Quantitative Cardiac Perfusion with Kolmogorov--Arnold Networks for Robust Myocardial Blood Flow Mapping

Background: Quantitative first-pass cardiovascular magnetic resonance (CMR) perfusion [1,2,3] enables pixelwise myocardial blood flow (MBF) and myocardial perfusion reserve (MPR), but optimization-based methods (e.g., nonlinear least squares and constrained deconvolution) are ill-posed, sensitive to initialization/regularization and arterial input function (AIF) scaling or delay, and computationally expensive per pixel; performance degrades with noise, motion, and partial volume. Black-box deep networks can be brittle to protocol shifts. We propose a Kolmogorov--Arnold Network (KAN) [4,5] for fast, robust MBF mapping. Compared with multilayer perceptrons (MLPs), KAN uses adaptive one-dimensional bases on sparse grids, yielding smooth, interpretable functions that support shape and non-negativity constraints, improve data/parameter efficiency, and enable fast voxelwise inference without iteration.

Methods: We built a KAN regressor and validated it in a controlled simulation. A single-peak AIF was modeled as a gamma variate [6] and convolved with a Fermi tissue response [3] parameterized by arrival time t₀ and dispersion τ. Curves had 50 time points; Gaussian noise with a standard deviation of 2% of the peak AIF was added. Inputs to the model concatenated the noisy AIF and tissue function (TF) (2 × 50 = 100). Outputs were [MBF, t₀, τ] with ranges MBF ∈ [0.5, 4.0] mL/min/g, t₀ ∈ [0, 15] s, τ ∈ [5, 30] s. Datasets: N_train=20,000, N_test=200. The KAN had widths [100, 30, 3], a (cubic) B-spline grid of 5, and was trained with L-BFGS for 100 steps using mean squared error (MSE).

Results: Figure 1 shows the simulated AIF (gamma variate) and corresponding tissue function after Fermi modeling. Figure 2 shows predicted vs. true MBF, t₀, and τ with good R²; predictions closely aligned with ground truth. The method was stable across the prescribed parameter ranges and noise level, supporting fast, accurate inference. Figure 3 visualizes learned network weights (darker = larger); KAN prunes redundant nodes, improving interpretability and efficiency, and higher weights coincide with high AIF amplitude.

Conclusion: A physiologically informed KAN enables accurate and fast quantitative perfusion in single-peak AIF simulations. This supports near real-time MBF estimation and scalable analyses for clinical and research workflows. Current limitations are that results are primarily simulation-based; future work will train and validate on multi-center real perfusion datasets with prospective evaluation and uncertainty quantification.

Arterial input function (AIF) modeled as a gamma-variate function (GVF) and the corresponding tissue function (TF) generated via a Fermi-constrained residue parameterized by arrival time $t_0$ and dispersion $\tau$. Curves have 50 time points; zero-mean Gaussian noise with a standard deviation of 2% of the peak AIF amplitude was added. Shown are the noisy AIF and TF signals used as model inputs.
Parameter accuracy. Scatter plot of predictedvs. true MBF, t₀, and τ with R².
Trained KAN network structure weights at different nodes, where darker nodes correspond to larger weights. The top output nodes (left to right) are MBF, t₀, and τ. The input nodes (bottom) correspond to AIF and TF time points.