Diagnostic criteria for RIF patients.

According to the definition of RIF proposed by EHSRE 2023 [12], the transfer of embryos considered viable fails to result in a positive pregnancy test for a given patient and is insufficient to consider further investigation and/or intervention. Considering that the recommended threshold for the cumulative predicted chance of implantation for RIF is 60%, when a couple does not successfully implant by transferring a certain number of embryos and the cumulative predicted chance of implantation associated with that number is greater than 60%, then they should be advised to undergo further investigations and/or treatment options.

For embryos of unknown euploidy [13], RIF is diagnosed in female patients under 35 years old after three or more embryo transfers (ET); for those aged 35 to 39, after four or more ETs; and for those aged 40 and above, after six or more ETs. For embryos with known ploidy status [14], RIF is diagnosed after two or more ETs.

Diagnostic criteria for FI patients.

FI patients are defined as patients who have not previously undergone fresh or frozen embryo transfer.

Inclusion criteria.

Patients met all four following criteria will be included.

• Aged between 21 to 45 years who are undergoing FET;
• Diagnosed as FI or RIF patients;
• Using the hormone replacement treatment (HRT) or a GnRH-a down-regulating hormone replacement protocol for FET endometrial preparation;
• Signing an informed consent form.

Exclusion criteria.

Patients met any one of the following criteria will be excluded.

• Diagnosed as severe primary or secondary conditions in the active phase, or mental disorders;
• Diagnosed with significant, untreated uterine malformations impacting uterine morphology, uterine fibroids exerting pressure on the uterine cavity, or ovarian cysts, as delineated by ultrasound;
• History of malignant neoplasms in any anatomical location;
• Presence of chromosomal abnormalities (excluding chromosomal polymorphisms).

Sample size calculation.

This study is a cross-sectional trial to establish a predictive model for endometrial receptivity and pregnancy outcomes using SVC to predict clinical pregnancy. The ultrasound assessments of uterine arteries and endometrial thickness are crucial for pre-implantation evaluation of endometrial receptivity, a study involving 78 FET patients (resulting in 45 clinical pregnancies, 57.7%) utilized elastic ultrasound imaging and nine predictive indicators based on basic information, achieving a predictive accuracy of 76.92% [15]. Sample size estimation was conducted using “pmsampsize” in R software [16]. According to the definition of RIF, at least two failed ETs were diagnosed as RIF. Assuming a clinical pregnancy rate of 30%, a minimum of 323 RIF patients were required for sample estimation. In a 1:1 ratio, 323 FI patients were also included. The code for sample size calculation is referenced in S1 Fig.

Instrument and collection preparation.

The SAMSUNG Hera-W10 Doppler Ultrasound Diagnostic System, equipped with an EV3-10B vaginal probe operating at 3.3 MHz, will serve as the instrument for ultrasound data acquisition. Patients will be directed to empty their bladders and adopt the lithotomy position. Subsequently, a disposable condom will be placed over the ultrasound probe, which will be evenly coated with ultrasound gel. The probe will then be gently and slowly inserted into the subject’s vagina, aiming to reach the posterior fornix for scanning and measurements. This vaginal ultrasound examination will be performed by a seasoned gynecological ultrasonographer with over ten years of experience.

Ultrasound acquisition patterns and content.

2D ultrasound pattern. In the two-dimensional grayscale mode, measurements of endometrial thickness, endometrial morphology, and endometrial motion will be conducted. Endometrial thickness will be determined by averaging three measurements of the distance between the anterior and posterior myometrium-endometrium interfaces, taken 1 cm from the endometrial apex. Detailed observation of endometrial echogenicity will be conducted, and the endometrium will be categorized into types A, B, and C based on the Gonen criteria [17]. Endometrial wave motion will be observed and documented for three minutes on the longitudinal midline section of the uterus with the probe stabilized and the patient breathing normally. Endometrial motion is classified into positive wave, negative wave, quiescent wave, bidirectional wave, local peristaltic wave according to the Ljland criteria [18].

