Predicting Multiomics Histopathology Features with Surface Parameterizations

Kai Huang; Zhong-Heng Tan; Wenlong Yu; Xiaowei Wang; Yan Ding; Shihui Xu; Zaozao Chen; Yi Zhang; Yun Liu; Wen-Wei Lin; Tiexiang Li; Shing-Tung Yau; Zhongze Gu

doi:10.1016/j.eng.2025.07.026

Engineering ›› 2026, Vol. 63 ›› Issue (8) :338 -351. DOI: 10.1016/j.eng.2025.07.026

Research

research-article

Predicting Multiomics Histopathology Features with Surface Parameterizations

Kai Huang ^a^,^#
, Zhong-Heng Tan ^b^,^c^,^g^,^#
, Wenlong Yu ^f
, Xiaowei Wang ^f
, Yan Ding ^f
, Shihui Xu ^e
, Zaozao Chen ^a^,^e
, Yi Zhang ^h
, Yun Liu ^h^,^*
, Wen-Wei Lin ^c^,^g
, Tiexiang Li ^b^,^c^,^g^,^*
, Shing-Tung Yau ^d^,^*
, Zhongze Gu ^a^,^*

Author information +

History +

PDF (5818KB)

Abstract

To improve patient stratification and therapeutic response prediction in computational pathology, clinical-grade decision-making has been enhanced by deep learning models, including those used for microsatellite instability (MSI) prediction and molecular subtype classification. However, prior models and training settings have been largely based on the natural image domain, which differs from histopathology data. To mitigate the inductive bias, we introduced surface parameterization, a geometric mapping from the surface to a suitable domain, to transform whole slide images into fixed-sized squares using conformal energy minimization (CEM) and stretch energy minimization (SEM) algorithms. These transformations are tissue-perceptive, enhancing the region of interest (e.g., cancerous areas) to improve model performance. For example, our method improved MSI prediction, achieving an area under the receiver operating characteristic curve (AUROC) of 0.87 for CEM and SEM with a reduced training set, compared with 0.70 for original slides. To validate its clinical applicability, we analyzed consensus molecular subtype (CMS) classification in 17 colorectal cancer (CRC) patients, with concordance rates of 47.1% (CEM) and 41.2% (SEM), outperforming the original slides (29.4%). As a proof-of-concept, we also linked CMS calls to organoid morphology, demonstrating that cystic organoids were more strongly associated with CMS3. This phenotypic feature may be integrated into CMS and used to improve the evaluation of tissue differentiation. Overall, our method provides new insight into the data processing of computational pathology and demonstrates the performance of state-of-the-art (SOTA) in multiomics prediction.

Graphical abstract

Keywords

Surface parameterization / Colorectal cancer / Consensus molecular subtype / Patient-derived organoids

Cite this article

Download citation ▾

Kai Huang, Zhong-Heng Tan, Wenlong Yu, Xiaowei Wang, Yan Ding, Shihui Xu, Zaozao Chen, Yi Zhang, Yun Liu, Wen-Wei Lin, Tiexiang Li, Shing-Tung Yau, Zhongze Gu. Predicting Multiomics Histopathology Features with Surface Parameterizations. Engineering, 2026, 63 (8) : 338-351 DOI:10.1016/j.eng.2025.07.026

登录浏览全文

4963

注册一个新账户忘记密码

1. Introduction

Colorectal cancer (CRC) is the third most commonly diagnosed malignancy globally and the second leading cause of cancer-related death [1]. Novel precision markers for diagnosis and prognosis have been used to stratify patients with early-stage CRC to refine the configuration of adjuvant therapy [2]. Histological markers stained on embedded and sectioned samples provide information, that is, information on tumor aggressiveness, patient prognosis, and therapeutic vulnerability, and thus have been translated into clinical decisions [3]. In particular, applications of artificial intelligence (AI) in histopathology have enhanced the pipeline to automate diagnostic tasks, predict outcomes and responses, and infer molecular alterations [4]. For example, deep learning can predict microsatellite instability (MSI) [5,6] and the consensus molecular subtype (CMS) [7] from hematoxylin and eosin (H&E)-stained CRC histology slides. To achieve clinical-grade performance, a large-scale multicentric evaluation of more than 13 000 CRC patients from 16 cohorts was performed to infer biomarkers, for example, MSI, B-type Raf kinase (BRAF), and Kirsten rat sarcoma viral oncogene homolog (KRAS), using a transformer-based preditor [8]. Therefore, initiatives for collecting ever larger and well-curated histopathology datasets require advances in training strategies and algorithmic frameworks, for example, self-supervised learning (SSL) and vision transformers [9]. Furthermore, foundation models that are trained with SSL have been scaled for slide-level learning (e.g., GigaPath [10]) to capture both local and global patterns across whole slides, attaining state-of-the-art (SOTA) performance in cancer subtyping and mutation prediction. However, such foundation models are usually trained on proprietary slides and are accessible only to well-funded groups with sufficient graphics processing units (GPUs) [8,10,11]. A hybrid backbone composed of convolutional neural network (CNN) and transformer networks, termed CTransPath [12], was trained on publicly available datasets, that is, the Cancer Genome Atlas (TCGA) and pathology AI platform (PAIP), which took approximately 250 h with 48 Nvidia V100 GPUs. To reduce the memory overhead, data-efficient clustering-constrained-attention multiple-instance learning (CLAM) [13] was proposed, which combines attention-based pooling aggregation and instance-level clustering to refine the feature space. This strategy could achieve decent performance when trained on smaller subsets, which depends on the specific task.

Despite these advances, there are challenges in building generalizable models that could be deployed for real-world clinical applications. One limitation is the domain shift between natural images and histopathology data, which is characterized by a long-tailed distribution of histological structures and a restricted scale of the region of interest and color space [11]. The majority of data augmentation approaches for patches involve stain normalization [14,15] to mitigate institution-specific bias without changing the geometric morphology or area of the cellular or tissue architecture. However, confounding image sections of histopathological slides, that is, background (BACK), debris (DEB), normal tissue areas, and cancerous areas, may be suboptimal configurations for training because the tissue of interest is normally the cancerous area, which is scarce, and nontumor cells receive too much attention from the model [16]. This inner-tissue class imbalance is heterogeneous among slides, especially those characterized by rare histological subtypes, such as neuroendocrine carcinoma and mucinous adenocarcinoma in CRC [17]. To overcome this tissue-specific long-tail distribution, morphology-based data normalization approaches are required to optimize the feature space. In addition, few articles address how such AI tools can be effectively employed in the context of translational research, particularly to integrate histological morphology with molecular subtypes of clinical tumor tissues and their in vitro culture, for example, patient-derived organoids (PDOs) [3].

