Lyapunov Exponent and Out-of-Time-Ordered Correlator's Growth Rate in a Chaotic System

It was proposed recently that the out-of-time-ordered four-point correlator (OTOC) may serve as a useful characteristic of quantum-chaotic behavior, because in the semi-classical limit, $\hbar \to 0$, its rate of exponential growth resembles the classical Lyapunov exponent. Here, we calculate the four-point correlator, $C(t)$, for the classical and quantum kicked rotor -- a textbook driven chaotic system -- and compare its growth rate at initial times with the standard definition of the classical Lyapunov exponent. Using both quantum and classical arguments, we show that the OTOC's growth rate and the Lyapunov exponent are in general distinct quantities, corresponding to the logarithm of phase-space averaged divergence rate of classical trajectories and to the phase-space average of the logarithm, respectively. The difference appears to be more pronounced in the regime of low kicking strength $K$, where no classical chaos exists globally. In this case, the Lyapunov exponent quickly decreases as $K \to 0$, while the OTOC's growth rate may decrease much slower showing higher sensitivity to small chaotic islands in the phase space. We also show that the quantum correlator as a function of time exhibits a clear singularity at the Ehrenfest time $t_E$: transitioning from a time-independent value of $t^{-1} \ln{C(t)}$ at $t < t_E$ to its monotonous decrease with time at $t>t_E$. We note that the underlying physics here is the same as in the theory of weak (dynamical) localization [Aleiner and Larkin, Phys. Rev. B 54, 14423 (1996); Tian, Kamenev, and Larkin, Phys. Rev. Lett. 93, 124101 (2004)] and is due to a delay in the onset of quantum interference effects, which occur sharply at a time of the order of the Ehrenfest time.Comment: 5+2 pages, 5+2 figures; accepted for publication in Phys. Rev. Lett., Vol. 118 (2017

CT texture analysis: a potential tool for prediction of survival in patients with metastatic clear cell carcinoma treated with sunitinib

BACKGROUND: To assess CT texture based quantitative imaging biomarkers in the prediction of progression free survival (PFS) and overall survival (OS) in patients with clear cell renal cell carcinoma undergoing treatment with Sunitinib. METHODS: In this retrospective study, measurable lesions of 40 patients were selected based on RECIST criteria on standard contrast enhanced CT before and 2 months after treatment with Sunitinib. CT Texture analysis was performed using TexRAD research software (TexRAD Ltd, Cambridge, UK). Using a Cox regression model, correlation of texture parameters with measured time to progression and overall survival were assessed. Evaluation of combined International Metastatic Renal-Cell Carcinoma Database Consortium Model (IMDC) score with texture parameters was also performed. RESULTS: Size normalized standard deviation (nSD) alone at baseline and follow-up after treatment was a predictor of OS (Hazard ratio (HR) = 0.01 and 0.02; 95% confidence intervals (CI): 0.00 – 0.29 and 0.00 – 0.39; p = 0.01 and 0.01). Entropy following treatment and entropy change before and after treatment were both significant predictors of OS (HR = 2.68 and 87.77; 95% CI = 1.14 – 6.29 and 1.26 – 6115.69; p = 0.02 and p = 0.04). nSD was also a predictor of PFS at baseline and follow-up (HR = 0.01 and 0.01: 95% CI: 0.00 – 0.31 and 0.001 – 0.22; p = 0.01 and p = 0.003). When nSD at baseline or at follow-up was combined with IMDC, it improved the association with OS and PFS compared to IMDC alone. CONCLUSION: Size normalized standard deviation from CT at baseline and follow-up scans is correlated with OS and PFS in clear cell renal cell carcinoma treated with Sunitinib

CT texture analysis can help differentiate between malignant and benign lymph nodes in the mediastinum in patients suspected for lung cancer

BACKGROUND: In patients with non-small-cell lung carcinoma NSCLC the lymph node staging in the mediastinum is important due to impact on management and prognosis. Computed tomography texture analysis (CTTA) is a postprocessing technique that can evaluate the heterogeneity of marked regions in images. PURPOSE: To evaluate if CTTA can differentiate between malignant and benign lymph nodes in a cohort of patients with suspected lung cancer. MATERIAL AND METHODS: With tissue sampling as reference standard, 46 lymph nodes from 29 patients were analyzed using CTTA. For each lymph node, CTTA was performed using a research software "TexRAD" by drawing a region of interest (ROI) on all available axial contrast-enhanced computed tomography (CT) slices covering the entire volume of the lymph node. Lymph node CTTA comprised image filtration-histogram analysis undertakes two stages: the first step comprised an application of a Laplacian of Gaussian filter to highlight fine to coarse textures within the ROI, followed by a quantification of textures via histogram analysis using mean gray-level intensity from the entire volume of the lymph nodes. RESULTS: CTTA demonstrated a statistically significant difference between the malignant and the benign lymph nodes (P = 0.001), and by binary logistic regression we obtained a sensitivity of 53% and specificity of 97% in the test population. The area under the receiver operating curve was 83.4% and reproducibility was excellent. CONCLUSION: CTTA may be helpful in differentiating between malignant and benign lymph nodes in the mediastinum in patients suspected for lung cancer, with a low intra-observer variance

