# Arterial Input Function (AIF) Correction Using AIF Plus Tissue Inputs with a Bi-LSTM Network

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## Abstract

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**Background:**The arterial input function (AIF) is vital for myocardial blood flow quantification in cardiac MRI to indicate the input time–concentration curve of a contrast agent. Inaccurate AIFs can significantly affect perfusion quantification.

**Purpose:**When only saturated and biased AIFs are measured, this work investigates multiple ways of leveraging tissue curve information, including using AIF + tissue curves as inputs and optimizing the loss function for deep neural network training.

**Methods**: Simulated data were generated using a 12-parameter AIF mathematical model for the AIF. Tissue curves were created from true AIFs combined with compartment-model parameters from a random distribution. Using Bloch simulations, a dictionary was constructed for a saturation-recovery 3D radial stack-of-stars sequence, accounting for deviations such as flip angle, T2* effects, and residual longitudinal magnetization after the saturation. A preliminary simulation study established the optimal tissue curve number using a bidirectional long short-term memory (Bi-LSTM) network with just AIF loss. Further optimization of the loss function involves comparing just AIF loss, AIF with compartment-model-based parameter loss, and AIF with compartment-model tissue loss. The optimized network was examined with both simulation and hybrid data, which included in vivo 3D stack-of-star datasets for testing. The AIF peak value accuracy and ${k}^{trans}$ results were assessed.

**Results**: Increasing the number of tissue curves can be beneficial when added tissue curves can provide extra information. Using just the AIF loss outperforms the other two proposed losses, including adding either a compartment-model-based tissue loss or a compartment-model parameter loss to the AIF loss. With the simulated data, the Bi-LSTM network reduced the AIF peak error from −23.6 ± 24.4% of the AIF using the dictionary method to 0.2 ± 7.2% (AIF input only) and 0.3 ± 2.5% (AIF + ten tissue curve inputs) of the network AIF. The corresponding ${k}^{trans}$ error was reduced from −13.5 ± 8.8% to −0.6 ± 6.6% and 0.3 ± 2.1%. With the hybrid data (simulated data for training; in vivo data for testing), the AIF peak error was 15.0 ± 5.3% and the corresponding ${k}^{trans}$ error was 20.7 ± 11.6% for the AIF using the dictionary method. The hybrid data revealed that using the AIF + tissue inputs reduced errors, with peak error (1.3 ± 11.1%) and ${k}^{trans}$ error (−2.4 ± 6.7%).

**Conclusions**: Integrating tissue curves with AIF curves into network inputs improves the precision of AI-driven AIF corrections. This result was seen both with simulated data and with applying the network trained only on simulated data to a limited in vivo test dataset.

## 1. Introduction

## 2. Methods

#### 2.1. Overview

#### 2.2. Data Preparation

#### 2.2.1. Simulated True AIF and Tissue Curves

#### 2.2.2. Saturated AIF

#### 2.3. Deep Neural Networks (DNNs)

#### 2.3.1. Loss Functions

#### 2.3.2. Networks

#### Bidirectional Long Short-Term Memory (Bi-LSTM)

#### Training, validation, and test datasets

#### 2.3.3. Hyperparameters

#### 2.3.4. Evaluation Metrics

#### 2.4. Applying the Trained Networks to In Vivo Data

## 3. Results

#### 3.1. The Number of Tissue Curves

#### 3.2. The Comparison of Three Loss Functions

#### 3.3. Comparison of AIF Inputs Only and AIF + Tissue Inputs: Hybrid Dataset

## 4. Discussion

^{−1}for normal brain tissue. In addition, the simulated tissue curves were drawn from a uniform distribution, which reflects a mix of normal and abnormal perfusion and washout. The diversity of k

_{ep}is known from blind estimation studies to provide more information regarding the AIF [13]. As well, the use of simulated datasets, while advantageous for controlled experimentation, does not replicate real-world scenarios. Therefore, there is a need to validate these findings with larger, diverse, and real-world datasets to understand the broader applicability of the results. The selection of a Bi-LSTM network is due to its outstanding performance in handling time-series data; however, other advanced networks, such as transformers and gated recurrent units, may be better choices for AIF corrections. Therefore, future development of new networks is important, especially for tackling hybrid data better.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**The workflow of AIF corrections using a Bi-LSTM network. The input is an incorrect AIF with tissue curves, and the output is a network-predicted AIF. The main body of the network uses a Bi-LSTM architecture consisting of multiple layers (M = 4), each incorporating both a forward and a backward LSTM unit to process time-series data.