Here, we report a surface parameterization-based method to modify the histological morphology of a CRC at the minimal expense of angular distortion and area distortion, namely, conformal energy minimization (CEM) [18] and stretch energy minimization (SEM) [19] algorithms (see Fig. 1(a) and Section 2 for details). A surface parameterization is a function that maps a complicated surface into another shaped domain (e.g., a unit disc or a unit square), constructing one-to-one correspondence between the surface and the shaped domain [18], [19], [20]. The geometry operation is highly suitable for handling intricate geometric structures while simplifying the task, for instance, brain tumor segmentation [21]. For irregular shapes such as those found in pathology slides, this operation can be viewed as a means of data normalization, harmonizing significant pixel and tissue category variations across slides into a suitable domain and facilitating neural network feature extraction (Figs. 1(b) and (c)). We therefore collected 1802 whole slide images (WSIs) from 573 patients according to the CRC subtyping consortium (CRCSC) [22] and transformed them into square-shaped images using CEM and SEM. We examined the impact of various transformation sizes and downsampling factors on the MSI classification task and predicted multiomics histopathology features of CRC (e.g., BRAF and KRAS mutations) using the optimized settings (Fig. 1(d)). We found that the transformed slides obtained using either CEM or SEM outperformed the original slides on most prediction tasks, with significant improvement in terms of the area under the receiver operating characteristic curve (AUROC). For example, for MSI classification, an improvement of 17% in the AUROC was attained using CEM and SEM compared with the original slides. This transformation has also been demonstrated to be generalizable to other computational pathology challenges, that is, non-small cell lung cancer (NSCLC) and renal cell carcinoma (RCC) classification and lymph node classification in breast cancer (CAMELYON17), suggesting a generic methodology that could be embedded into the standard computational pathology pipeline (Fig. 1(e)).

To achieve clinical-grade translation, we recruited 17 CRC patients, including 13 individuals who underwent surgical procedures and 4 individuals who underwent biopsy procedures; predicted their CMS calls from the transformed slides; and found that at best, 40% concordance could be achieved according to bulk RNA sequencing. As a proof-of-concept, we cultured CRC PDOs in vitro to explore the association between histopathology and the heterogeneous morphology of PDOs using CMS. We classified the PDOs into cystic and solid subtypes via image-based profiling and assigned them to the CMS, with more cystic organoids accounting for the CMS3 subtype. In summary, our proposed method could achieve SOTA performance in predicting multiomics histopathology features of CRC and could be utilized to bridge the gap between CRC histopathology and organoid morphology by decoding the molecular subtypes.

2. Material and methods

Surface parameterization is a geometric mapping technique that transforms a given surface into a suitable domain, often used in computational geometry, graphics, and biomedical imaging [20]. It involves mapping a complex surface, such as a histopathology slide, onto a structured, fixed-size representation while minimizing distortions in angles (conformal mapping) or areas (area-preserving mapping). By employing CEM and SEM, surface parameterization enhances the preservation of local structures, thereby improving downstream computational tasks such as classification and multiomics prediction.

2.1. Details of conformal map and area-preserving map

Let $ \Omega=\{(x, y)\} \in \mathbb{R}^{2} and \Omega^{\prime}=\{(u, v)\} \in \mathbb{R}^{2}$ be two domains on the two-dimensional (2D) plane, respectively, where $ (x, y)$ and $ (u, v)$ represent the coordinates of the points in Ω and Ω′, respectively. Let f be a map from the source domain Ω to the target domain Ω′, satisfying $ f(x, y)=(u, v)$. A conformal map satisfies Cauchy–Riemann equations

(1)$ \frac{\partial u}{\partial x}=\frac{\partial v}{\partial y}, \frac{\partial u}{\partial y}=-\frac{\partial v}{\partial x}$

From Eq. (1), the Jacobian matrix of f can be written as

$ \begin{array}{l}J_{f}=\left[\begin{array}{cc}\frac{\partial u}{\partial x} & \frac{\partial u}{\partial y} \\\frac{\partial v}{\partial x} & \frac{\partial v}{\partial y}\end{array}\right]=\left[\begin{array}{cc}\frac{\partial u}{\partial x} & -\frac{\partial v}{\partial x} \\\frac{\partial v}{\partial x} & \frac{\partial u}{\partial x}\end{array}\right]=\left[\begin{array}{cc}a & -b \\b & a\end{array}\right], \text { with } a \\=\frac{\partial u}{\partial x}=\frac{\partial v}{\partial y}, b=\frac{\partial v}{\partial x}=-\frac{\partial u}{\partial y}\end{array}$

which means that the map f is a composite of rotational and scaling transformation, thereby guaranteeing the angle invariant up to the conformal map. Intuitively, a conformal map preserves the local shape of the domain but scales the local size, since $ \operatorname{det}\left(J_{f}\right)=a^{2}+b^{2} $ is not a constant on Ω (Figs. S1(a) and (b) in Appendix A). In practice, the conformal map can be obtained by solving the least square problem of Eq. (1), for example,

$ f^{*}=\underset{f}{\operatorname{argmin}} E_{\mathrm{C}}(f):=\frac{1}{2} \int_{\Omega}\left(\frac{\partial u}{\partial x}-\frac{\partial v}{\partial y}\right)^{2}+\left(\frac{\partial u}{\partial y}+\frac{\partial v}{\partial x}\right)^{2} \mathrm{~d} \sigma$

where dσ represents the area element on the domain Ω. The least square term E_C(f) is also referred to as the conformal energy; hence, this computational approach is termed CEM [18,23].

