Subject-Specific Low-Field MRI Synthesis via a Neural Operator

Sub ject-Sp ecific Lo w-Field MRI Syn thesis via a Neural Op erator Ziqi Gao 1 , Nic ha Dvornek 1 , 2 , Xiaoran Zhang 1 , Gigi Galiana 1 , 2 , Heman t T agare 1 , 2 , and T o dd Constable 1 , 2 1 Departmen ts of Biomedical Engineering, Y ale Universit y 2 Departmen t of Radiology & Biomedical Imaging, Y ale Univ ersity ziqi.gao@yale.edu Abstract. Lo w-field (LF) magnetic resonance imaging (MRI) impro ves accessibilit y and reduces costs but generally has low er signal-to-noise ra- tios and degraded contrast compared to high field (HF) MRI, limiting its clinical utility . Simulating LF MRI from HF MRI enables virtually ev al- uating nov el imaging devices and developing LF algorithms. Existing lo w field sim ulators rely on noise injections and smo othing, which fails to cap- ture the contrast degradation seen in LF acquisitions. T o this end, we in- tro duce an end-to-end LF-MRI synthesis framew ork that learns HF to LF image degradation directly from a small num b er of paired HF-LF MRIs. Sp ecifically , we introduce a nov el H F to L F co ordinate–image decoupled neural O p erator (H2LO) to mo del the underlying degradation pro cess, and tailor it to capture high-frequency noise textures and dedicated im- age structure. Experimental results in T1w and T2w MRI demonstrate that H2LO pro duces more faithful simulated low-field images than ex- isting parameterized noise synthesis mo del and popular image-to-image translation mo dels. F urthermore, it improv es p erformance in do wnstream image enhancemen t tasks, show casing its p oten tial to enhance LF MRI diagnostic capabilities. Keyw ords: Neural Op erator · Low-field MRI · Image Synthesis · Image Enhancemen t 1 In tro duction Lo w-field (LF) magnetic resonance imaging (MRI) offers improv ed accessibility and reduced cost compared to con ven tional high-field (HF) systems [2, 14, 17, 18, 24], yet generally pro duces images with low er signal-to-noise ratio (SNR), reduced spatial resolution, and diminished tissue contrast [1, 5, 8, 11, 13, 16], lim- iting its clinical utility . Establishing the clinical v alue of nov el LF-MRI devices relies on prosp ectiv e clinical studies [2, 14, 17, 24], whic h t ypically in volv e cohorts ranging from tens to o ver one h undred sub jects. Assembling such v alidation co- horts often takes y ears [2, 14], creating a bottleneck for rapid device developmen t and ev aluation. 2 Gao et al. In-silico retrosp ectiv e analysis [1] offers a complementary strategy to accel- erate prosp ectiv e clinical trials and device developmen t by synthesizing sub ject- sp ecific LF images from publicly a v ailable HF datasets. The HF-to-LF trans- formation can be learned from a small num b er of paired HF–LF scans, whic h are considerably easier to acquire than the large cohorts required for prosp ective v alidation. Arnold et al. prop osed a parameterized noise-and-smo othing mo del that minimizes discrepancies in global histogram features using three sub ject pairs [1]. How ev er, this approach assumes a monotonic intensit y transformation and therefore cannot faithfully capture the non-linear, tissue-specific con trast shifts induced by field strength changes [16]. In particular, differen tial rel axation effects may alter the relative positions of tissue sub peaks (e.g., white matter and gra y matter) within the in tensity distribution, leading to inaccurate anatomical con trast in the synthesized LF images. Consequently , it has limited capacity to represen t broader con trast v ariations across field strengths (Fig. 2(a), second column; (d), purple line). T o capture b oth SNR degradation and con trast changes, we formulate the HF-to-LF transformation as a field-strength–dep enden t transformation of the underlying MR signal and learn it in an end-to-end manner. Although this prob- lem can b e viewed from an image-to-image (I2I) translation p ersp ectiv e [7, 23], HF-to-LF translation