An algebraic formula, deep learning and a novel SEIR-type model for the COVID-19 pandemic

The most extensively used mathematical models in epidemiology are the susceptible-exposed-infectious-recovered (SEIR) type models with constant coefficients. For the first wave of the COVID-19 epidemic, such models predict that at large times equilibrium is reached exponentially. However, epidemiological data from Europe suggest that this approach is algebraic. Indeed, accurate long-term predictions have been obtained via a forecasting model only if it uses an algebraic as opposed to the standard exponential formula. In this work, by allowing those parameters of the SEIR model that reflect behavioural aspects (e.g. spatial distancing) to vary nonlinearly with the extent of the epidemic, we construct a model which exhibits asymptoticly algebraic behaviour. Interestingly, the emerging power law is consistent with the typical dynamics observed in various social settings. In addition, using reliable epidemiological data, we solve in a numerically robust way the inverse problem of determining all model parameters characterizing our novel model. Finally, using deep learning, we demonstrate that the algebraic forecasting model used earlier is optimal.

An end-to-end assessment on the accuracy of adaptive radiotherapy in an MR-linac

PURPOSE

To develop and demonstrate an end-to-end assessment procedure for adaptive radiotherapy (ART) within an MR-guided system.

METHODS AND MATERIALS

A 3D printed pelvic phantom was designed and constructed for use in this study. The phantom was put through the complete radiotherapy treatment chain, with planned internal changes made to model prostate translations and shape changes, allowing an investigation into three ART techniques commonly used. Absolute dosimetry measurements were made within the phantom using both gafchromic film and alanine. Comparisons between treatment planning system (TPS) calculations and measured dose values were made using the gamma evaluation with criteria of 3 mm/3% and 2 mm/2%.

RESULTS

Gamma analysis evaluations for each type of treatment plan adaptation investigated showed a very high agreement with pass rates for each experiment ranging from 98.10% to 99.70% and 92.60% to 97.55%, for criteria of 3%/3 mm and 2%/2 mm respectively. These pass rates were consistent for both shape and position changes. Alanine measurements further supported the results, showing an average difference of 1.98% from the TPS.

CONCLUSION

The end-to-end assessment procedure provided demanding challenges for treatment plan adaptations to demonstrate the capabilities and achieved high consistency in all findings.

Mathematical models and deep learning for predicting the number of individuals reported to be infected with SARS-CoV-2

We introduce a novel methodology for predicting the time evolution of the number of individuals in a given country reported to be infected with SARS-CoV-2. This methodology, which is based on the synergy of explicit mathematical formulae and deep learning networks, yields algorithms whose input is only the existing data in the given country of the accumulative number of individuals who are reported to be infected. The analytical formulae involve several constant parameters that were determined from the available data using an error-minimizing algorithm. The same data were also used for the training of a bidirectional long short-term memory network. We applied the above methodology to the epidemics in Italy, Spain, France, Germany, USA and Sweden. The significance of these results for evaluating the impact of easing the lockdown measures is discussed.

Evolution of multi-parametric MRI quantitative parameters following transrectal ultrasound-guided biopsy of the prostate

BACKGROUND

To determine the evolution of prostatic multi-parametric magnetic resonance imaging (mp-MRI) signal following transrectal ultrasound (TRUS)-guided biopsy.

METHODS

Local ethical permission and informed written consent was obtained from all the participants (n=14, aged 43-69, mean 64 years). Patients with a clinical suspicion of prostate cancer (PSA range 2.2-11.7, mean 6.2) and a negative (PIRAD 1-2/5) pre-biopsy mp-MRI (pre-contrast T1, T2, diffusion-weighted and dynamic-contrast-enhanced MRI) who underwent 10-core TRUS-guided biopsy were recruited for additional mp-MRI examinations performed at 1, 2 and 6 months post biopsy. We quantified mp-MRI peripheral zone (PZ) and transition zone (TZ) normalized T2 signal intensity (nT2-SI); T1 relaxation time (T10); diffusion-weighted MRI, apparent diffusion coefficient (ADC); dynamic contrast-enhanced MRI, maximum enhancement (ME); slope of enhancement (SoE) and area-under-the-contrast-enhancement-curve at 120 s (AUC120). Significant changes in mp-MRI parameters were identified by analysis of variance with Dunnett's post testing.