On the other hand, an area-preserving map has a constant Jacobian determinant, for example,

(2)$\operatorname{det}\left(J_{f}\right)=c(\text { constant })$

The Jacobian determinant is typically conceptualized as a local area ratio between Ω′ and Ω. Eq. (2) implies that the scaling of the map f is the uniform among the entire domain Ω. Consequently, an area-preserving map guarantees local size invariance, yet it distorts shapes due to the fact that Eq. (1) are not satisfied (Fig. S1(c) in Appendix A). In practice, the area-preserving map can be obtained by solving the optimization problem [19].

$ f^{*}=\underset{f}{\operatorname{argmin}} E_{\mathrm{S}}(f):=\int_{\Omega} \operatorname{det}\left(J_{f}\right)^{2} \mathrm{~d} \sigma$

Given that the area of the target domain Ω′ is fixed, the resulting map f∗ is area-preserving according to the Euler-Lagrange equation [24]. The term E_Sf is referred to as the stretch energy; hence, this computational approach is termed SEM [19].

In practice, the entire transformation includes: ① delineating a minimal convex region encompassing the tissue; ② determining the dimension of the transformation; and ③ locally deforming the convex region into squares of the specified size.

The minimum convex region includes all the pixels of the target tissue, which can be detected and extracted automatically. In practical computations, we extend the tissue by 100 pixels (approximately 1% of the image size) on the left, right, top, and bottom directions, respectively, due to the relatively large conformal/area-preserving distortions near the region boundary in the subsequent CEM/SEM procedure.

The CEM optimization problem is solved by the quasi-Newton method (BFGS) [23] with the initial guess being a harmonic map f, which satisfies Δf=0 with a Dirichlet boundary condition. In addition, the SEM optimization problem is solved by the fixed-point iteration [19] with the initial guess being the map resulting from CEM or the harmonic map. The convergence criteria of both CEM and SEM are that the difference between the results of two consecutive iterations is less than 10^-5. The computational complexity of both CEM and SEM is O(kn²), where k is the number of the iteration (generally less than 100) and n is the number of the vertices in the target region. Despite their iterative nature, these transformations are computationally efficient and can be executed on standard personal computers. The algorithms achieve convergence within reasonable time frames even for moderately complex geometries.

2.2. Patch classification and multiomics prediction for whole slides

The whole pipeline includes: data preprocessing, patch feature extraction, and feature aggregation that yields the prediction. In the data preprocessing step, we segmented, partitioned, and stain-normalized the patches according to the standard pipeline of histolab [25]. Some bad patches, for example, with artifacts or few foreground objects, were filtered. For patch classification, we used the pre-trained CTransPath [12], a hybrid backbone composed of CNN and transformer networks, to extract patch features with representations of dimension 768 for every patch, followed by a linear head for binary classification. For whole-slide prediction, we merged all patch embeddings of one slide into a transformer-based aggregation module to yield the prediction [8]. Briefly, the module transformed the input embeddings of dimension 768 to 512 through a linear projection followed by the ReLU activation, and added a class token to the input, that was passed to the transformer block. After the patch fusion through multi-headed self-attention, the output class token of size 1 × 512 was passed to a multilayer perceptron (MLP) head to yield the prediction.

For experimental setup, we used the Adam optimizer [26] with learning rate of 0.001. The number of epochs was set at 10 and the batch size was 128 for patch classification and 1 for whole-slide prediction.

In the generalization performance test, the training configuration of the patch encoder was slightly different. The dimension of each patch embedding was 768 for CTransPath [12] and CONCH [27], 1536 for Prov-GigaPath [10], and 1024 for UNI [28]. We used the Adam optimizer with learning rate of 0.0001. All experiments were carried out using four Nvidia V100 GPUs.

2.3. CRC tissue classification

We trained the CRC tissue classifier with NCT-CRC-HE-100 K and CRC-VAL-HE-7 K datasets, previously reported by Kather et al. [29]. The NCT-CRC-HE-100 K contained 100 000 patches of 224 × 224 pixels at 0.5 µm per pixel from 86 H&E-stained slides, and the CRC-VAL-HE-7 K consisted of 7180 patches from 50 H&E-stained slides. Each patch was labelled by one of nine tissue classes: adipose (ADI), BACK, DEB, lymphocytes (LYM), mucus (MUC), smooth muscle (MUS), normal colon mucosa (NORM), cancer-associated stroma (STR), and colorectal adenocarcinoma epithelium (TUM). We augmented these patches by random-resize, horizontal-flip, and vertical-flip before feeding into a ResNet34 model [30]. The model was fine-tuned using an Adam optimizer with one-cycle scheduler and maximum learning rate of 0.01. The number of epochs was set at 10 and the batch size was 64. The final validation accuracy was 0.91.

2.4. Bulk RNA sequencing

Total RNA was isolated from each CRC tissue sample using RNAmini kit (Qiagen, Germany). RNA quality was examined by gel electrophoresis and with Qubit (Thermo Fisher Scientific, USA). For RNA sequencing, strand-specific libraries were constructed using the TruSeq RNA sample preparation kit (Illumina, USA), and sequencing was carried out using the Illumina Novaseq 6000 instrument. The raw data was handled by Skewer and data quality was checked by FastQC (v0.11.2). Clean reads were aligned to the human genome hg38 using spliced transcripts alignment to a reference (STAR). The expression of the transcript was calculated by fragments per kilobase of exon model per million mapped reads (FPKM) using Perl.

2.5. Ethics

All CRC patients were recruited from the First Affiliated Hospital of Nanjing Medical University and the patients and derived organoids information have been summarized in Table S1 in Appendix A. the study was approved by the Ethics Committee of the First Affiliated Hospital of Nanjing Medical University (ethics approval number: 2024-SRFA-684). All patients gave written informed consent before tumor surgery and biopsy were performed.