differs from conv en tional pixel-level appearance mappings: it requires mo deling how field strength alters the con tinuous spatial signal, in- cluding its frequency conten t and con trast b eha vior. In our experiments, p opular pixel-wise I2I models [7, 23] are unable to simultaneously capture LF textures and accurately mo del contrast changes (3 r d and 4 th columns of Figure 2(a)). Therefore, w e propose a no vel high-frequency preserving 3D neural operator (H2LO), a ligh tw eight co ordinate-based netw ork designed to mo del this transfor- mation while preserving high-frequency structural information, and demonstrate its p erformance on b oth T1w and T2w MRI. Besides LF MRI synthesis, we further demonstrate that H2LO supp orts LF algorithm developmen t as a faithful data augmentation technique. W e consider the LF image enhancement task [13, 8, 11, 4, 9], which aims to transform LF MRI in to HF-like MRI to improv e diagnostic utilit y . W e augment an existing sup er- vised LF image enhancement mo del [13], by simulating LF MRI from another public con ven tional MRI dataset, thereby creating additional LF–HF pairs. In summary , our con tributions are threefold. First, to supp ort virtual clin- ical trials and algorithm developmen t for no vel MRI devices, we introduce the first end-to-end framew ork for LF MRI synthesis. Second, we formulate HF-to- LF translation as an op erator learning problem. Building up on a theoretically b ounded neural op erator architecture [12], H2LO is tailored for preserving high- frequency in 3D volumetric data. Third, we compare H2LO with p opular I2I translation netw orks and an LF sim ulator in terms of b oth synthesis qualit y and do wnstream utilit y , demons trating superior p erformance on T1w and T2w MRI. Sub ject-Sp ecific Lo w-Field MRI Syn thesis via a Neural Op erator 3 Fig. 1. Ov erview of the High-to-Low field Op erator (H2LO) framework. The architec- ture maps HF MRI volumes to a contin uous LF representation using a branch-trunk net work optimized via p oin twise in tensity fidelit y and gradien t regularization. 2 Metho d 2.1 Problem F ormulation Let I H F ∈ R H × W × D and I LF ∈ R H × W × D denote a spatially aligned pair of HF and LF 3D MRI volumes acquired at differen t magnetic field strengths. F rom the p erspective of MRI signal formation, image intensit y dep ends on field- strength–dep enden t relaxation prop erties (e.g., T1 and T2) and SNR c harac- teristics. Changing the magnetic field strength therefore alters the underlying signal resp onse and its spatial frequency b eha vior, rather than merely mo dify- ing v oxel-wise intensities. W e in terpret eac h discretized MRI v olume acquired at field strength E as samples from an underlying contin uous spatial s ignal f E : Ω ⊂ R 3 → R . Sp ecifi- cally , I H F [ i, j, k ] = f H F ( x i,j,k ) , I LF [ i, j, k ] = f LF ( x i,j,k ) , where { x i,j,k } denotes the sampling grid. Under this function-space formulation, HF-to-LF (H2L) translation amounts to learning a field-strength–dep endent op erator T H F → LF : f H F 7→ f LF . Let u := f H F for notation simplicity . W e approximate T H F → LF with a neural op erator G θ suc h that ˆ f LF ( x ) = G θ ( u )( x ) , x ∈ Ω . This operator persp ective models H2L translation as a mapping b et w een function spaces rather than a fixed-grid vo xel regression, aligning the formulation with the con tinuous nature of MR signal formation. 