CT-based texture analysis potentially provides prognostic information complementary to interim fdg-pet for patients with hodgkin's and aggressive non-hodgkin's lymphomas

OBJECTIVES: The purpose of this study was to investigate the ability of computed tomography texture analysis (CTTA) to provide additional prognostic information in patients with Hodgkin's lymphoma (HL) and high-grade non-Hodgkin's lymphoma (NHL). METHODS: This retrospective, pilot-study approved by the IRB comprised 45 lymphoma patients undergoing routine 18F-FDG-PET-CT. Progression-free survival (PFS) was determined from clinical follow-up (mean-duration: 40 months; range: 10-62 months). Non-contrast-enhanced low-dose CT images were submitted to CTTA comprising image filtration to highlight features of different sizes followed by histogram-analysis using kurtosis. Prognostic value of CTTA was compared to PET FDG-uptake value, tumour-stage, tumour-bulk, lymphoma-type, treatment-regime, and interim FDG-PET (iPET) status using Kaplan-Meier analysis. Cox regression analysis determined the independence of significantly prognostic imaging and clinical features. RESULTS: A total of 27 patients had aggressive NHL and 18 had HL. Mean PFS was 48.5 months. There was no significant difference in pre-treatment CTTA between the lymphoma sub-types. Kaplan-Meier analysis found pre-treatment CTTA (medium feature scale, p=0.010) and iPET status (p<0.001) to be significant predictors of PFS. Cox analysis revealed that an interaction between pre-treatment CTTA and iPET status was the only independent predictor of PFS (HR: 25.5, 95% CI: 5.4-120, p<0.001). Specifically, pre-treatment CTTA risk stratified patients with negative iPET. CONCLUSION: CTTA can potentially provide prognostic information complementary to iPET for patients with HL and aggressive NHL

MRI texture analysis parameters of contrast-enhanced T1-weighted images of Crohn's disease differ according to the presence or absence of histological markers of hypoxia and angiogenesis

PURPOSE: To investigate if texture analysis parameters of contrast-enhanced MRI differ according to the presence of histological markers of hypoxia and angiogenesis in Crohn's disease (CD). METHODS: Seven CD patients (mean age 38 (19-75), 3 male)) undergoing ileal resection underwent 3T MR enterography including axial ultrafast spoiled gradient-echo T1 post IV gadolinium chelate. Regions of interest were placed in bowel destined for resection and registered to trans-mural histological sections (n = 28 across 7 bowel sections) via MRI of the resected specimen. Microvessel density (MVD) and staining for markers of hypoxia (HIF 1α) and angiogenesis (VEGF) were performed. Texture analysis features were derived utilizing an image filtration-histogram technique at spatial scaling factor (SSF) 0-6 mm, including mean, standard deviation, mean of positive pixels, entropy, kurtosis and skewness and compared according to the presence or absence of histological markers of hypoxia/angiogenesis using Mann-Whitney U/Kruskal-Wallis tests and with the log of MVD using simple linear regression. RESULTS: Mean, standard deviation and mean of positive pixels were significantly lower in sections expressing VEGF. For example at SSF 6 mm, median (inter-quartile range) of mean, standard deviation and mean of positive pixels in those with VEGF expression were 150.1 (134.7), 132.4 (49.2) and 184.0 (91.4) vs. 362.5 (150.2), 216.3 (100.1) and 416.6 (80.0) in those without (p = 0.001, p = 0.004 and p = 0.001), respectively. There was a significant association between skewness and MVD (ratio 1.97 (1.15-3.41)) at SSF = 2 mm. CONCLUSIONS: Contrast-enhanced MRI texture analysis features significantly differ according to the presence or absence of histological markers of hypoxia and angiogenesis in CD

Validation as New Imaging Biomarker

Background In order to select patients most likely to benefit for thrombolysis and to predict patient outcome in acute ischemic stroke, the volumetric assessment of the infarcted tissue is used. However, infarct volume estimation on Diffusion weighted imaging (DWI) has moderate interrater variability despite the excellent contrast between ischemic lesion and healthy tissue. In this study, we compared volumetric measurements of DWI hyperintensity to a simple maximum orthogonal diameter approach to identify thresholds indicating infarct size >70 ml and >100 ml. Methods Patients presenting with ischemic stroke with an NIHSS of ≥ 8 were examined with stroke MRI within 24 h after symptom onset. For assessment of the orthogonal DWI lesion diameters (od- values) the image with the largest lesion appearance was chosen. The maximal diameter of the lesion was determined and a second diameter was measured perpendicular. Both diameters were multiplied. Od-values were compared to volumetric measurement and od-value thresholds identifying a lesion size of > 70 ml and > 100 ml were determined. In a selected dataset with an even distribution of lesion sizes we compared the results of the od value thresholds with results of the ABC/2 and estimations of lesion volumes made by two resident physicians. Results For 108 included patients (53 female, mean age 71.36 years) with a median infarct volume of 13.4 ml we found an excellent correlation between volumetric measures and od-values (r2 = 0.951). Infarct volume >100 ml corresponds to an od-value cut off of 42; > 70 ml corresponds to an od-value of 32. In the compiled dataset (n = 50) od-value thresholds identified infarcts > 100 ml / > 70 ml with a sensitivity of 90%/ 93% and with a specificity of 98%/ 89%. The od-value offered a higher accuracy in identifying large infarctions compared to both visual estimations and the ABC/2 method. Conclusion The simple od-value enables identification of large DWI lesions in acute stroke. The cutoff of 42 is useful to identify large infarctions with volume larger than 100 ml. Further studies can analyze the therapeutic utility of this new method

