Up-Net: a generic deep learning-based time stepper for parameterized spatio-temporal dynamics

In the age of big data availability, data-driven techniques have been proposed recently to compute the time evolution of spatio-temporal dynamics. Depending on the required a priori knowledge about the underlying processes, a spectrum of black-box end-to-end learning approaches, physics-informed neural networks, and data-informed discrepancy modeling approaches can be identified. In this work, we propose a purely data-driven approach that uses fully convolutional neural networks to learn spatio-temporal dynamics directly from parameterized datasets of linear spatio-temporal processes. The parameterization allows for data fusion of field quantities, domain shapes, and boundary conditions in the proposed Up-Net architecture. Multi-domain Up-Net models, therefore, can generalize to different scenes, initial conditions, domain shapes, and domain sizes without requiring re-training or physical priors. Numerical experiments conducted on a universal and two-dimensional wave equation and the transient heat equation for validation purposes show that the proposed Up-Net outperforms classical U-Net and conventional encoder–decoder architectures of the same complexity. Owing to the scene parameterization, the Up-Net models learn to predict refraction and reflections arising from domain inhomogeneities and boundaries. Generalization properties of the model outside the physical training parameter distributions and for unseen domain shapes are analyzed. The deep learning flow map models are employed for long-term predictions in a recursive time-stepping scheme, indicating the potential for data-driven forecasting tasks. This work is accompanied by an open-sourced code

Visualization of Abscess Formation in a Murine Thigh Infection Model of Staphylococcus aureus by 19F-Magnetic Resonance Imaging (MRI)

Background: During the last years, 19 F-MRI and perfluorocarbon nanoemulsion (PFC) emerged as a powerful contrast agent based MRI methodology to track cells and to visualize inflammation. We applied this new modality to visualize deep tissue abscesses during acute and chronic phase of inflammation caused by Staphylococcus aureus infection. Methodology and Principal Findings: In this study, a murine thigh infection model was used to induce abscess formation and PFC or CLIO (cross linked ironoxides) was administered during acute or chronic phase of inflammation. 24 h after inoculation, the contrast agent accumulation was imaged at the site of infection by MRI. Measurements revealed a strong accumulation of PFC at the abscess rim at acute and chronic phase of infection. The pattern was similar to CLIO accumulation at chronic phase and formed a hollow sphere around the edema area. Histology revealed strong influx of neutrophils at the site of infection and to a smaller extend macrophages during acute phase and strong influx of macrophages at chronic phase of inflammation. Conclusion and Significance: We introduce 19 F-MRI in combination with PFC nanoemulsions as a new platform to visualize abscess formation in a murine thigh infection model of S. aureus. The possibility to track immune cells in vivo by this modality offers new opportunities to investigate host immune response, the efficacy of antibacterial therapies and th

19F magnetic resonance imaging of perfluorocarbons for the evaluation of response to antibiotic therapy in a Staphylococcus aureus infection model.

BACKGROUND: The emergence of antibiotic resistant bacteria in recent decades has highlighted the importance of developing new drugs to treat infections. However, in addition to the design of new drugs, the development of accurate preclinical testing methods is essential. In vivo imaging technologies such as bioluminescence imaging (BLI) or magnetic resonance imaging (MRI) are promising approaches. In a previous study, we showed the effectiveness of (19)F MRI using perfluorocarbon (PFC) emulsions for detecting the site of Staphylococcus aureus infection. In the present follow-up study, we investigated the use of this method for in vivo visualization of the effects of antibiotic therapy. METHODS/PRINCIPAL FINDINGS: Mice were infected with S. aureus Xen29 and treated with 0.9% NaCl solution, vancomycin or linezolid. Mock treatment led to the highest bioluminescence values during infection followed by vancomycin treatment. Counting the number of colony-forming units (cfu) at 7 days post-infection (p.i.) showed the highest bacterial burden for the mock group and the lowest for the linezolid group. Administration of PFCs at day 2 p.i. led to the accumulation of (19)F at the rim of the abscess in all mice (in the shape of a hollow sphere), and antibiotic treatment decreased the (19)F signal intensity and volume. Linezolid showed the strongest effect. The BLI, cfu, and MRI results were comparable. CONCLUSIONS: (19)F-MRI with PFCs is an effective non-invasive method for assessing the effects of antibiotic therapy in vivo. This method does not depend on pathogen specific markers and can therefore be used to estimate the efficacy of antibacterial therapy against a broad range of clinically relevant pathogens, and to localize sites of infection

Representative MR-slice series showing the hollow sphere formed by PFC at chronic phase.