2.2 H2LO: High-to-Low Field Op erator W e parameterize G θ utilizing branch-trunk factorization following DeepONet [12]. T o let lo cal tissue contrast mo dulate the op erator resp onse at each vo xel, w e ex- tend the original form ulation: while DeepONet’s branch co efficien ts are global summaries of the input function, our branch pro duces spatially v arying co effi- cien ts by reading from a dense CNN feature field. The resulting op erator takes the form G θ ( u )( x ) = P X k =1 b k ( u, x ) t k ( x ) + β . (1) 4 Gao et al. where b k ( u, x ) are spatially v arying field co efficien ts, t k ( x ) are co ordinate-dependent basis functions, and β is a learnable bias term. As shown in Fig. 1, our framew ork comprises (1) a branc h netw ork and (2) a trunk netw ork. Br anch network. The branch is a 3D image encoder that maps the input vol- ume to a dense feature field F ( u ) ∈ R P × H × W × D . W e adopt a ligh tw eight 3D con volutional architecture from SRResNet [10]. F or eac h query lo cation x i,j,k , the coefficient vector b ( u, x i,j,k ) ∈ R P is obtained by reading the feature vector at the corresp onding v oxel. This pro duces spatially v arying op erator co efficien ts while requiring only a single enco der forward pass p er volume. T runk network. The co ordinate basis functions t k ( x ) are parameterized by a sin usoidal representation netw ork (SIREN) [19] with four lay ers: one input sine la yer, t wo hidden sine lay ers, and a linear output lay er pro ducing P = 128 out- puts. Each sine lay er computes sin( ω 0 Wx + b ) with SIREN initialization. Sinu- soidal activ ations enable accurate mo deling of high-frequency spatial structures, preserving fine anatomical b oundaries in the synthesized image. 2.3 T raining and Inference The total training loss combines an in tensity fidelity term and a lo cal gradient regularization term: L = L 1 + λ g rad L g rad . The L 1 term enforces zero-order fidelit y ov er N randomly sampled vo xel co ordinates { x n } N n =1 : L 1 = 1 N N X n =1   G θ ( u )( x n ) − f LF ( x n )   . Reconstructing high-fidelity details requires further regularization of the local b eha vior of the learned operator. W e therefore in tro duce a first-order consistency term b y penalizing discrepancies betw een spatial deriv atives of the predicted and target functions o ver randomly cropp ed sub-volumes: L g rad = 1 B B X b =1 X d ∈{ x,y ,z }   ∂ d G θ ( u ) − ∂ d f LF   2 L 2 ( V b ) , (2) where V b ⊂ Ω denotes the b -th randomly sampled sub-volume in a training iteration, B is the num b er of such sub-volumes, and ∂ d denotes differentiation along spatial dimension d . In practice, spatial deriv atives are approximated using first-order deriv ativ es of a 3D Gaussian kernel G σ ( r ) = (2 π σ 2 ) − 3 / 2 exp  − ∥ r ∥ 2 2 σ 2  , with deriv ative filters k d ( r ) = − r d σ 2 G σ ( r ) . The discrete implementation b ecomes L g rad = 1 B B X b =1 X d ∈{ x,y ,z }    ˆ V b ∗ k d − V b ∗ k d    2 F , (3) where ˆ V b and V b denote the predicted and ground-truth sub-v olumes, resp ec- tiv ely , and ∥ · ∥ F denotes the F rob enius norm ov er the discrete vo xel grid. Sub ject-Sp ecific Lo w-Field MRI Syn thesis via a Neural Op erator 5 Gaussian deriv atives pro vide noise-robust and rotationally symmetric gra- dien t estimates suited to low-SNR MRI. Matc hing spatial deriv atives enforces first-order consistency of the op erator output, complementing the zero-order in- tensit y constraint. Once trained, the synthesized LF volume is obtained by ev aluating the learned op erator on the discrete sampling grid: ˆ I LF [ i, j, k ] = ˆ f LF ( x i,j,k ) . 3 Exp erimen ts 3.1 Lo w Field MRI Syn thesis A high-fidelit y HF-to-LF transformation is essen tial for reliable in-silico ret- rosp ectiv e clinical trials for no vel LF device developmen t, where only a small cohort of paired HF–LF scans—compared to the h undreds typically required in prosp ectiv e studie s [14]—is a v ailable to learn the mapping. In this study , w e rigorously ev aluate the synthesis performance of H2LO against related metho ds. Dataset and Metrics. W e train and ev aluate on differen t partitions of the ds006557 dataset [21], which consists of 23 sub jects scanned at b oth high-field (3T GE) and low-field (64mT Hyp erfine) conditions. Both T1w and T2w con- trasts are a v ailable, with one T1w sub ject excluded due to missing data. All v ol- umes are skull-stripp ed using SynthStrip [6] and registered to a common space via ANT s [20], yielding paired