Pinning the Balloon
Poster No:
2109
Submission Type:
Abstract Submission
Authors:
Rodrigo Avaria-Saldías1, Astrid Cancino1, Steren Chabert1, Rodrigo Salas1
Institutions:
1Universidad de Valparaiso, Valparaiso, Valparaiso.
First Author:
Co-Author(s):
Introduction:
BOLD signals reflect hemodynamic and metabolic brain responses (Ogawa & Sung, 2007). Incorporating prior knowledge in machine learning mitigates limited data and enhances generalization. Physics-informed neural networks (PINNs), proposed by Raissi et al. (2019), integrate data with mathematical operators like differential equations to solve or discover models from observations. The Balloon Model (BM) (Friston et al., 2000) explains neurovascular coupling and BOLD response but is challenging to identify due to noise (Rosa et al., 2015). Embedding the BM in a PINN enables BOLD reconstruction by leveraging physiological insights. This work develops a BM-constrained PINN method for reconstructing BOLD signals.
Methods:
The BM describes BOLD as a nonlinear, dynamic system with 4 normalized state variables (Fig. 1): blood influx fin(t), CMRO2 m(t), blood volume v(t), and dHb concentration q(t). BM equations are shown in Fig. 1. A PINN incorporates the BM with a loss function that penalizes deviations from data and physics. This function is a weighted sum of 3 components, as stated in Fig 1. We heuristically set wdata=0.69,wODE=0.29, & wIC=0.02.
The network has multiple outputs (one per BM equation), 14 linear layers with varying neurons and activations, and takes time as input (details in Fig. 1)
The method was developed in Python 3.10 using Pythorch 2.3.1 and CUDA 12.1. Capacity and accuracy were evaluated via 3 experiments with equal configurations: 35,000 iterations; Adam optimizer; initial learning rate = 4×10−3 with decay by 0.5 every 2500 iterations.
1. BOLD Reconstruction from Noiseless Simulated Data: We performed training with an onset time t0=1s for the boxcar stimulus I(t) in equations for fin & m.
2. Retrieve the BOLD from Noisy Simulated Data: Training configuration was reused with additive noise. This noise does not replicate characteristics from fMRI data but assesses the robustness.
3. Application to in-vivo Data from Previous Passive Motor Design Study: The goal is to obtain BOLD reconstructions, retrieve state variables, and explore insights from the model when applied to observational data, thereby validating the PINN in a practical setting. Images were acquired on a 1.5T scanner (GE, USA) from a 52-y.o. male with an ischemic core. Variable inter-stimulus intervals yielded 11 activations. Postcentral gyri were the ROI for BOLD extraction. Baseline correction was done by subtracting the 21s signal mean (pre-stimulus). Informed consent was obtained, and the study was approved by the Regional Ethics Committee (Resolution 3730-2021 SSVA San Antonio).
Simulated data were generated from BM solutions using parameters from Maith et al. (2022). 40 regularly spaced samples with Gaussian noise N(0,σ2=0.01) added as needed.
The network has multiple outputs (one per BM equation), 14 linear layers with varying neurons and activations, and takes time as input (details in Fig. 1)
The method was developed in Python 3.10 using Pythorch 2.3.1 and CUDA 12.1. Capacity and accuracy were evaluated via 3 experiments with equal configurations: 35,000 iterations; Adam optimizer; initial learning rate = 4×10−3 with decay by 0.5 every 2500 iterations.
1. BOLD Reconstruction from Noiseless Simulated Data: We performed training with an onset time t0=1s for the boxcar stimulus I(t) in equations for fin & m.
2. Retrieve the BOLD from Noisy Simulated Data: Training configuration was reused with additive noise. This noise does not replicate characteristics from fMRI data but assesses the robustness.
3. Application to in-vivo Data from Previous Passive Motor Design Study: The goal is to obtain BOLD reconstructions, retrieve state variables, and explore insights from the model when applied to observational data, thereby validating the PINN in a practical setting. Images were acquired on a 1.5T scanner (GE, USA) from a 52-y.o. male with an ischemic core. Variable inter-stimulus intervals yielded 11 activations. Postcentral gyri were the ROI for BOLD extraction. Baseline correction was done by subtracting the 21s signal mean (pre-stimulus). Informed consent was obtained, and the study was approved by the Regional Ethics Committee (Resolution 3730-2021 SSVA San Antonio).
Simulated data were generated from BM solutions using parameters from Maith et al. (2022). 40 regularly spaced samples with Gaussian noise N(0,σ2=0.01) added as needed.
Results:
See Results in Figure 2
Conclusions:
A PINN-based method constrained by the Balloon model was developed, effectively reconstructing BOLD signals effectively, even in presence of noise. It provides an explanation for BOLD signals acquired at conventional TR and 1.5T field strengths by retrieving 4 underlying state variables of the BM (q, v, fin, and m). Our approach demonstrates potential for personalized biophysical interpretations of BOLD dynamics.e.g. real data presented here signals' inter-hemispheric differences may be driven by an interplay between q and v, rather than by fin and m.
Further work is needed to refine alternative formulations and evaluate the proposed method's robustness and accuracy. This study highlights the potential of PINNs for analyzing BOLD and extracting meaningful physiological information. The ability to perform regression using the Balloon model opens new alternatives for investigating brain hemodynamics. Further development of this approach could lead to significant advancements in our understanding of neurovascular coupling and the interpretation of fMRI data.
Further work is needed to refine alternative formulations and evaluate the proposed method's robustness and accuracy. This study highlights the potential of PINNs for analyzing BOLD and extracting meaningful physiological information. The ability to perform regression using the Balloon model opens new alternatives for investigating brain hemodynamics. Further development of this approach could lead to significant advancements in our understanding of neurovascular coupling and the interpretation of fMRI data.
Modeling and Analysis Methods:
Activation (eg. BOLD task-fMRI)
Exploratory Modeling and Artifact Removal
Methods Development
Other Methods 2
Physiology, Metabolism and Neurotransmission:
Cerebral Metabolism and Hemodynamics 1
Keywords:
Cerebral Blood Flow
Computational Neuroscience
Data analysis
FUNCTIONAL MRI
Machine Learning
Modeling
Other - Physics-Based Deep Learning ; Biophysical Modelling ; Physically Informed Neural Networks (PINNs) ; Balloon Model
1|2Indicates the priority used for review
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Provide references using APA citation style.
Karniadakis, G. E., Kevrekidis, I. G., Lu, L., Perdikaris, P., Wang, S., & Yang, L. (2021). Physics-informed machine learning. Nature Reviews Physics, 3(6), 422–440. https://doi.org/10.1038/s42254-021-00314-5
Maith, O., Dinkelbach, H. Ü., Baladron, J., Vitay, J., & Hamker, F. H. (2022). BOLD Monitoring in the Neural Simulator ANNarchy. Frontiers in Neuroinformatics, 16, 790966. https://doi.org/10.3389/fninf.2022.790966
Ogawa, S., & Sung, Y.-W. (2007). Functional magnetic resonance imaging. Scholarpedia, 2(10), 3105. https://doi.org/10.4249/scholarpedia.3105
Raissi, M., Perdikaris, P., & Karniadakis, G. E. (2019). Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 378, 686–707. https://doi.org/10.1016/j.jcp.2018.10.045
Rosa, P. N., Figueiredo, P., & Silvestre, C. J. (2015). On the distinguishability of HRF models in fMRI. Frontiers in Computational Neuroscience, 9. https://doi.org/10.3389/fncom.2015.00054