<p>The depicted mouse received PFC at day 8 post infection. Images were recorded 24 h after administration. ¹⁹F-SSFP CSI overlay on ¹H-TSE image of PFC group mouse shows strong accumulation of PFC at the rim of abscess area. (Slice Thickness: 1 mm, FOV 25×25 mm², Co: Control tube filled with PFC dilution, R: right side, L: left side of the imaged mouse).</p

Representative MR Images of acute soft-tissue infection.

<p>A, B) Mouse received PFC at day 2 post infection. Images were recorded 24 h after administration. C, D) Mouse received CLIO at day 2 post infection and was imaged 24 h after administration. A) Transverse T₂ map of PFC group mouse shows hyperintensity within infected muscle (arrow). B) ¹⁹F-SSFP CSI overlay on ¹H-TSE image of PFC treated mouse shows strong accumulation of PFC at the rim of abscess area. C) Transverse T₂ map of CLIO group mouse shows hyper-intense area diffusely circumscribed by dark spots (arrow). D) T₂* weighted image shows diffusely distributed susceptibility effects in the infected muscle (arrow). (Co: Control tube filled with PFC dilution, R: right side, L: left side of the imaged mouse).</p

Histological appearance of acute soft-tissue infection.

<p>A, C) Mice received CLIO at day 2 post infection and were imaged 24 h after administration. The muscle was recovered immediately after imaging. B) Mice received PFC at day 2 post infection. Images were recorded 24 h after administration. The muscle was recovered immediately after imaging. A) HE-staining shows that infiltrate in CLIO group mice consists mainly of granulocytes. C) Iron-specific staining demonstrates iron deposits in granulocytes and macrophages (iron appears blue). B) HE-staining of PFC group mouse reveals strong immune cell infiltrate mainly consisting of granulocytes.</p

Representative MR-slice series showing the time course of PFC accumulation following administration at acute phase.

<p>Mouse received PFC at day 2 p.i. and was imaged every 48 h beginning at d3 p.i.. The upper row of images shows T₂ weighted MR-slices, the lower row the corresponding ¹⁹F-SSFP CSI overlays on ¹H-TSE images. ¹⁹F signal could be visualized in all measurements until d9 p.i. (end point).</p

Histological appearance of chronic soft-tissue infection.

<p>A, C) Mice received CLIO at day 2 post infection. Images were recorded 24 h after administration. The muscle was recovered immediately after imaging. B) Mice received PFC at day 2 post infection and were imaged 24 h after administration. The muscle was recovered immediately after imaging. A) Macrophages and Granulocytes are embedded in granulation tissue at the abscess rim of CLIO group mice. C) Iron-specific staining demonstrates iron deposits in granulocytes and macrophages (iron appears blue). B) HE-staining of PFC group mice reveals macrophages and granulocytes in fibroblast-enriched granulation tissue similar to CLIO group mice.</p

Representative MR Images of chronic soft-tissue infection.

<p>A, B) Mouse received PFC at day 8 post infection. Images were recorded 24 h after administration. C, D) Mouse received CLIO at day 8 post infection and was imaged 24 h after administration. A) Transverse T₂ map of PFC group mouse shows large hyper-intensity area within infected muscle (arrow). B) ¹⁹F-SSFP CSI overlay on ¹H-TSE image of PFC group mouse shows strong accumulation of PFC at the rim of abscess area. C) Transverse T₂ map of CLIO group mouse shows hyper-intense area circumscribed by a dark rim (arrows). D) T₂* weighted image shows strong susceptibility effects around the infected muscle in a hollow sphere pattern (arrows (Co: Control tube filled with PFC dilution, R: right side, L: left side of the imaged mouse).</p

Representative MR-slice series showing the hollow sphere formed by PFC at acute phase.

<p>The depicted mouse received PFC at day 2 after start of infection. Images were recorded 24 h after administration. ¹⁹F-SSFP CSI overlay on ¹H-TSE image of PFC group mouse shows strong accumulation of PFC at the rim of the abscess area.(Slice Thickness: 1 mm, FOV 25×25 mm², Co: Control tube filled with PFC dilution, R: right side, L: left side of the imaged mouse).</p