v olumes of size 208 × 256 × 256 . Each v olume is nor- malized to [0 , 1] via max normalization. W e perform 5-fold cross-v alidation, with eac h fold using 13-14 sub jects for training, 2 for v alidation, and 7 for testing. Re- construction qualit y is measured using peak signal-to-noise ratio (PSNR, in dB), structural similarit y index (SSIM, in %), and normalized cross-correlation (NCC) b et w een reconstructed and ground-truth images. Additionally , histogram-based metrics are used to assess intensit y-distribution fidelit y , including W asserstein distance (W ASS), histogram NCC (HNCC), Bhattacharyy a distance (BHA T), and Jensen-Shannon (JS) divergence computed from intensit y histograms. F or histogram analysis, only foreground vo xels are included using the ground-truth mask threshold ( I H F > 0 . 01 ). Comparison Metho ds. W e compare our metho d with three categories of ap- proac hes. (1) Image-to-image (I2I) tr anslation , whic h learns a direct mapping b et w een HF and LF MRI v oxels. W e include Pix2Pix [7] and DiffI2I [23] as represen tative GAN-based and diffusion-based mo dels, resp ectiv ely . (2) Physics- inspir e d LF MRI simulation [1], which appro ximates the LF acquisition process through noise mo deling and spatial smo othing k ernels. (3) Conditional implicit neur al r epr esentation (INR) , whic h emplo ys co ordinate-based architectures sim- ilar to ours. Specifically , we adopt the 3D MRI implemen tation from [22], an extension of LI IF [3] designed for volumetric MRI data. Implemen tation. The branch netw ork adopts a light w eight 3D CNN enco der [10] with five conv olutional la y ers (k ernel size 3 3 , channels 32–32–64–64–128) with ReLU activ ations, whic h pro duces a spatially-resolved feature map of dimension P = 128 . The trunk net work is a 4-la yer SIREN MLP (width 256, ω 0 = 30 ) that 6 Gao et al. maps normalized 3D co ordinates to P basis function v alues. F or L 1 , N is set to 8000. F or L g rad , w e set σ = 1 . 0 with a 5 × 5 × 5 k ernel based on h yp erparameter searc h on v alidation sets and B is set to 1. W e train for 500 ep o c hs using A dam with an initial learning rate of 10 − 4 and cosine annealing to 10 − 6 . 3.2 Lo w Field MRI Enhancemen t In this study , we examine the downstream utility of H2LO as a data engine for LF MRI enhancement, show casing its ability to supp ort LF algorithm developmen t. W e use an existing public HF dataset and simulate corresponding LF MRI using our trained HLFO. Generated HF-LF pairs thereby augment sup ervised LF MRI enhancemen t mo dels. Datasets and Metrics. The HF dataset is prepro cessed 3T images from Open- neuro ds005752 [15], which con tains 184 sub jects with both T1w and T2w scans. These were split into 147/29 sub jects for train/v alidation using a fixed random seed and an 80/20 partition. F or eac h sub ject, LF counterparts for eac h HF structural MR volumes were generated (T1w and T2w a v ailable), with a typical v oxel grid size of 208 × 256 × 256. All images are intensit y-normalized to [0,1] and skull stripping is applied with SynthStrip. Real LF-HF pairs in ds006557 w ere retained for finetuning (using the training partition men tioned in Section 3.1) and ev aluation (using the testing partition). Comparison Metho ds. (1) R e al LF and Conventional Data A ugmentations : T o increase data v ariation while preserving in tensity consistency , we apply ran- dom paired in-plane augmen tations (axial H,W flip and 90 ° rotations) to LF-HF training patches and k eep the depth axis unc hanged. (2) Synthetic (Pr e)tr aining and R e al LF Finetuning : W e generate syn thetic LF inputs from pretrained HF- to-LF mo dels including ours and comparison metho ds listed in Section 3.1. Implemen tations. The PF-SR architecture [13] was adopted as the backbone net work. Since the present task fo cuses on same-resolution enhancement rather than sup er-resolution, the 3D sub-pixel conv olution upsampling mo dule was re- mo ved. The final output is obtained via vo xel-wise addition of the predicted residual and the original LF input. Pretraining w as conducted on syn thetic LF– HF image pairs with matched contrast, following the training proto col describ ed in [13]. The mo del was subsequently fine-tuned on real LF–HF pairs using the same backbone and optimizer configuration. During fine-tuning, a cosine decay learning rate schedule was emplo yed, with an initial learning rate of 2 × 10 − 6 , a 4-ep o c h warm-up phase starting from 0 . 