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On the Diagnosis of Aortic Dissection with Impedance Cardiography: A Bayesian Feasibility Study Framework with Multi-Fidelity Simulation Data^{ †}

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## Abstract

**:**

## 1. Introduction

## 2. The Physical Model

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## 3. Bayesian Multi-Fidelity Scheme

## 4. Results & Discussion

## 5. Conclusions & Outlook

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Sample Availability

## References

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**Figure 1.**Illustration of a dissected aorta. Left: The whole organ. Right: Close-up to the entry tear [2]. Blood pushes from the anatomically correct cavity (medical parlance: true lumen) through a tear into the aortic wall. The tear grows and builds another cavity (medical parlance: false lumen), affecting blood circulation unfavourably.

**Figure 3.**Left: CAD Model of Thorax with dissected Aorta. Right: Ground view on True Lumen and False Lumen [4].

**Figure 4.**Left: Low fidelity mesh, geometry represented by ~10,000 tetrahedral elements. Right: High fidelity mesh, geometry represented by ~300,000 tetrahedral elements.

**Figure 5.**Data. Negative real part of the impedance measured with the probe electrodes indicated in Figure 3 (left). Simulations were done for one cardiac cycle with a time step of 50 ms and with 25 values of the false lumen radius (5 mm–25 mm) with the HiFi model (red) and the LoFi model (black).

**Figure 6.**Resulting expectations and uncertainty bands (2$\sigma $) for the HiFi impedances. Red (Bayes) and Blue (brute force).

**Figure 7.**Linear regression at peak systole (t = 200 ms). Predictive probability of HiFi impedances given the LoFi impedances, trained with two data points corresponding to the minimum and maximum used false lumen radius.

**Table 1.**Comparison of computational resources. Each experiment was performed on 20 cores in parallel (with trivial parallelization) on Xeon E5-2640 with 8GB RAM/CPU. Degrees of freedom vary from time instance to time instance since the aortic radius is a function of time. In Figure 6, we compare the Brute Force HiFi results (blue) with the Bayesian HiFi results (red). The LoFi results are a mere means to compute the Bayesian HiFi results and thus not shown, yet their computational effort is documented since needed to quantify the reduction of the computational effort.

Model | Degrees of Freedom | Samples | CPU Time [s] | Wall Clock Time [s] |
---|---|---|---|---|

LoFi | 9000–15,000 | 25 | 39,500 | 1975 |

Brute Force HiFi | 100,000–550,000 | 25 | 192,480 | 9624 |

Bayesian HiFi | 25 LoFi, 2 HiFi | 54955 | 2748 |

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## Share and Cite

**MDPI and ACS Style**

Ranftl, S.; Melito, G.M.; Badeli, V.; Reinbacher-Köstinger, A.; Ellermann, K.; Linden, W.v.d.
On the Diagnosis of Aortic Dissection with Impedance Cardiography: A Bayesian Feasibility Study Framework with Multi-Fidelity Simulation Data. *Proceedings* **2019**, *33*, 24.
https://doi.org/10.3390/proceedings2019033024

**AMA Style**

Ranftl S, Melito GM, Badeli V, Reinbacher-Köstinger A, Ellermann K, Linden Wvd.
On the Diagnosis of Aortic Dissection with Impedance Cardiography: A Bayesian Feasibility Study Framework with Multi-Fidelity Simulation Data. *Proceedings*. 2019; 33(1):24.
https://doi.org/10.3390/proceedings2019033024

**Chicago/Turabian Style**

Ranftl, Sascha, Gian Marco Melito, Vahid Badeli, Alice Reinbacher-Köstinger, Katrin Ellermann, and Wolfgang von der Linden.
2019. "On the Diagnosis of Aortic Dissection with Impedance Cardiography: A Bayesian Feasibility Study Framework with Multi-Fidelity Simulation Data" *Proceedings* 33, no. 1: 24.
https://doi.org/10.3390/proceedings2019033024