**Figure 2.**The investigation of the optimal number of tissue curves for the network input. The case of no tissue indicates the application of the AIF-only loss, while the number of tissue curves varied from 1 to 10. The AIF peak value error in (

**A**) and the ${k}^{trans}$ error in (

**B**) were two evaluation metrics.

**Figure 3.**The comparison of network-predicted AIFs produced with the three proposed loss functions. The most accurate result was achieved using only the AIF loss, as shown in (

**A**), with a mean absolute error (MAE) of 0.03. A slightly higher MAE was observed with the addition of parameter loss, as indicated in (

**B**), while the AIF plus tissue loss, presented in (

**C**), led to a significant underestimation in the network’s AIF prediction.

**Figure 4.**The comparison of AIF curves when trained exclusively with AIF-only input (

**A**) or in combination with tissue curves (

**B**), using the hybrid data. The input AIF curve, generated using the dictionary method (in green), serves as a baseline to highlight improvements in the network-predicted AIF. The AIF plus tissue inputs yielded a lower MAE across the board—best, median, and worst—compared to the AIF-only input.

**Figure 5.**Statistical analysis of ${k}^{trans}$ values for two different network inputs (AIF-only and AIF + tissue) using the hybrid data. The Bland–Altman plot illustrates the difference between ${k}^{trans}$ values derived from network AIFs and true AIFs from the test set. The correlation plot showcases the linear fit (with a blue line), while the black dotted line represents the ideal fit. Each red circle above represents ${k}^{trans}$ from a slice.

**Figure 6.**The comparison of network-predicted AIFs produced with the three ways of network inputs. Across scenarios (

**A**–

**C**), where the network was fed with AIF-only, tissue-only, and AIF plus tissue inputs, respectively, the AIF plus tissue inputs resulted in the most precise AIF estimates, achieving the lowest MAE in comparison to the other input methods.

**Table 1.**The percentage error of AIF peak value and ${k}^{trans}$ produced using the three loss functions applied with various weight ratios of loss terms.

Weights Ratio | AIF Peak Value Error % | k^{trans} Error % |
---|---|---|

1:0 (or AIF loss only) | 0.3 ± 2.5 | 0.3 ± 2.1 |

α:β = 1:1 | 0.9 ± 2.5 | –1.0 ± 2.3 |

α:β = 1:10 | 0.2 ± 3.2 | 1.1 ± 3.4 |

α:β = 1:100 | –1.3 ± 4.4 | 2.3 ± 4.1 |

α:δ = 1:1 | 0.7 ± 4.1 | 0.4 ± 3.3 |

α:δ = 1:10 | 76.5 ± 2.6 | –337.4 ± 48.8 |

α:δ = 1:100 | 78.2 ± 2.3 | –374.1 ± 43.0 |

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**MDPI and ACS Style**

Huang, Q.; Le, J.; Joshi, S.; Mendes, J.; Adluru, G.; DiBella, E.
Arterial Input Function (AIF) Correction Using AIF Plus Tissue Inputs with a Bi-LSTM Network. *Tomography* **2024**, *10*, 660-673.
https://doi.org/10.3390/tomography10050051

**AMA Style**

Huang Q, Le J, Joshi S, Mendes J, Adluru G, DiBella E.
Arterial Input Function (AIF) Correction Using AIF Plus Tissue Inputs with a Bi-LSTM Network. *Tomography*. 2024; 10(5):660-673.
https://doi.org/10.3390/tomography10050051

**Chicago/Turabian Style**

Huang, Qi, Johnathan Le, Sarang Joshi, Jason Mendes, Ganesh Adluru, and Edward DiBella.
2024. "Arterial Input Function (AIF) Correction Using AIF Plus Tissue Inputs with a Bi-LSTM Network" *Tomography* 10, no. 5: 660-673.
https://doi.org/10.3390/tomography10050051