5 × the base learning rate, and a min- im um learning rate of 5 × 10 − 7 . Exp eriments are conducted on NVIDIA H200, A100 and R TX A5000 GPUs. 4 Results 4.1 Lo w Field MRI Syn thesis W e present our main results of synthesis p erformance in T ab. 1 and Fig. 2(a) and (d). F rom T ab. 1, our method consisten tly achiev es the b est p erformance Sub ject-Sp ecific Lo w-Field MRI Syn thesis via a Neural Op erator 7 (c) (d) (b) (a) Fig. 2. Visualization of generated LF MRIs and ablation studies. (a) Generated T1w (upp er rows) and T2w (low er ro ws) LF images using multiple metho ds. Ev en ro ws visualize the absolute differences b et ween simulated and real LF images. (b) Ablation of m ultiple comp onen ts in our mo del. (c) T esting results of the 5-fold ablation study . (d) Comparison of histograms for LF images generated by Arnold et al. [1] and our metho d. T1 Method PSNR(dB) ↑ SSIM(%) ↑ NCC ↑ W ASS ↓ HNCC ↑ BHA T ↓ JS ↓ Param. HF Image 23.52 ± 0.44 89.96 ± 0.34 0.9222 ± 0.0035 0.1211 ± 0.0107 0.5130 ± 0.0436 0.2148 ± 0.0218 0.1495 ± 0.0130 – Arnold et. al. [1] 14.97 ± 1.16 87.80 ± 1.56 0.9466 ± 0.0069 0.1099 ± 0.0103 0.5759 ± 0.0423 0.1009 ± 0.0231 0.0823 ± 0.0160 4 Pix2Pix [7] 26.46 ± 0.33 92.25 ± 0.27 0.9561 ± 0.0032 0.0403 ± 0.0046 0.8302 ± 0.0530 0.0448 ± 0.0106 0.0358 ± 0.0080 4.86M DiffI2I [23] 27.16 ± 0.54 92.50 ± 0.83 0.9609 ± 0.0054 0.0330 ± 0.0046 0.9028 ± 0.0145 0.0364 ± 0.0065 0.0287 ± 0.0047 16.39M Conditional INR [22] 27.59 ± 0.33 93.90 ± 0.32 0.9650 ± 0.0029 0.0327 ± 0.0031 0.8642 ± 0.0132 0.0426 ± 0.0055 0.0342 ± 0.0043 0.85M Ours 28.98 ± 0.27 94.76 ± 0.22 0.9749 ± 0.0017 0.0288 ± 0.0049 0.9294 ± 0.0141 0.0218 ± 0.0068 0.0186 ± 0.0057 0.58M T2 Method PSNR(dB) ↑ SSIM(%) ↑ NCC ↑ W ASS ↓ HNCC ↑ BHA T ↓ JS ↓ Param. HF Image 24.36 ± 0.28 90.14 ± 0.35 0.8059 ± 0.0090 0.0583 ± 0.0017 0.4818 ± 0.0479 0.1759 ± 0.0103 0.1442 ± 0.0081 – Arnold et. al. [1] 23.43 ± 0.15 90.42 ± 0.44 0.8297 ± 0.0061 0.1094 ± 0.0030 0.0415 ± 0.0269 0.3626 ± 0.0108 0.2709 ± 0.0067 4 Pix2Pix [7] 25.45 ± 0.28 91.42 ± 0.46 0.8611 ± 0.0095 0.0259 ± 0.0031 0.9609 ± 0.0124 0.0212 ± 0.0043 0.0180 ± 0.0036 4.86M DiffI2I [23] 26.88 ± 0.23 92.33 ± 0.36 0.8937 ± 0.0074 0.0364 ± 0.0037 0.9017 ± 0.0203 0.0486 ± 0.0056 0.0430 ± 0.0049 16.39M Conditional INR [22] 27.80 ± 0.37 93.78 ± 0.43 0.9147 ± 0.0065 0.0260 ± 0.0022 0.8729 ± 0.0491 0.0504 ± 0.0145 0.0439 ± 0.0119 0.85M Ours 28.37 ± 0.38 94.29 ± 0.48 0.9257 ± 0.0064 0.0244 ± 0.0050 0.9458 ± 0.0094 0.0221 ± 0.0027 0.0205 ± 0.0024 0.58M T able 1. Quantitativ e results of LF MRI synthesis. The mean ± standard deviation across five-fold cross-v alidation are rep orted. The b est and second-b est metho ds are highligh ted in b old and underline, resp ectiv ely . across almost all metrics for b oth T1 and T2 contrasts. F or T2 synthesis, Pix2Pix ac hieves the b est results in part of the histogram-related statistics. Ho wev er, the Pix2Pix column in Fig. 2(a) shows that its visual results exhibit unnatural grid- lik e artifacts (which also o ccur in DiffI2I), and suc h artifacts are not desirable for high-fidelity retrosp ectiv e studies on nov el devices. F rom the same figure, w e can also observe that our metho d ac hieves the highest visual alignment with real LF images. F rom Fig. 2(a), Conditional INR pro duces ov erly smo othed LF images, while Arnold et al. sim ulate noise patterns but fail to prop erly mo del con trast changes, as reflected in the histogram comparison in Fig. 2(d). In con- trast, our method main tains both strong quantitativ e performance and more visually coheren t and anatomically faithful results. 