2.6. CRC tissue processing and organoid culture

Upon receiving the surgical or biopsy samples, they were divided into three portions: one for bulk RNA sequencing, one for H&E staining, and the remaining one was cut into soybean shaped granules of 3-5 mm³ and washed with 1× phosphate-buffered saline (PBS) three to four times with 3% penicillin/streptomycin (Gibco, USA). Then, the tissue was minced and added to 1 mL PBS, then to transferred into a 15 mL centrifugal tube. The tissue fragments were then digested with Collagenase II (5 mg∙mL⁻¹; Solarbio, China) and Y-27632 (10 μmol∙L^-1; MCE, USA) for 20-40 min at 37 °C before embedding into Matrigel. Pipet the digested tissue onto a 100 μm strainer on a 50 mL plastic tube and transfer the solution to a fresh 15 mL centrifugal tube, which then been centrifuged at 1500 r·min⁻¹ at 4 °C for 5 min. After aspirating the supernatant, wash pellet three times with 10 mL PBS. Then the pellet was resuspended in 30 μL Matrigel and solidified in a prewarmed 24-well plate at 37 °C for 20 min. Carefully add 500 μL expansion medium supplemented with 10 μmol∙L^-1 Y-27632 to each well and return the plate to the incubator. The expansion medium contained advanced Dulbecco’s modified eagle medium F12 (ADMEM/F12; Gibco) with penicillin/streptomycin, 10 mmol∙L^-1 4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid (HEPES; Gibco), GlutaMAX (Gibco), B-27 supplement (Gibco), 100 ng∙mL⁻¹ recombinant Noggin (PeproTech, USA), 1 mmol∙L^-1 N-acetylcysteine (Sigma-Aldrich, USA), 10 mmol∙L^-1nicotinamide (Sigma-Aldrich), 10 μmol∙L^-1 SB202190 (Sigma-Aldrich), 50 ng∙mL⁻¹ epidermal growth factor (EGF; Gibco), 500 nmol∙L^-1 A8301 (Tocris Bioscience, UK), and 10 nmol∙L^-1 prostaglandin E2 (PGE2; MCE).

For organoid passaging, flush the organoids with 1 mL ice-cold PBS per well and transfer to a 15 mL centrifugal tube. Centrifuge the organoids at 1500 r·min⁻¹ at 4 °C for 5 min and remove supernatant. The organoids were then digested with 1 mL TrypLE (Gibco) and pipetted up and down for 1 min, and then centrifuged at 1500 r·min⁻¹ at 4 °C for 5 min. Wash the pellet again using 1 mL PBS and remove supernatant. Resuspend pellet with 30 μL Matrigel per well in a prewarmed 24 well plate. When the Matrigel has polymerized for 30 min, 500 μL expansion medium described above was added.

2.7. CMS calls from CMS classifier

We derived CMS calls from CMS classifier [22] as the ground truth for concordance validation. The FPKM-formatted expression data was log-scaled and subjected to the CMS classifier based on a random forest (RF) predictor. We used RF nearest CMS as the ground truth for Sankey diagrams (networkD3, v0.4). External datasets, Farin et al. [31] (n = 28), Kim et al. [32] (n = 12), and Cho et al. [33] (n = 87), were gathered to validate the association between CMS calls and organoid morphologies. Fisher’s exact test was used to assess specific morphological features (e.g., cystic vs non-cystic) across CMS groups. All tests were two-sided, and p values less than 0.05 were considered statistically significant (Table S2 in Appendix A).

2.8. Image-based profiling identifies organoid morphological subtypes

We classified the organoids into cystic and solid subtypes by image-based profiling [34]. Briefly, one image would be labelled as “cystic” if more than 90% of the organoids in the field of view exhibited monolayered and hollow structures, and as “solid” subtype if the aggregated or grape-shaped organoids. All images were captured with Olympus IX83 inverted microscope and cellSens Dimension v1.18 platform (Olympus Corporation, Japan).

2.9. Code and data availability

Detailed information on code and data availability can be found in Appendix A.

3. Results

3.1. Data-efficient transformation for patch classification

We tested our method on the MSI prediction task in randomly selected whole slides from the curated CRCSC cohort (Fig. 2(a), Table S3 in Appendix A). The slides were transformed with CEM and SEM (see Section 2 for details) separately and partitioned into 256 × 256 patches before CTransPath [12] training. We initially investigated the impact of varying transformation sizes on performance through two distinct approaches. The first approach involved maintaining variable image dimensions within the dataset, which were adjusted according to the dimensions of the original slides. We averaged the dimensions of images of different sizes in the dataset and labeled them lv1-4. (Fig. 2(b)). The second approach entailed scaling image dimensions across all slides to a uniform size, ranging from 15 000 to 30 000 pixels (Fig. 2(c)). We evaluated the patch-level classification accuracy (ACC) for both approaches using five-fold cross-validation. For each fold, we randomly partitioned the dataset into a training set (90% of the cases) and a validation set (10% of the cases), which were dependent on each transformation. To explore the data efficiency of our method, we sampled subsets of the training set, accounting for 60% and 20% of the data in the variable-dimensional dataset and 60% and 30% of the data in the fixed-dimensional dataset of the total cases during cross-validation.

We found a moderate improvement in model performance on lv1 and lv2 after applying CEM and SEM compared with that of the slides before transformation. However, no improvement was observed for lv3 and lv4, with the of lv4 actually decreasing by approximately 8% and 10% with CEM and SEM, respectively (Fig. 2(b)). We further confirmed the same observation using two additional models, namely attentionmil [35] and transformer [8] (Figs. S2(a) and (b) in Appendix A). The model’s performance decreases as the image size increases, regardless of the proportion of the training set used. Therefore, we next compared the ACCs of the two transformations at four image size levels (Fig. 2(d), Figs. S2(b) and (c) in Appendix A). We indeed found that the model’s performance decreases level-dependently, with this effect being more pronounced with 60% and full training sets. However, the ACC of lv2 reached 93.51% with only the 20% training set and 95.17% with the 60% dataset for CEM transformation. We also noted that with smaller subsets of the training set, the AttentionMIL and transformer could achieve satisfactory performance (ACC > 90%), demonstrating that our method is data efficient.

We noted that CEM and SEM transformation worked especially well with lv2 (Figs. 2(b) and (d)), likely due to the consistent image dimensions in this group, which are approximately 20 000 pixels. This conclusion is based on the assumption that the consistency of image dimensions accounts for the results. To test our hypothesis, we further explored the transformations with fixed image sizes (Figs. 2(c) and (e)). Interestingly, the performance of both CEM and SEM exceeded that of the original slides across all image sizes when the full training set was used. Compared with CEM, SEM showed marginally reduced performance on smaller subsets, for example, 30% of the training set, relative to the original slides (Fig. 2(c)). The inverse relationship between the fixed image size and model performance, regardless of the percentage of the training set, is also obvious (Fig. 2(e)). We compared the ACC of different models based on CEM/SEM transformation and original slides under the full training set and confirmed the necessity of image dimension consistency for robust performance (Table S4 in Appendix A).

