Background: Automated estimation of Pulmonary function test (PFT) results from Computed Tomography (CT) could advance the use of CT in screening, diagnosis, and staging of restrictive pulmonary diseases. Estimating lung function per lobe, which cannot be done with PFTs, would be helpful for risk assessment for pulmonary resection surgery and bronchoscopic lung volume reduction.

Purpose: To automatically estimate PFT results from CT and furthermore disentangle the individual contribution of pulmonary lobes to a patient's lung function.

Methods: We propose I3Dr, a deep learning architecture for estimating global measures from an image that can also estimate the contributions of individual parts of the image to this global measure. We apply it to estimate the separate contributions of each pulmonary lobe to a patient's total lung function from CT, while requiring only CT scans and patient level lung function measurements for training. I3Dr consists of a lobe-level and a patient-level model. The lobe-level model extracts all anatomical pulmonary lobes from a CT scan and processes them in parallel to produce lobe level lung function estimates that sum up to a patient level estimate. The patient-level model directly estimates patient level lung function from a CT scan and is used to re-scale the output of the lobe-level model to increase performance. After demonstrating the viability of the proposed approach, the I3Dr model is trained and evaluated for PFT result estimation using a large data set of 8 433 CT volumes for training, 1 775 CT volumes for validation, and 1 873 CT volumes for testing.

Results: First, we demonstrate the viability of our approach by showing that a model trained with a collection of digit images to estimate their sum implicitly learns to assign correct values to individual digits. Next, we show that our models can estimate lobe-level quantities, such as COVID-19 severity scores, pulmonary volume (PV), and functional pulmonary volume (FPV) from CT while only provided with patient-level quantities during training. Lastly, we train and evaluate models for producing spirometry and diffusion capacity of carbon mono-oxide (DLCO) estimates at the patient and lobe level. For producing Forced Expiratory Volume in one second (FEV1), Forced Vital Capacity (FVC), and DLCO estimates, I3Dr obtains mean absolute errors (MAE) of 0.377 L, 0.297 L, and 2.800 mL/min/mm Hg respectively. We release the resulting algorithms for lung function estimation to the research community at https://grand-challenge.org/algorithms/lobe-wise-lung-function-estimation/ CONCLUSIONS: I3Dr can estimate global measures from an image, as well as the contributions of individual parts of the image to this global measure. It offers a promising approach for estimating PFT results from CT scans and disentangling the individual contribution of pulmonary lobes to a patient's lung function. The findings presented in this work may advance the use of CT in screening, diagnosis, and staging of restrictive pulmonary diseases as well as in risk assessment for pulmonary resection surgery and bronchoscopic lung volume reduction.