8 Gao et al. T1 T2 Method PSNR(dB) SSIM(%) PSNR(dB) SSIM(%) Sub jects Ep och Real LF 30.12 92.93 29.26 92.61 13 200 Flip & Rotate 29.49 92.06 28.50 91.98 13 (*8) 400 Arnold et. al. [1] 30.37 93.48 29.39 92.75 13+147 150+50 Pix2Pix [7] 30.39 93.77 29.59 93.17 13+147 150+50 DiffI2I [23] 30.27 93.33 29.52 93.01 13+147 150+50 Conditional INR [22] 30.10 92.97 29.34 92.97 13+147 150+50 Ours 30.55 93.71 30.02 93.72 13+147 150+50 T able 2. Quantitativ e result of LF MRI enhancemen t augmented with synthetic data. The best and second-b est methods are highlighted in b old and underline, resp ectively . 4.2 Lo w Field MRI Enhancemen t T able 2 summarizes the enhancemen t p erformance under differen t data aug- men tation strategies. In tensity-preserving conv en tional augmentation (flip & ro- tation) do es not improv e p erformance ov er real-only training, indicating that simple transformations are insufficient to comp ensate for limited LF data. In con trast, incorp orating synthetic LF images consistently maintains or improv es p erformance. Comparison across synthesis metho ds suggests that effective LF mo deling requires b oth contrast and noise degradation mo deling. Arnold et al. primarily sim ulate noise, providing texture cues but lacking accurate contrast mo deling. Conditional INR captures contrast shifts but pro duces ov erly smo oth results with limited noise characteristics. By mo deling b oth contrast changes and noise degradation, our metho d ac hieves the b est result for both T1w and T2w MRI. 4.3 Ablation Study The ablation results for T1 synthesis are shown in Fig. 2(b)–(d). Visual compar- isons in Fig. 2(b) indicate that the high-frequency gradien t loss ( L f req ) impro ves lo cal detail reconstruction and yields sharp er LF textures. Histogram analysis in Fig. 2(b) and (d) further shows that incorp orating SIREN enhances con trast mo deling and contributes to finer structural representation. Quantitativ e results are rep orted in Fig. 2(c). Interestingly , ours w/o. SIREN ac hieves the highest PSNR and SSIM, while the full mo del ranks second. Ho wev er, visual insp ection sho wn in Fig. 2(b) suggests that the full mo del b etter preserves subtle anatomical details and pro duces more realistic LF characteristics. 5 Conclusion and F uture W ork W e present H2LO, a neural op erator–based framework for sub ject-sp ecific low- field MRI syn thesis from high-field acquisitions. By formulating HF-to-LF trans- lation as an op erator learning problem, H2LO captures contrast shifts and high- frequency texture changes induced by field strength v ariation. Exp erimen ts on T1w and T2w MRI demonstrate impro ved syn thesis fidelit y ov er con ven tional Sub ject-Sp ecific Lo w-Field MRI Syn thesis via a Neural Op erator 9 sim ulators and representativ e image-to-image translation mo dels. Moreov er, syn- thetic LF images generated by H2LO enhance downstream LF image enhance- men t p erformance, supp orting its use for virtual clinical ev aluation and algo- rithm dev elopment in emerging low-field MRI systems. A limitation of this study is that it includes only healthy sub jects. While this enables controlled ev aluation, generalization to pathological cases remains to b e established, as lesions or atrophy ma y alter the HF-to-LF mapping. F uture w ork will extend the framework to clinical cohorts with diverse pathologies. In addition, the study is conducted on a limited num ber of paired sub jects, reflect- ing curren t data av ailability and aligning with virtual clinical trial settings. T o ensure metho dological robustness, we mitigate the limited sample size through 5-fold cross-v alidation. F uture work will v alidate the prop osed metho d on larger and more div erse cohorts as such data b ecome av ailable. References 1. 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