We next conducted experiments to assess the performance of different downsampling scales under CEM and SEM transformation using 5× and 10× factors (Fig. 2(f), Fig. S2(c)). Owing to the need to downsample images prior to transformation, the number of effective pixels in intermediate images produced at different scales varies, which can lead to discrepancies in model performance. Overall, the ACC with a 10× downsampling factor was slightly inferior to that with a 5× downsampling factor, regardless of the transformation size or the proportion of the training set (Fig. 2(f)). This is reasonable given that a smaller downsampling scale preserves more effective pixels in the intermediate images, thereby minimizing distortion during the subsequent upsampling process after transformation. In addition, CEM transformations outperformed SEM transformations under most settings of fixed image size, especially with the 30% training set, which may be attributed to the conformal properties of CEM. Overall, we demonstrated that both image transformation methods could achieve SOTA classification performance on the MSI prediction task while also offering a data-efficient approach to reduce memory overhead.

3.2. Surface parameterization facilitates tissue component control

One benefit of surface parameterization is the ability to convert an irregular manifold domain to a shaped domain (e.g., a disc or a square), which is important because many numerical solutions to problems in irregular manifolds are infeasible. For example, irregular inputs, such as noise, outliers, or unconventional patterns, may cause the predictions of the neural network to become unstable and unreliable. For complex medical image processing tasks, various surface parameterization-based methods have been introduced. For example, an optimal mass transportation (OMT) algorithm has been proposed to convert an irregular three-dimensional (3D) brain image to a cube while maintaining minimal deformation [21,36]. One of the advantages of OMT is its ability to selectively expand the brain tumor region, thereby enabling the model to better perceive the region of interest.

To investigate the tissue ratio of CRC whole-slide images after CEM and SEM transformation, we trained a tissue component classifier with public datasets of NCT-CRC-HE-100 K and CRC-VAL-HE-7 K [29], with each tile labeled as one of nine possible tissue classes: ADI, BACK, DEB, LYM, MUC, MUS, NORM, STR, and TUM (Fig. S3(a) in Appendix A). We classified each partitioned tile of the original slides, transformed the images into one of nine categories, and calculated the proportion of tiles for each category as the tissue ratio (Figs. S3(b)-(j) in Appendix A). As the fixed image size increased, the proportion of all tissue categories (TISSUE) other than the BACK decreased, whereas the proportion of BACK increased. Moreover, for transformed images, the proportion of TISSUE was consistently greater and the proportion of BACK was consistently lower than those of the original slides. This demonstrated that the transformation process enlarged the tissue component and that a smaller transformation size corresponded to a larger expansion ratio, regardless of whether CEM or SEM was used (Figs. 2(g) and (h)). We also compared the ratios of TISSUE and BACK for transformations with a downsampling factor of 10× and observed a similar trend (Fig. S3(k) in Appendix A). Additionally, compared with 5×, the BACK ratio was greater and the TISSUE ratio was lower at 10×, which corresponded to the accuracy performance of the models under the two downsampling factors (Fig. 2(f), Fig. S3(l) in Appendix A). In summary, using a trained tissue classifier, we obtained the variations in tissue proportions before and after transformation. This demonstrated that our method can enhance tissue areas, thereby facilitating better model cognition and learning of the region of interest.

3.3. Transformer-based multiomics prediction for CRC whole slides

To validate our method in a larger dataset and connect high-resolution pathology images with multiomics aberrations, we collected 1802 WSIs from 573 CRC patients according to the CRCSC, including information on sex, disease stage, MSI status, KRAS/BRAF mutation, and CMS subtyping, for each case (Fig. S4(a) and Table S5 in Appendix A). Because smaller image sizes can elicit improved model performance, we transformed these slides into fixed size images of 5000 × 5000 pixels using CEM and SEM and partitioned them into patches before feeding them into a transformer-based feature extractor. To predict multiomics aberrations, we adopted a fully transformer architecture to extract features using pretrained weights of CTransPath [12] and aggregated features within one slide into final predictions in a weakly supervised framework (Fig. 3(a)). Our multiomics prediction pipeline included three kinds of tasks: single biomarker inference (e.g., KRAS/BRAF mutation prediction), multiple subtype classification (e.g., CMS subtyping), and survival outcome prediction (e.g., patient overall survival (OS) and progression-free intervals (PFIs)) (Fig. 3(a)). We used the AUROC and the area under the precision recall curve (AUPRC) as metrics to assess the models’ performance to avoid bias introduced by imbalanced datasets of target biomarkers [8]. The cross-validation and data splitting strategies remained consistent with the patch-level classification.

We found that the transformed images obtained by either CEM or SEM outperformed the original slides on most prediction tasks. For example, for BRAF mutation inference, the AUROC of the held-out validation set reached 0.90 ± 0.007 and 0.90 ± 0.010 after CEM and SEM transformation, respectively, surpassing the original value of 0.83 ± 0.035 (Fig. 3(b)). Additionally, for KRAS mutation inference and MSI status prediction, the AUROC reached 0.83 ± 0.017 and 0.84 ± 0.014, and 0.87 ± 0.008 and 0.87 ± 0.015 for CEM and SEM, respectively, representing improvements of 4% and 17% compared with the original slides (Figs. 3(c) and (d)). Our results could exceed or attain parity with the SOTA performance of Wagner et al. [8] and Tsai et al. [37]. We noted a high AUPRC score of over 0.95 for MSI prediction, either by CEM or SEM transformation, despite a class imbalance of 14.5% MSI-high samples in the CRCSC dataset (Fig. 3(d), Fig. S4(a)). Moreover, the AUPRCs of the BRAF/KRAS prediction improved by approximately 16.4% and 8.8% compared with those of the original slides, especially for a strong class imbalance of 10.1% mutated BRAF within the dataset (Figs. 3(b) and (c), Fig. S4(a)).

