# Contribution of Interval Linear Algebra to the Ongoing Discussions on Multiple Breath Washout Test

## TL;DR

This paper introduces an interval least squares approach using interval linear algebra to improve data fitting in lung function testing, revealing limitations of current sensors and inaccuracies in common models for the nitrogen washout process.

## Contribution

It presents a novel interval least squares method for handling uncertainties in lung function tests, offering new insights into measurement accuracy and modeling assumptions.

## Key findings

- Current sensors lack the precision for verified predictions.
- The commonly used nitrogen washout model is incorrect.
- Interval linear algebra can significantly speed up computations.

## Abstract

In the paper the interval least squares approach to estimate/fit data with interval uncertainties is introduced. The solution of this problem is discussed from the perspective of interval linear algebra. Using the interval linear algebra carefully, it is possible to significantly speed up the computation in specialized cases. The interval least squares approach is then applied to lung function testing method - Multiple breath washout test (MBW). It is used for algebraic handling of uncertainties arising during the measurement. Surprisingly, it sheds new light on various aspects of this procedure - it shows that the precision of currently used sensors does not allow verified prediction. Moreover, it proved the most commonly used curve to model the nitrogen washout process from lung to be wrong. Such insight contributes to the ongoing discussions on the possibility to predict clinically relevant indices (e.g., LCI).