquisitions were computed and compared with the Kc values. Good correlation (r > 0.70) was obtained between Kc and SCR, acquired between 80-120 min after FDOPA administration with frames of 10 or 20 min and both methods were able to separate the FDOPA-uptake of healthy controls from that of the PD model (SCR -28%, Kc -71%). The present study concludes that Kc and SCR can be trustfully used to discriminate partially lesioned rats from healthy controls.

Clinical imaging equipment technological advancements offer insight into the evolution of mathematical techniques used to estimate parameters necessary to characterize the microvasculature and, thus, differentiate normal tissues from abnormal ones. These parameters are blood flow (F), capillary endothelial permeability surface area product (PS), vascular fraction (ve), and extravascular extracellular space size (EES,ve). There are a number of well-established approaches that exist in the literature; however, their analysis is restricted by complexity and is heavily influenced by noise. On the other hand, these characteristics can also be calculated using simpler and straightforward approaches such as Up-Slope Method (USM) and Graphical Analysis (GA). The review looks into the theoretical background and clinical uses of these methodologies, as well as the applicability of these techniques in various sections of the human body.

Numerous methods have been proposed as measures of quality of glycemic control resulting in confusion regarding the best choice of metric to use by clinicians and researchers. Some methods use a single metric such as HbA1c, Mean Glucose, %Time In Range (%TIR), or Coefficient of Variation (%CV). Others use a combination of up to seven metrics, for example, Q-Score, Comprehensive Glucose Pentagon (CGP), and Personal Glycemic State (PGS). A recently proposed Composite continuous Glucose monitoring index utilizes three metrics: %TIR, Time Below Range (%TBR), and standard deviation (SD) of glucose. This review proposes that only two metrics can be sufficient when monitoring an individual patient or when comparing two or more forms of management interventions. These two metrics comprise (1) a measure of efficacy such as Mean Glucose, HbA1c, %TIR, or %Time Above Range (%TAR) and (2) a measure of safety based on risk of hypoglycemia such as %TBR, Low Blood Glucose Index (LBGI), or frequency of specified types of hypoglycemic events per patient year. By analysis of the two-dimensional graphical and statistical relationships between metrics for safety and efficacy and by testing identity versus nonidentity of these relationships, one can improve sensitivity for detection of the effects of medications and of other therapeutic interventions, avoid the need for arbitrary scoring systems for glucose values falling within versus outside the target range, and offer the advantage of conceptual and practical simplicity.

OBJECTIVE: Myocardial blood flow (MBF) is measured with 82Rb using non-linear, least-squares computerised modelling. The study aim was to explore the feasibility of Gjedde-Patlak-Rutland (GPR) graphical analysis as a simpler method for measuring MBF.
METHODS: Patients had myocardial perfusion imaging using adenosine (n = 45) or regadenoson (n = 33) for stressing. Blood 82Rb clearance into myocytes (K1) was measured from Cedar-Sinai QPET software using the modified Crone-Renkin equation of Lortie et al. (K1 = [1-0.77 × e-B/MBF] × MBF) to convert K1 to MBF (ml/min/100 ml), where B (63 ml/min/100 ml) is myocardial permeability-surface area product. Using aorta or left ventricular cavity (LV) to measure arterial blood 82Rb concentration, blood 82Rb clearance into myocardium (Z) was measured from GPR analysis based on data acquired between 1 and 3 min post-injection. As units of K1 and Z are, respectively, ml/min/ml intracellular space and ml/min/ml total tissue including extracellular space, myocardial extracellular fluid volume (ECV) is 1 - [Z/K1]. Using Z/K1 (see Results) to modify its index, the Lortie equation was changed to Z = (1-0.77 × [Formula: see text]e-BZ/MBFZ)*MBFZ, following which MBFZ was calculated from Z. In GPR analysis, spillover of activity from LV to myocardium conveniently \'drops out\' in the intercept of the plot.
RESULTS: Both agents increased myocardial blood flow almost equally. ECV was ~ 35 ml/100 ml at rest, increasing to ~ 40 ml/100 ml after stress. Z/K1, averaged between stress, rest, stressing agents and arterial ROI, was 0.62, so BZ was taken as 39 (i.e. 0.62 × 63) ml/min/100 ml. Based on LV, MBFZ (y) correlated with MBF (x): y = 0.43x + 22 ml/min/100 ml; r = 0.84; n = 156). Their respective stress/rest ratios showed a moderate correlation (r = 0.64; n = 78).
CONCLUSIONS: GPR analysis offers promise as a valid and analytically simpler technique for measuring myocardial blood flow, which, as with any clearance measured from GPR analysis, has units of ml/min/ml total tissue volume, and merits development as a polar map display.

Although Guyton\'s graphical analysis of cardiac output-venous return has become a ubiquitous tool for explaining how circulatory equilibrium emerges from heart-vascular interactions, this classical model relies on a formula for venous return that contains unphysiological assumptions. Furthermore, Guyton\'s graphical analysis does not predict pulmonary venous pressure, which is a critical variable for evaluating heart failure patients\' risk of pulmonary edema. Therefore, the purpose of the present work was to use a minimal closed-loop mathematical model to develop an alternative to Guyton\'s analysis. Limitations inherent in Guyton\'s model were addressed by 1) partitioning the cardiovascular system differently to isolate left ventricular function and lump all blood volumes together, 2) linearizing end-diastolic pressure-volume relationships to obtain algebraic solutions, and 3) treating arterial pressures as constants. This approach yielded three advances. First, variables related to morbidities associated with left ventricular failure were predicted. Second, an algebraic formula predicting left ventricular function was derived in terms of ventricular properties. Third, an algebraic formula predicting flow through the portion of the system isolated from the left ventricle was derived in terms of mechanical properties without neglecting redistribution of blood between systemic and pulmonary circulations. Although complexities were neglected, approximations necessary to obtain algebraic formulas resulted in minimal error, and predicted variables were consistent with reported values.

The most crowded individuals in a population often compete for space and develop a regular pattern of spacing. Such regularity is not normally recognized because it occurs within high-density regions of a populated area showing overall aggregation. Thus competition for space, as reflected by spatial pattern, often goes undetected when standard tests for spatial randomness are used. The test described in this paper makes use of truncated samples of nearest-neighbour distances arranged in ascending order, so that only the pattern of spacing of the most crowded individuals is analysed. This is the basis of Pielou\'s test (1962, 1977) for spatial competition. An advantage of the approach described is that the density of the most crowded individuals is determined graphically. The graphical method also provides a means for choosing an appropriate, non-arbitrary, truncation point for the test. The test was applied to two samples of singing crickets to demonstrate the procedure. The biological significance of the spacing patterns identified is discussed.