"Textural analysis of multiparametric MRI detects transition zone prostate cancer"

OBJECTIVES: To evaluate multiparametric-MRI (mpMRI) derived histogram textural-analysis parameters for detection of transition zone (TZ) prostatic tumour. METHODS: Sixty-seven consecutive men with suspected prostate cancer underwent 1.5T mpMRI prior to template-mapping-biopsy (TPM). Twenty-six men had 'significant' TZ tumour. Two radiologists in consensus matched TPM to the single axial slice best depicting tumour, or largest TZ diameter for those with benign histology, to define single-slice whole TZ-regions-of-interest (ROIs). Textural-parameter differences between single-slice whole TZ-ROI containing significant tumour versus benign/insignificant tumour were analysed using Mann Whitney U test. Diagnostic accuracy was assessed by receiver operating characteristic area under curve (ROC-AUC) analysis cross-validated with leave-one-out (LOO) analysis. RESULTS: ADC kurtosis was significantly lower (p < 0.001) in TZ containing significant tumour with ROC-AUC 0.80 (LOO-AUC 0.78); the difference became non-significant following exclusion of significant tumour from single-slice whole TZ-ROI (p = 0.23). T1-entropy was significantly lower (p = 0.004) in TZ containing significant tumour with ROC-AUC 0.70 (LOO-AUC 0.66) and was unaffected by excluding significant tumour from TZ-ROI (p = 0.004). Combining these parameters yielded ROC-AUC 0.86 (LOO-AUC 0.83). CONCLUSION: Textural features of the whole prostate TZ can discriminate significant prostatic cancer through reduced kurtosis of the ADC-histogram where significant tumour is included in TZ-ROI and reduced T1 entropy independent of tumour inclusion. KEY POINTS: MR textural features of prostate transition zone may discriminate significant prostatic cancer; Transition zone (TZ) containing significant tumour demonstrates a less peaked ADC histogram; TZ containing significant tumour reveals higher post-contrast T1-weighted homogeneity; The utility of MR texture analysis in prostate cancer merits further investigation

Chemotherapy-Response Monitoring of Breast Cancer Patients Using Quantitative Ultrasound-Based Intra-Tumour Heterogeneities

© 2017 The Author(s). Anti-cancer therapies including chemotherapy aim to induce tumour cell death. Cell death introduces alterations in cell morphology and tissue micro-structures that cause measurable changes in tissue echogenicity. This study investigated the effectiveness of quantitative ultrasound (QUS) parametric imaging to characterize intra-tumour heterogeneity and monitor the pathological response of breast cancer to chemotherapy in a large cohort of patients (n = 100). Results demonstrated that QUS imaging can non-invasively monitor pathological response and outcome of breast cancer patients to chemotherapy early following treatment initiation. Specifically, QUS biomarkers quantifying spatial heterogeneities in size, concentration and spacing of acoustic scatterers could predict treatment responses of patients with cross-validated accuracies of 82 ± 0.7%, 86 ± 0.7% and 85 ± 0.9% and areas under the receiver operating characteristic (ROC) curve of 0.75 ± 0.1, 0.80 ± 0.1 and 0.89 ± 0.1 at 1, 4 and 8 weeks after the start of treatment, respectively. The patients classified as responders and non-responders using QUS biomarkers demonstrated significantly different survivals, in good agreement with clinical and pathological endpoints. The results form a basis for using early predictive information on survival-linked patient response to facilitate adapting standard anti-cancer treatments on an individual patient basis

Co-Evolution of quasispecies: B-cell mutation rates maximize viral error catastrophes

Co-evolution of two coupled quasispecies is studied, motivated by the competition between viral evolution and adapting immune response. In this co-adaptive model, besides the classical error catastrophe for high virus mutation rates, a second ``adaptation-'' catastrophe occurs, when virus mutation rates are too small to escape immune attack. Maximizing both regimes of viral error catastrophes is a possible strategy for an optimal immune response, reducing the range of allowed viral mutation rates to a minimum. From this requirement one obtains constraints on B-cell mutation rates and receptor lengths, yielding an estimate of somatic hypermutation rates in the germinal center in accordance with observation.Comment: 4 pages RevTeX including 2 figure