To test the data efficiency, we truncated the patches of each slide to sizes of 5000, 1000, and 300 (on par with CEM and SEM) and tested their AUROCs in single biomarker prediction (Figs. S4(b) and (c) in Appendix A). No significant performance increase was observed when the number of patches used was even increased from one-tenth to the full amount. For example, the AUROC of the MSI prediction was 0.70 with a patch size of 300, whereas it was 0.73 with a patch size of 5000 (origin_lv0, Fig. S4(b)). We noted that the transformation equalized the histogram of the patch count with normal distributions compared with long-tailed distributions of the original slides (Fig. S4(c)). We also performed CRC tissue category classification on the transformed cohort and calculated the average proportion of each category (Fig. 3(e)). Obviously, the proportion of BACK was reduced by approximately half after undergoing CEM or SEM transformation, from 60% to 30%. The ratio of the TUM component significantly increased from 16.5% to 25.4% for CEM and to 22.3% for SEM algorithms (Fig. 3(e)).

Because CEM and SEM transform the original slides into smaller squares, we aimed to investigate the differences between directly downsampling the original slides and performing transformations. This helps eliminate the confounding effects of downsampling on model performance. We performed three-level sampling of pyramid-like slides, namely, lv0-2, ranging from up to 80 000 patches per slide at lv0 to 350 patches at lv2 (Fig. S4(c)). Although the AUROCs for single biomarker prediction increased with increasing sampling level, they still presented relative differences, for instance, of 4.4% and 4.2%, compared with those of the CEM and SEM techniques (Fig. 3(f)). This discrepancy may be attributed to the long-tail distribution of patches derived from the original slides (Fig. S4(c)). Although the patch numbers at lv2 are quite close to those of CEM and SEM, the patch distributions for CEM and SEM more closely resembled a normal distribution, facilitating feature scaling and stable training. We also visualized the clustering patterns of extracted features per slide and found that the feature clustering at lv0 was relatively dispersed; however, by lv2, it became more aggregated, resembling the patterns observed in CEM and SEM (Fig. S4(d) in Appendix A).

For multiple subtype classification, we conducted experiments to correlate histopathology patterns with the CpG island methylator phenotype (CIMP), which is characterized by extensive hypermethylation of promoter CpG island regions, leading to the silencing of multiple tumor suppressor genes [38]. The AUROCs for CIMP-high, CIMP-low, and CIMP-negative samples exceeded those of the original samples after CEM and SEM by approximately 14%, 3%, and 8%, respectively (Fig. S5(a) in Appendix A). For survival outcome prediction, we adopted Weibull modeling [37,39] to predict the disease-free interval (DFI), disease-specific survival (DSS), OS, and PFI. Both transformations could significantly identify two prognostic groups with log-rank tests in the held-out validation set (Figs. S5(b) and (c) in Appendix A). In summary, we conducted multiomics prediction on the CRCSC dataset and validated the SOTA performance and data efficiency of our method. Additionally, we disentangled the confounding effects with direct downsampling from the original slides.

3.4. Surface parameterization is generalizable to other pathology classification challenges

To demonstrate the algorithm as a generic methodology, we transformed the pathology slides from TCGA-NSCLC, TCGA-RCC, and CAMELYON17 datasets via CEM and SEM and evaluated the classification performance (Figs. S6(a)-(c) in Appendix A). The TCGA-NSCLC dataset consists of lung squamous cell carcinoma (TCGA-LUSC) and lung adenocarcinoma (TCGA-LUAD) datasets, covering a total of 400 formalin-fixed paraffin-embedded (FFPE) slides. TCGA-RCC data were collected for the classification of kidney chromophobe renal cell carcinoma (TCGA-KICH), kidney renal clear cell carcinoma (TCGA-KIRC), and kidney renal papillary cell carcinoma (TCGA-KIRP), and comprise 520 FFPE slides. The CAMELYON17 dataset was used for classifying the lymph node metastases of breast cancer at the slide level, including macrometastases, micrometastases, isolated tumor cells, and negative samples, comprising 482 slides. We found that the transformed slides surpassed the original slides in terms of AUROC scores when the CTransPath patch encoder was used (Fig. S6(d) in Appendix A). For example, the mean AUROC values of CEM and SEM are 0.71 and 0.72 for NSCLC but 0.65 for the original slides (5000 patches). We benchmarked other patch encoders against the datasets, including CONCH [27], Prov-GigaPath [10], and UNI [28] (Figs. S6(e)-(g) in Appendix A). The overall performance has improved significantly, especially for NSCLC and RCC, with minimal differences observed among CEM, SEM, and the original slides, presumably attributed to the foundation model’s unsupervised representation learning at scale. Notably, for CAMELYON17, the AUROC score of the original slides outperformed that of CEM and SEM and increased with an increasing number of patches, except for the CTransPath encoder (Fig. S6(d)-(g)). This suggested that the model’s performance is also influenced by specific datasets and patch encoders.

We also compared the proposed method with StainGAN normalization [40] against the TCGA-NSCLC, TCGA-RCC, and CAMELYON17 datasets using the CTransPath patch encoder (Table S6 in Appendix A). We found that the StainGAN-based color normalization achieved only limited improvements compared with the CEM/SEM transformation, demonstrating the superiority of our approach.

3.5. CMS prediction and mapping relationship with CMS classifier-based calls

CMS stratification was first proposed by Guinney et al. [22] and has been widely used for the molecular subtyping of CRC on the basis of RNA expression, including CMS1 (14%, MSI immune), CMS2 (37%, canonical), CMS3 (13%, metabolic), and CMS4 (23%, mesenchymal). Some image-based profiling has been reported to infer CMS calls from histological slides, such as imCMS [7,41], a cost-effective tool that is used to associate complex tissue patterns with molecular phenotype.

For our pipeline of multiple subtype classification, we also predicted the CMS phenotype for the transformed images and original slides (Figs. 4(a) and (b), Fig. S7(a) in Appendix A). The results revealed that the mean AUROCs of CEM and SEM were 0.80 and 0.75, respectively, surpassing the original value of 0.62 and attaining parity with the classification performance of the imCMS tested on the TCGA cohort [7] (AUROC scores: 0.81 at 3× and 0.80 at 12× magnification, p = 0.058). The imCMS classifier reached an AUROC of 0.84 on the TCGA test set through domain adversarial training, which was proposed to mitigate inherent biological heterogeneity with a low ratio of CMS1 cases.

