Methods for using machine learning and mechanistic models for biological feature mapping with multiparametric MRI
Described here are systems and methods for generating and implementing a hybrid machine learning and mechanistic model to produce biological feature maps, or other measurements of biological features, based on an input of multiparametric magnetic resonance or other images. The hybrid model can include a combination of a machine learning model and a mechanistic model that takes as an input multiparametric MRI, or other imaging, data to generate biological feature maps (e.g., tumor cell density maps), or other measures or predictions of biological features (e.g., tumor cell density). The hybrid models have capabilities of learning individual-specific relationships between imaging features and biological features.
1. A method for constructing and implementing a hybrid machine learning and mechanistic model to predict biological feature data, the steps of the method comprising:
constructing a hybrid machine learning and mechanistic model by:
(i) accessing training data with a computer system, the training data including labeled data and unlabeled data;
(ii) training a machine learning model based on the training data, generating output that includes a trained machine learning model;
(iii) augmenting the machine learning model using a mechanistic model that mathematically describes at least one of a biological process or a physiological process associated with a biological feature, generating a hybrid model comprising a hybrid machine learning and mechanistic model; and
generating predicted biological feature data by inputting multiparametric magnetic resonance images to the hybrid model.
2. The method as recited in claim 1 , wherein the mechanistic model is a proliferation-invasion model that mathematically describes a rate of change of cell density as a function of invasion of cells into nearby tissues and proliferation of cells.
3. The method as recited in claim 1 , wherein the labeled data in the training data comprises image-localized biopsy data and the unlabeled data in the training data comprises multiparametric magnetic resonance images.
4. The method as recited in claim 3 , wherein the labeled data are augmented with virtual biopsy data comprising cell density data that are generated using the mechanistic model.
5. The method of claim 1 , wherein the machine learning model is a semi-supervised learning (SSL) model.
6. The method of claim 5 , wherein the SSL model is a graph-based SSL model, and wherein augmenting the machine learning model using the mechanistic model comprises estimating edge weights as a function of localized features in the unlabeled data and of cell density values estimated by the mechanistic model.
7. The method of claim 6 , wherein the SSL model includes incorporating a Proliferation-Invasion (PI)-estimated regional cell density into a graph-based SSL using:
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wherein L is a number of biopsy samples in a training dataset, y l is a pathologically measured tumor cell density for the l-th biopsy sample, x l contains features computed from a localized region of multiparametric MRI corresponding to a biopsy location and a tumor density prediction of the mechanistic model, ƒ(x l ) is a predictive function for cell density, (y l −ƒ(x l )) 2 is a loss function that measures a discrepancy between the pathologically measured cell density and a predicted density of each biopsy sample, ƒ is a function on a reproducing kernel Hilbert space (RKHS), K , with a Mercer kernel K, ∥ƒ∥ K 2 is a norm on K , γ A is a tuning parameter, f contains predictive density for each labeled and unlabeled sample, Σ i,j w ij is a sum of all edge weights in a graph used by the graph-based SSL.
8. The method of claim 1 , wherein the multiparametric magnetic resonance images include images of T1 with contrast, T2 weighted, Echo-planar imaging (EPI) with contrast, mean diffusivity (MD), fractional anisotropy (FA), and relative cerebral blood volume (rCBV).
9. The method of claim 1 , wherein the hybrid model includes tuning parameters configured to minimize a mean absolute prediction error (MAPE) of the region of interest.
10. The method of claim 9 , wherein the tuning parameters include patient-specific tuning parameters trained for each subject to minimize the MAPE of the specific subject.
11. The method of claim 9 , wherein the tuning parameters include uniform tuning parameters configured to minimize the MAPE across all subjects.
12. The method of claim 11 , wherein the mechanistic model is a Proliferation Invasion (PI) model of the form:
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wherein c(x,t) is a tumor cell density, D(x) is a net rate of diffusion, ρ is a net rate of proliferation, and K is a cell carrying capacity.