Physiological trend analysis of a novel cardio-pulmonary model during a preload reduction manoeuvre

Preserving multi-dimensional information: A hypersphere method for parameter space analysis

Background

Physiological modelling often involves models described by large numbers of variables and significant volumes of clinical data. Mathematical interpretation of such models frequently necessitates analysing data points in high-dimensional spaces. Existing algorithms for analysing high-dimensional points either lose important dimensionality or do not describe the full position of points. Hence, there is a need for an algorithm which preserves this information.

Methods

The most-distant uncovered point (MDUP) hypersphere method is a binary classification approach which defines a collection of equidistant N-dimensional points as the union of hyperspheres. The method iteratively generates hyperspheres at the most distant point in the interest region not yet contained within any hypersphere, until the entire region of interest is defined by the union of all generated hyperspheres. This method is tested on a 7-dimensional space with up to 35.8 million points representing feasible and infeasible spaces of model parameters for a clinically validated cardiovascular system model.

Results

For different numbers of input points, the MDUP hypersphere method tends to generate large spheres away from the boundary of feasible and infeasible points, but generates the greatest number of relatively much smaller spheres around the boundary of the region of interest to fill this space. Runtime scales quadratically, in part because the current MDUP implementation is not parallelised.

Conclusions

The MDUP hypersphere method can define points in a space of any dimension using only a collection of centre points and associated radii, making the results easily interpretable. It can identify large continuous regions, and in many cases capture the general structure of a region in only a relative few hyperspheres. The MDUP method also shows promise for initialising optimisation algorithm starting conditions within pre-defined feasible regions of model parameter spaces, which could improve model identifiability and the quality of optimisation results.

Single measurement estimation of central blood pressure using an arterial transfer function

BACKGROUND

Central blood pressure (BP) better reflects the loading conditions on the major organs and is more closely correlated with future cardiovascular events. The increased invasiveness and risk of infection prevents the routine measurement of central BP. Arterial transfer functions can provide central BP estimates from clinically available peripheral measurements. However, current methods are either generalized, potentially lacking the ability to adapt to inter and intra subject variability, or individualized based on additional, clinically unavailable, pulse transit time measurements. This work proposes a novel, self-contained method for individualizing an arterial transfer function from a single peripheral pressure measurement, capable of accurately estimating central BP in a range of hemodynamic conditions.

METHODS

Pulse wave analysis of femoral BP waves was employed to formulate initial approximations of central BP and arterial inlet flow waveforms, to serve as objective functions for the identification of all model parameters. Root mean squared error (RMSE), and systolic and pulse pressure errors were assessed with respect to invasive aortic BP measurements in a seven (7) porcine endotoxin experiments. Systolic and pulse pressure errors were analysed using Bland-Altman analysis. Method accuracy is also compared with an idealized transfer function, derived using the measured aortic-femoral pulse transit time and minimizing the RMSE of model output pressure with respect to reference aortic pressure, a generalized transfer function model, and invasive femoral pressure measurements.

RESULTS

Mean bias and limits of agreement (95% CI) for the proposed method were 1.0(-4.6, 6.7)mmHg and -1.0(-6.6, 4.6)mmHg for systolic and pulse pressure, respectively, compared to 3.6(-0.9, 8.2)mmHg and 2.7(-1.8, 7.3)mmHg for the generalized transfer function model. Mean bias and limits of agreement for femoral pressure measurements were -6.4(-15.0, 2.3)mmHg and -9.4(-18.1, -0.8)mmHg, for systolic and pulse pressure, respectively. The pooled mean and standard deviation of the RMSE produced by the single measurement method, relative to reference aortic pressure, was 4.3(1.1)mmHg, consistent with estimates produced by the idealized transfer function, 3.9(1.2)mmHg, and improving of the generalized transfer function, 4.6(1.4)mmHg.

CONCLUSIONS

The proposed single measurement method provides accurate central BP estimates from routinely available peripheral pressure measurements, and nothing else. The method allows for the individualization of transfer functions on a per patient basis to better capture changes in patient condition during the progression of disease and subsequent treatment, at no additional clinical cost.

Modelling patient specific cardiopulmonary interactions

Mechanical ventilation is well known for having detrimental effects on the cardiovascular system, particularly when using high positive end-expiratory pressure. High positive end-expiratory pressure levels cause a decrease in stroke volume, which, under normal conditions, usually bring about a decrease in stressed blood volume. Stressed blood volume, defined as the total pressure generating volume of the cardiovascular system, has been shown to be a potential index of fluid responsiveness, making it a potentially important diagnostic tool. Generally, respiratory and haemodynamic care are provided independently of one another. However, that positive end-expiratory pressure alters both stroke volume and stressed blood volume suggests both the pulmonary and cardiovascular state should be conjointly optimised and used to guide positive end-expiratory pressure. However, the complex and patient-specific nature of cardiopulmonary interactions which occur during mechanical ventilation presents a challenge for accurate modelling of respiratory and cardiovascular interactions required to better optimise care. Previous models attempting to incorporate cardiopulmonary interactions have suffered from poor reliability at higher PEEP levels, largely due to an exaggerated effect of intrathoracic pressure on the cardiovascular system. A new parameter, alpha, is added to a previously validated cardiopulmonary model, to modulate the percentage of intrathoracic pressure applied to the vena cava and left ventricle. The new parameter aims to increase reliability under high PEEP conditions as well as provide a patient specific solution to modelling cardiopulmonary interactions. The results from the identified optimal alpha are compared to the original model to investigate how this new parameter may be used to create a more patient-specific cardiopulmonary model, which would be better suited for guidance of care in the ICU.