Search results for: convolution backprojection

Authors: Sajad Khaliq Dar, Dipanjan Goswami, Arshad H. Khuroo, Mohd. Akhtar, Pulak Kumar Metia, Sudershan Kumar

Abstract:

Background: Development of modified-release oral dosage formulations (OSD) like tacrolimus in narrow therapeutic categories, together with high levels of intra-individual variability, impose greater challenges. The risk assessment for bioequivalence studies requires developing a suitable design through pilot studies involving the comparison of multiple formulations of the same product with a marketed product to understand the in-vivo behaviour. These formulations could have varying coating levels and other minor quantitative differences to achieve the desired release rate for the final product. Although small-scale studies are critical before the conduct of full-scale Pharmacokinetic (PK) studies, regulatory agencies evaluate critical bioavailability attributes (CBA) before approving the submitted dossiers. Since Tacrolimus is a BCS Class II drug, therefore developing the extended-release formulation, in addition to associated challenges, provides an opportunity to present the In vitro-in vivo correlations (IVIVC) to regulatory agencies, not only to exhibit product quality but also to reduce the burden of additional human trials and cost involved to them for bringing the product to market. Objective: The objective of this study was to develop a Level-A In vitro - In vivo Correlation (IVIVC) model for Sun Pharma’s test formulation Tacrolimus ER tablet 4mg and extend its application to a widened dissolution window of 25% at 2.5 hours (critical release time) sampling time point. Experimental Procedure: Post the conduct of two in-vivo studies, a pilot study evaluating two test prototypes on 24 subjects (under fasting) and a pivotal study having 50 subjects (under fasting), the observed pharmacokinetic profile was used for IVIVC model development. The dissolution media used was 0.005% HPC + 0.25% SLS in Water 900 mL at pH 4.50 using USP II (Paddle) apparatus with alternative sinkers operated at 100 RPM. The sampling time points were chosen to mimic the drug absorption in vivo. The dissolution best fit to data was obtained using Makoid Banakar kinetics. Then deconvolution, anchoring to concepts of the single compartment by Wagner Nelson method was applied for tacrolimus slow-release formulation batch with film coating weight build-up of 5.4% (used in pilot bio study), medium release with Hypromellose (retard-release exhibit batch used in the pivotal study) and fast release formulation batch with film coating weight build-up of 5.05% (used in pilot bio study). Results and Conclusion: The results were deemed acceptable as prediction errors for internal and external validation were < 3% depicting in-vitro drug release mimics in-vivo absorption. Moreover, the prediction result for the Test/Reference ratio was <15% for all test formulations and widening dissolution (i.e., 39%-64% drug release at 2.5hrs) predictions were well within 80-125% when compared against Envarsus XR (reference drug). This IVIVC-validated model can be used in the futuristic exploration of dose titration with 1mg tacrolimus ER OSD as a surrogate for In-vivo bioequivalence trials.

Keywords: pharmacokinetics, BCS, oral dosage form, Bioavailability, intra-individual variability

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Authors: Reza Nematirad, Anil Pahwa, Balasubramaniam Natarajan

Abstract:

Time series data consist of successive data points collected over a period of time. Accurate prediction of future values is essential for informed decision-making in several real-world applications, including electricity load demand forecasting, lifetime estimation of industrial machinery, traffic planning, weather prediction, and the stock market. Due to their critical relevance and wide application, there has been considerable interest in time series forecasting in recent years. However, the proliferation of sensors and IoT devices, real-time monitoring systems, and high-frequency trading data introduce significant intricate temporal variations, rapid changes, noise, and non-linearities, making time series forecasting more challenging. Classical methods such as Autoregressive integrated moving average (ARIMA) and Exponential Smoothing aim to extract pre-defined temporal variations, such as trends and seasonality. While these methods are effective for capturing well-defined seasonal patterns and trends, they often struggle with more complex, non-linear patterns present in real-world time series data. In recent years, deep learning has made significant contributions to time series forecasting. Recurrent Neural Networks (RNNs) and their variants, such as Long short-term memory (LSTMs) and Gated Recurrent Units (GRUs), have been widely adopted for modeling sequential data. However, they often suffer from the locality, making it difficult to capture local trends and rapid fluctuations. Convolutional Neural Networks (CNNs), particularly Temporal Convolutional Networks (TCNs), leverage convolutional layers to capture temporal dependencies by applying convolutional filters along the temporal dimension. Despite their advantages, TCNs struggle with capturing relationships between distant time points due to the locality of one-dimensional convolution kernels. Transformers have revolutionized time series forecasting with their powerful attention mechanisms, effectively capturing long-term dependencies and relationships between distant time points. However, the attention mechanism may struggle to discern dependencies directly from scattered time points due to intricate temporal patterns. Lastly, Multi-Layer Perceptrons (MLPs) have also been employed, with models like N-BEATS and LightTS demonstrating success. Despite this, MLPs often face high volatility and computational complexity challenges in long-horizon forecasting. To address intricate temporal variations in time series data, this study introduces Times2D, a novel framework that parallelly integrates 2D spectrogram and derivative heatmap techniques. The spectrogram focuses on the frequency domain, capturing periodicity, while the derivative patterns emphasize the time domain, highlighting sharp fluctuations and turning points. This 2D transformation enables the utilization of powerful computer vision techniques to capture various intricate temporal variations. To evaluate the performance of Times2D, extensive experiments were conducted on standard time series datasets and compared with various state-of-the-art algorithms, including DLinear (2023), TimesNet (2023), Non-stationary Transformer (2022), PatchTST (2023), N-HiTS (2023), Crossformer (2023), MICN (2023), LightTS (2022), FEDformer (2022), FiLM (2022), SCINet (2022a), Autoformer (2021), and Informer (2021) under the same modeling conditions. The initial results demonstrated that Times2D achieves consistent state-of-the-art performance in both short-term and long-term forecasting tasks. Furthermore, the generality of the Times2D framework allows it to be applied to various tasks such as time series imputation, clustering, classification, and anomaly detection, offering potential benefits in any domain that involves sequential data analysis.

Keywords: derivative patterns, spectrogram, time series forecasting, times2D, 2D representation

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