RESULTS

Diffuse signal changes were observed post-biopsy throughout the PZ. No significant signal change occurred following biopsy within the TZ. Left and right PZ mean nT2-SI (left PZ: 5.73, 5.16, 4.90 and 5.12; right PZ: 5.80, 5.10, 4.84 and 5.05 at pre-biopsy, 1, 2 and 6 months post biopsy, respectively) and mean T10 (left PZ: 1.02, 0.67, 0.78, 0.85; right PZ: 1.29, 0.64, 0.78, 0.87 at pre-biopsy, 1, 2 and 6 months post biopsy, respectively) were reduced significantly (P<0.05) from pre-biopsy values for up to 6 months post biopsy. Significant changes (P<0.05) of PZ-ME and AUC120 were observed at 1 month but resolved by 2 months post biopsy. PZ ADC did not change significantly following biopsy (P=0.23-1.0). There was no significant change of any TZ mp-MRI parameter at any time point following biopsy (P=0.1-1.0).

CONCLUSIONS

Significant PZ (but not TZ) T2 signal changes persist up to 6 months post biopsy, whereas PZ and TZ ADC is not significantly altered as early as 1 month post biopsy. Caution must be exercised when interpreting T1- and T2-weighted imaging early post biopsy, whereas ADC images are more likely to maintain clinical efficacy.

Multiparametric MRI for detection of radiorecurrent prostate cancer: added value of apparent diffusion coefficient maps and dynamic contrast-enhanced images

BACKGROUND

Multiparametric magnetic resonance imaging (mp-MRI) is increasingly advocated for prostate cancer detection. There are limited reports of its use in the setting of radiorecurrent disease. Our aim was to assess mp-MRI for detection of radiorecurrent prostate cancer and examine the added value of its functional sequences.

METHODS

Thirty-seven men with mean age of 69.7 (interquartile range, 66-74) with biochemical failure after external beam radiotherapy underwent mp-MRI (T2-weighted, high b-value, multi-b-value apparent diffusion coefficient (ADC) and dynamic contrast-enhanced (DCE) imaging); then transperineal systematic template prostate mapping (TPM) biopsy. Using a locked sequential read paradigm (with the sequence order above), two experienced radiologists independently reported mp-MRI studies using score 1-5. Radiologist scores were matched with TPM histopathology at the hemigland level (n=74). Accuracy statistics were derived for each reader. Interobserver agreement was evaluated using kappa statistics.

RESULTS

Receiver-operator characteristic area under curve (AUC) for readers 1 and 2 increased from 0.67 (95% confidence interval (CI), 0.55-0.80) to 0.80 (95% CI, 0.69-0.91) and from 0.67 (95% CI, 0.55-0.80) to 0.84 (95% CI, 0.76-0.93), respectively, between T2-weighted imaging alone and full mp-MRI reads. Addition of ADC maps and DCE imaging to the examination did not significantly improve AUC for either reader (P=0.08 and 0.47 after adding ADC, P=0.90 and 0.27 after adding DCE imaging) compared with T2+high b-value review. Inter-reader agreement increased from k=0.39 to k=0.65 between T2 and full mp-MRI review.

CONCLUSIONS

mp-MRI can detect radiorecurrent prostate cancer. The optimal examination included T2-weighted imaging and high b-value DWI; adding ADC maps and DCE imaging did not significantly improve the diagnostic accuracy.

Acceleration of motion-compensated PET reconstruction: ordered subsets-gates EM algorithms and a priori reference gate information

Patient motion during positron emission tomography scans leads to significant resolution loss and image degradation. Motion-compensated image reconstruction (MCIR) algorithms have proven to be reliable correction methods given accurate deformation fields. However, although ordered subsets (OS) are widely used to speed up the convergence, OS-MCIR algorithms are still computationally expensive. This study concentrates on acceleration of OS-MCIR algorithms through two methods: combining OS with motion subsets and use of an initial estimate based on reference gate data. These approaches were compared to two existing OS-MCIR algorithms and post-reconstruction registration using data from the NCAT phantom. The methods were evaluated in terms of noise, lesion bias and contrast-to-noise ratio (CNR). The straightforward combination of motion subsets with projection subsets (OSGEM) produced inferior results (lower CNR, p < 0.01) to existing OS-MCIR algorithms. The addition of a spacer step using data from all gates to OSGEM resulted in an algorithm (SS-OSGEM) that generated images that were statistically consistent with those from existing OS-MCIR algorithms (no significant difference in CNR, p > 0.05) at one third of the computational expense. The use of a reference gate initial estimate (MCDOi) resulted in comparable image quality in terms of bias and CNR (p > 0.05) at half the computational burden. This study indicates that MCDOi and SS-OSGEM in particular are attractive accelerated OS-MCIR approaches.