Anmar Abdul-Rahman

The low explanatory power of a mixed effects linear model in evaluating interactions between retinal vascular pulse amplitude, intraocular pressure, and intracranial pressure suggests that these interactions are driven by non-linear dynamics. However, mathematical models inherently balance interpretability with predictive capability, and models explaining substantial variance may compromise interpretive clarity, a well-recognized limitation of artificial intelligence models, known as the black box problem. To explore these interactions, a generalized additive mixed model (GAMM) was applied to retinal venous and arterial pulse amplitude data in relation to intraocular and intracranial pressures. Each GAMM, constrained to prioritize interpretability, utilized 51 basis functions, and successfully achieved convergence. Partial effect plots and three-dimensional interaction visualizations were generated, revealing the geometric nature of these physiological relationships. The arterial and venous GAMMs explained 49.21 and 62.96% of the deviance respectively, describing a complex three-dimensional surface with pronounced curvature at intracranial pressures exceeding 25 cm water. Consistent with findings from a previously reported linear mixed-effects model, elevated intracranial pressure had an antipodal effect on the vascular pulse amplitude manifest as a reduction in venous and augmentation of the arterial pulse amplitudes.

Even with the powerful statistical parameters derived from the Extreme Gradient Boost (XGB) algorithm, it would be advantageous to define the predicted accuracy to the level of a specific case, particularly when the model output is used to guide clinical decision-making. The probability density function (PDF) of the derived intracranial pressure predictions enables the computation of a definite integral around a point estimate, representing the event’s probability within a range of values. Seven hold-out test cases used for the external validation of an XGB model underwent retinal vascular pulse and intracranial pressure measurement using modified photoplethysmography and lumbar puncture, respectively. The definite integral ±1 cm water from the median (DI_ICP) demonstrated a negative and highly significant correlation (-0.5213±0.17, p< 0.004) with the absolute difference between the measured and predicted median intracranial pressure (Diff_ICPmd). The concordance between the arterial and venous probability density functions was estimated using the two-sample Kolmogorov-Smirnov statistic, extending the distribution agreement across all data points. This parameter showed a statistically significant and positive correlation (0.4942±0.18, p< 0.001) with Diff_ICPmd. Two cautionary subset cases (Case 8 and Case 9), where disagreement was observed between measured and predicted intracranial pressure, were compared to the seven hold-out test cases. Arterial predictions from both cautionary subset cases converged on a uniform distribution in contrast to all other cases where distributions converged on either log-normal or closely related skewed distributions (gamma, logistic, beta). The mean±standard error of the arterial DI_ICP from cases 8 and 9 (3.83±0.56%) was lower compared to that of the hold-out test cases (14.14±1.07%) the between group difference was statistically significant (pICP, and the two sample Kolmogorov-Smirnov statistic may provide individualized predictive accuracy parameters.

Objective: Using the novel imaging method of high-speed modified photoplethysmography we measured the retinal venous pulse wave velocity in a single case. Results: A healthy 30-year-old subject underwent high-speed modified photoplethysmography (120 frames per second) with simultaneous ophthalmodynamometry at 26 Meditron units. A video of the optic nerve was analyzed using custom software. A harmonic regression model was fitted to each pixel in the time series and used to quantify the retinal vascular pulse wave parameters. Retinal venous pulsation at the optic disc was observed as a complex dynamic wall motion, whereas contraction commenced at a point in the vein at the center of the optic disc, and progressed centrifugally. The empirically estimated retinal venous pulse wave velocity at this segment was approximately 22.24694 mm/s. This measurement provides an estimate for future studies in the field.

The ideal Intracranial pressure (ICP) estimation method should be accurate, reliable, cost-effective, compact, and associated with minimal morbidity/mortality. To this end several described non-invasive methods in ICP estimation have yielded promising results, however the reliability of these techniques have yet to supersede invasive methods of ICP measurement. Over several publications, we described a novel imaging method of Modified Photoplethysmography in the evaluation of the retinal vascular pulse parameters decomposed in the Fourier domain, which enables computationally efficient information filtering of the retinal vascular pulse wave. We applied this method in a population of 21 subjects undergoing lumbar puncture manometry. A regression model was derived by applying an Extreme Gradient Boost (XGB) machine learning algorithm using retinal vascular pulse harmonic regression waveform amplitude (HRW_a), first and second harmonic cosine and sine coefficients (a_n1,2, b_n1,2) among other features. Gain and SHapley Additive exPlanation (SHAP) values ranked feature importance in the model. Agreement between the predicted ICP mean, median and peak density with measured ICP was assessed using Bland-Altman bias±standard error. Feature gain of intraocular pressure (IOP_i) (arterial = 0.6092, venous = 0.5476), and of the Fourier coefficients, a_n1 (arterial = 0.1000, venous = 0.1024) ranked highest in the XGB model for both vascular systems. The arterial model SHAP values demonstrated the importance of the laterality of the tested eye (1.2477), which was less prominent in the venous model (0.8710). External validation was achieved using seven hold-out test cases, where the median venous predicted ICP showed better agreement with measured ICP. Although the Bland-Altman bias from the venous model (0.034±1.8013 cm water (p<0.99)) was lower compared to that of the arterial model (0.139±1.6545 cm water (p<0.94)), the arterial model provided a potential avenue for internal validation of the prediction. This approach can potentially be integrated into a neurological clinical decision algorithm to evaluate the indication for lumbar puncture.