In the two-dimensional color mode, with the uterus longitudinally bisected along its midline axis, the subendometrial region is demarcated as extending 3mm beyond the endometrial margin. Utilizing two-dimensional color Doppler flow imaging (CDFI), the perfusion of the endometrium and subendometrial areas will be assessed, classifying the flow patterns into Type I, II, and III according to the Applebaum criteria [7]. Subsequently, the CDFI is employed to delineate the uterine sagittal section, orthogonal to the long axis of the uterine cavity, where blood flow measurements are conducted. The color imaging technique is used to visualize the uterine arteries, with the sampling gate sequentially positioned at the cervix, both sides of the corpus, and the junction of the myometrium and endometrium to obtain stable blood flow spectrograms. Measurements are taken only after a minimum of consecutive stable waveforms are observed. The resultant parameters of uterine arterial blood flow encompass the peak systolic velocity (PSV), end diastolic velocity (EDV), time-averaged maximum velocity (TAMV), time-averaged peak velocity (TAPV), mean pressure gradient (PGmean), systolic/diastolic ratio (S/D), resistivity index (RI), and pulsatility index (PI).

The MV-FlOW^™ technology employs advanced clutter filters to evaluate low-velocity blood flow signals. To facilitate MV-FlOW^™ sample acquisition, the sensor is positioned and the imaging adjusted to focus on the endometrium and the uterus, thereby enabling a quantitative assessment of blood perfusion. The Volumetric Index of Microvascularity (VI^MV) is computed automatically as the ratio of blood-filled pixels to the total number of pixels within the region of Interest (ROI; VI^MV = n_blood/n_total). By activating MV-FlOW^™, the operator achieves optimal visualization of the vascular tree. In this study, the ROI encompasses the entire uterus, and the VI^MV is determined by the proportion of endometrial blood flow pixels to the total blood flow pixels within the uterus. The parameters for the MV-Flow on the Hera-W10 system are standardized as follows: Gain at 54; Frame Average set to 8; Output Power at 90; Dynamic Range of 50; Alpha Blending at 70%; Color Map selected as 2; LumiFlow set to 2; Mechanical Index (MI) at 1.3; Thermal Index (TIs) at 0.3; and Depth calibrated to 6 cm.

3D ultrasound pattern. Initiating the power Doppler flow imaging mode, the sensitivity is adjusted to a heightened state to observe the branching patterns of endometrial blood flow. Subsequently, the CrystalVue^™ mode is activated to delineate the endometrial contour, yielding a three-dimensional representation of the uterine endometrium. This process automatically calculates the endometrial volume (EV), the vascularization index (VI), the flow index (FI), and the vascular flow index (VFI).

Data statistics.

Data analysis was conducted using the SAS 9.4 statistical software (SAS Institute, Cary, NC, USA) by an independent statistician. Comparisons between the two groups will be performed as follows. For quantitative data, independent sample t-tests, analysis of variance, or Kruskal-Wallis H tests were employed; for categorical data, chi-square tests or Fisher’s exact probability method were utilized. All statistical analyses are two-sided, with P < 0.05 considered statistically significant.

Clinical prediction model.

Machine Learning Algorithm. In this study, the SVC algorithm was selected for machine learning applications. All computations were executed using the Sklearn package within Python 3.10.

Data Preprocessing. Altogether four steps of data preprocessing were applied in this study. First, we will remove the outliers and organize the data. As for missing value filling, we will conduct KNN Imputer for continuous variables, and Simple Imputer for categorical variables. The Spearman correlation analysis was first conducted to evaluate the relationship between all predictive feature variables and clinical pregnancy outcomes (Spearman’s correlation coefficient more than 0.2 were significant). Eventually, we removed low-variance (Variance Threshold = 0.8) variables and highly correlated variables (r²>0.8).

Prediction Variable Selection. Thereafter, a SVC model was constructed using the remaining feature variables. The filtered feature subset was then input into the established model to rank the feature weights. These weights indicate the contribution of each feature to the determination of the SVC hyperplane. In accordance with the LIBSVM manual, SVC_coef was employed as the feature weight to compute the permutation importance of the features, with the feature exhibiting the maximum value of the mean ± standard deviation being deemed the most valuable predictive indicator.

Model performance evaluation. The dataset for the predictive model was partitioned into a training set and an internal validation set in a 7:3 ratio, with internal validation of the model conducted using cross-validation techniques. The accuracy of the classification results was assessed through the use of a confusion matrix. For binary classification tasks, sample cases can be categorized into four scenarios based on their actual class and the predicted class by the trained model: true positives (TP), false positives (FP), true negatives (TN), and false negatives (FN). The model’s accuracy was evaluated using the precision ratio (P) and recall rate (R). Ultimately, the F1 score was employed to synthesize both precision and recall. Additionally, the model’s performance was evaluated using the receiver operating characteristic (ROC) curve and the area under the curve (AUC).