To investigate the context of real-world clinical translation for image-based CMS calling, we recruited 17 CRC patients, including 13 surgical patients and 4 biopsy patients (Table S1), and predicted their CMS calls from the transformed images and the original slides. We scanned a total of 25 digital slides and calculated the component ratio using the trained tissue classifier. The results revealed that the proportion of BACK in the transformed images was reduced by approximately half, and the MUS component was significantly increased, particularly with the SEM algorithm (Fig. S7(b) in Appendix A).

Before making predictions, we first validated the concordance of the CMS classifier [22], which was used as the ground truth, with the CRCSC reports (Fig. S7(c) and Table S5 in Appendix A)). In the CRCSC, the characteristics of CMS were also heterogeneous, with a low ratio of CMS1 (13.3%) and CMS3 (12.6%) (Fig. S4(a)). This is consistent with the reported clinical molecular features. For example, CMS1 lesions were frequently diagnosed in right-sided lesions, whereas CMS2 lesions were more common in left-sided lesions (Fig. S7(d) and Table S7 in Appendix A). We also conducted a Cox proportional hazards analysis on the CRCSC and found that CMS4 represented a worse PFI (CMS4 vs CMS2, hazard ratio (HR): 1.651, p = 0.017; CMS4 vs CMS3, HR: 2.092, p = 0.018; Table S8 in Appendix A). However, in terms of OS and recurrence-free survival (RFS), CMS4 does not have a significant adverse effect on prognosis, as reported by Guinney et al. [22]. This finding may be attributable to the CRCSC lacking adequate external cohorts. We assigned more cases classified by the RF model with a lower posterior probability than the single-sample predictor (SSP), for example, 80.3% concordance could be achieved by the RF model (Fig. S7(c)).

We next compared the concordance of the CMS calls for the transformed images and the original slides from the CRC patients using the RF model. The average concordance of five-fold cross validation reached 32.9% for CEM and 35.3% for SEM, outperforming the original slides of 19.1% (Fig. 4(c)). Regarding the best fold, the concordance reached 47.1% for the CEM and 41.2% for the SEM (Fig. 4(d)). This finding suggested that our method could promote the concordance of CMS calls under validation of the CMS classifier.

3.6. Associations between CMS and derived organoid morphological subtypes

Histological differentiation leads to morphological variation in in vitro organoids, along with the evolution of key pathways, molecular subtypes, and lineage factors, which has been proven by, for example, pancreatic ductal adenocarcinoma [42] and gastroenteropancreatic neuroendocrine neoplasms [43]. As a proof-of-concept, we cultured CRC organoids from 17 patients to explore the relationships between CMS and the morphological subtypes of the organoids (Figs. 5(a) and (b)). Our previous work reported two morphological subtypes of CRC organoids, namely, the cystic and solid subtypes, using image-based profiling [34]. Here, we used the same pipeline to classify the organoids into these two subtypes and assigned them to the expression-based CMS calls using the RF model (Fig. 5(c)). We found that solid organoids were frequently observed in CMS1 (75%), CMS2 (60%), and CMS4 (100%), whereas cystic subtypes were more commonly associated with CMS3 (100%) (p = 0.029, Fisher’s exact test; Fig. 5(d), Table S2). To further validate our findings, we collected external metadata from Farin et al. [31] (n = 28), Kim et al. [32] (n = 12), and Cho et al. [33] (n = 87), which comprised CRC organoids with diverse morphologies and their CMS calls. Similarly, the solid subtypes were predominantly concentrated in CMS1, CMS2, and CMS4, whereas cystic organoids were primarily observed in CMS3 (Figs. 5(e)-(j), Table S2). CMS3 is typically characterized by metabolic dysregulation and precursor lesions of tubular adenoma [44]. It has been reported that those organoids derived from well-differentiated adenoma or adenocarcinoma maintain monolayered cystic structures lined with a single lumen [45]. However, poorly differentiated or undifferentiated adenocarcinomas exhibit grape-shaped solid types without epithelial polarity [17]. We also noted that partial cystic organoids were observed in CMS2 (40% in Fig. 5(d), 10% in Fig. 5(f), 16% in Fig. 5(h), and 5% in Fig. 5(j)), featuring activated Wnt signaling and the canonical adenoma-carcinoma route [44]. The association between Wnt activity and CRC cystic organoids has been discussed. For example, extrinsic mitogen-activated protein kinase kinase (MEK) inhibitors can induce the reorganization of cystic organoids by upregulating Wnt signaling and intestinal stemness signatures [34,46,47], which is reminiscent of quiescent or slow-cycling revival stem cells [48]. It has been reported that such revival-like stem cells can form spheroid organoids after helminth-induced injury [49] or upon exposure to fibroblast-derived prostaglandin E2 (PGE2) [50] and macrophage-derived transforming growth factor (TGFB1) [51], which adapt to suboptimal niches and are resistant to chemotherapy. However, cell-intrinsic oncogenic mutations may dominate colonic stem cell differentiation over stromal cues [52], especially for single adenomatous polyposis coli (APC) mutations in wild-type colon organoids harboring strictly cystic morphologies [53]. Moreover, those organoids from oncogenic mutations, for example, APC and KRAS, best align with CMS2 [52,54], suggesting that the cystic organoids observed here may reflect critical mutation drivers for CRC initiation. This morphological plasticity of organoids may serve as a potential biomarker for CRC stratification and prognosis. In summary, we have incorporated new organoid phenotypic features into the traditional CMS classification, which reflects in vivo histological traits.