The Heisenberg-Gabor uncertainty principle defines the limits of information resolution in both time and frequency domains. The limit of resolution discloses unique properties of a time series by frequency decomposition. However, classical methods such as Fourier analysis are limited by spectral leakage, particularly in longitudinal data with shifting periodicity or unequal intervals. Wavelet transformation provides a workable compromise by decomposing the signal in both time and frequency through translation and scaling of a basis function followed by correlation or convolution with the original signal. This study aimed to compare the accuracy of predictive models in mental arithmetic in time and frequency domains. Analysis of the author's response time at mental arithmetic using a soroban was modeled for two periods, an initial period (T_I = 68 days), and a return period (T_R = 170 days) both separated by an interval of 370 days. The median (min,max) response times in seconds (s) was longer for all tasks during the T_I compared to the T_R period (p < 0.001), for addition [CT_Add 62 (45, 127) vs 50 (38, 75) s] and summation [CT_Sum 68 (47, 108) vs 57(43, 109) s]. Response times were longer for errors regardless of the study period or task. There was an increasing phase difference for the addition and summation tasks during the T_I period toward the end of the series 49.65^o compared to the T_R period where the phase difference between the two tasks was only 2.05^o, indicating that both tasks are likely demonstrating similar learning rates during the latter study period. A comparison between time and time/frequency domain forecasts for an additional 100 tasks demonstrated higher accuracy of the maximum overlap discrete wavelet transform (MODWT) model, where the mean absolute percentage error ranged between 5.48 and 8.19% and that for the time domain models [autoregressive integrated moving average (ARIMA), generalized autoregressive conditional heteroscedasticity (GARCH)] was 6.16–10.80%.

Background: Internal limiting membrane (ILM) drape sign is an important OCT characteristic of Macular telangiectasia type 2 (MacTel 2). Described here is a case where masking of the ILM drape sign occurred with bilateral foveal detachments in a patient with MacTel 2. Case presentation: A 64-year old female was diagnosed with MacTel 2, four years prior to the current presentation on the basis of an OCT demonstrating bilateral ILM drape sign. Fluorescein angiography showed bilateral dilated, ectatic capillaries and late phase dye leak. At the current presentation there was bilateral gradual visual impairment over two months due to bilateral foveal detachments. Treatment with intravitreal Bevacizumab resulted in unmasking of the pre-existing ILM drape sign at 12 weeks. Visual acuity was reduced to counting fingers in the left eye with the neovascular membrane as a consequence of sub-retinal fibrosis, while the right eye maintained a vision of 6/12. A difference in the stage of the disease at presentation determined the long-term visual outcome after seven years of observation. Conclusion: Foveal detachment can influence the OCT detectability of pre-existing foveal cystoid lesions. Visual prognosis at the final follow up was consistent with the interocular disparity of the disease stage at presentation.

An ideal performance evaluation metric would be predictive, objective, easy to administer, estimate the variance in performance, and provide a confidence interval for the level of uncertainty. Time series forecasting may provide objective metrics for predictive performance in mental arithmetic. Addition and summation (addition combined with subtraction) using the Japanese Soroban computation system was undertaken over 60 days. The median calculation time in seconds for adding 10 sequential six digit numbers [CT_Add) was 63 s (interquartile range (IQR) = 12, range 48–127 s], while that for summation (CT_Sum) was 70 s (IQR = 14, range 53–108 s), and the difference between these times was statistically significant p < 0.0001. Using the mean absolute percentage error (MAPE) to measure forecast accuracy, the autoregressive integrated moving average (ARIMA) model predicted a further reduction in both CT_Add to a mean of 51.51 ± 13.21 s (AIC = 5403.13) with an error of 6.32%, and CT_Sum to a mean of 54.57 ± 15.37 s (AIC = 3852.61) with an error of 8.02% over an additional 100 forecasted trials. When the testing was repeated, the actual mean performance differed by 1.35 and 4.41 s for each of the tasks, respectively, from the ARIMA point forecast value. There was no difference between the ARIMA model and actual performance values (p-value CT_Add = 1.0, CT_Sum=0.054). This is in contrast to both Wright's model and linear regression (p-value < 0.0001). By accounting for both variability in performance over time and task difficulty, forecasting mental arithmetic performance may be possible using an ARIMA model, with an accuracy exceeding that of both Wright's model and univariate linear regression.