4. Discussion

CRC typically results from a series of histological and molecular changes that transform normal epithelia into adenoma and even carcinoma [55]. Organoids recapitulate in vivo histological characteristics and molecular alterations [3]. Even for some rare cases, for example, neuroendocrine carcinoma and mucinous adenocarcinoma [17], organoids can reproduce the histological features of clinical samples while retaining specific markers. During histological differentiation, the morphology of an organoid changes from a glandular and cystic shape, corresponding to well-differentiated tissue, to a discohesive and solid shape of poorly differentiated tissue [3]. Therefore, organoid morphology could serve as an indicator of in vivo histopathology that has been underexplored. Drug-induced phenotypic profiling of CRC organoids revealed a drug mechanism of action, linking cystic morphology with leucine-rich repeat-containing G-protein coupled receptor 5 (LGR5) stemness [47]. However, some exogenous factors [34] or the extracellular matrix [56] may affect the morphology of organoids, which is unfavorable for bona fide reconstitution of tumor histopathology. Therefore, in addition to essential cellular components, such as stromal or immune cells, a minimal context of niche factors is required to calibrate the culture conditions. Farin et al. [31] constructed an organoid-stroma biobank to assess therapeutic responses to the CMS4 subtype. They reported that factor-reduced medium and cancer-associated fibroblasts (CAFs) could restore subtype-specific (CMS2 and CMS4) transcriptomic features. Interestingly, the reported CMS concordance between primary tissues and derived organoids was only 16.6%, whereas it increased to 46.6% after organoid xenotransplantation, demonstrating the essential role of CAFs in maintaining the subtype-specific tumor microenvironment. Therefore, the current CMS stratification method for CRC organoids is insufficient for recapitulating the histopathology of primary tissue and may require the integration of morphological subtypes of organoids. We propose that cystic or solid organoids preferentially occupy different CMS subtypes (Figs. 5(c)-(j)), which could assist in evaluating tissue differentiation quality. In addition, several novel classification methodologies have been proposed, including intrinsic epithelial status (I), microsatellite status (M), and presence of fibrosis (F), termed “IMF” classification [57]; pathway-derived subtypes (PDSs) [58]; and colorectal cancer prognostic subtypes (CRPSs) [59]. However, the relationships between these methodologies and the morphological subtypes of organoids require further validation through molecular experiments, including single-cell sequencing technologies, particularly to explore intratumoral heterogeneity.

On the other hand, inferring molecular alterations from histology, particularly high-resolution digital pathology slides, has become commonplace. Deep learning or machine learning can capture subtle patterns from slides that experts may not recognize to execute tumor grading, predict therapy outcomes, and infer biomarker mutations [4], [5], [6], [7], [8], [9], [10], [11], [12], [13]. For example, imCMS serves as a cost-effective tool to associate complex tissue patterns with the CMS phenotype [7,41]. Our proposed transformation pipelines could predict the CMS calls with an improvement in concordance compared with the original slides (Fig. 4(d)). However, one limitation of our study is the relatively small number of clinical samples available for evaluation. The restricted sample size may reduce the statistical power and generalizability of the findings, especially when evaluating performance across diverse CMS subtypes or integrating multimodal data. This may also hinder the ability to assess the model’s performance robustly in real-world clinical scenarios. Future studies incorporating larger, multi-institutional datasets with broader clinical representations will be essential to fully validate and refine the proposed approach.

In this work, we employed surface parameterization to transform irregular tissues into regular squares using conformal maps and area-preserving maps. The conformal map can preserve the local shape of the tissues while scaling the local size. Therefore, the partitioned square patches on the transformed tissue correspond to square domains of different sizes in the original image. Compared with the traditional approach, the conformal map can further capture multiscale information, which enhances the predictive performance. On the other hand, the area-preserving map preserves the local size while distorting the local shape. Hence, the partitioned patches correspond to the anisotropic domains (e.g., prisms, rectangles, and parallelograms) in the original image. These geometrically diverse patches provide richer training data compared to traditional approaches, further improving model performance.

However, two limitations warrant investigating further. The first is that the surface parameterizations induce greater distortions near the boundary of the transformed domain, particularly in the nonconvex domain. To mitigate this issue, we search an extended convex domain to reduce the distortion of the tissue domain. However, for tissues with highly nonconvex shapes, this approach results in many invalid pixels, resulting in computational inefficiency with limited practical improvement. The second limitation is how to control the scale of the conformal map and the anisotropy of the area-preserving map. Theoretically, a conformal map is uniquely determined for given source and target domains. Hence, there is no flexibility in manually adjusting local scaling. A potential solution is to relax the conformal map to allow user-controlled scaling. On the other hand, the area-preserving map is not unique, and the anisotropy is not currently controlled. Therefore, incorporating anisotropy constraints into the SEM procedure to achieve more desirable transformations will be a focus of our future work.

During patch classification and multiomics prediction, many tasks can achieve the performance of a full training set using only 60% or even 20% training data, which is important for rare case classification and clinical outcome prediction [11,13]. The data-efficient property of our algorithm enables accurate predictions even with sparse training data, which can be synergistically combined with micro/nanomotors and biomimetic nanorobots for real-time, in situ diagnostics [60], [61], [62], [63], [64]. This integration is especially promising for edge-computing-based clinical applications, allowing rapid decision-making and reducing reliance on large-scale centralized data processing. In addition, the long-tailed distribution of histological structures and restricted scale of the region of interest, for example, cancerous tissue or cancer-associated stroma, could be reconciled by the transformation, bridging the gap between the inductive biases of learning algorithms and the data distribution for computational pathology. We noted that the transformation equalized the histogram of the tissue ratio and patch count, despite the absence of any tailored designs, demonstrating that our method is self-adapted to the pathology domain. Furthermore, although variations in tissue preparation, staining, and scanning are known confounding factors, the consistent performance of our method across heterogeneous datasets, such as the TCGA-NSCLC, TCGA-RCC, and CAMELYON17 datasets, suggests that the proposed approach is robust to such domain shifts to a certain extent. Nonetheless, future work incorporating explicit domain adaptation may further enhance its generalizability. This generalizability has also been validated across different patch encoders, that is, CONCH, Prov-GigaPath, and UNI (Fig. S6). Future research will reveal that the transformation may further improve performance, especially for foundation models, thereby becoming a standard data processing technique in computational pathology pipelines.

References

Publishing order | Descend order by publishing year | Descend order by cited within

[1]	Siegel RL, Wagle NS, Cercek A, Smith RA, Jemal A. Colorectal cancer statistics, 2023. CA Cancer J Clin 2023;73:233-54.

[2]	Skrede OJ, De Raedt S, Kleppe A, Hveem TS, Liestøl K, Maddison J, et al. Deep learning for prediction of colorectal cancer outcome: a discovery and validation study. Lancet 2020; 395:350-60.

[3]	Fujii M, Sekine S, Sato T. Decoding the basis of histological variation in human cancer. Nat Rev Cancer 2024; 24:141-58.

[4]	Shmatko A, Ghaffari Laleh N, Gerstung M, Kather JN. Artiﬁcial intelligence in histopathology: enhancing cancer research and clinical oncology. Nat Cancer 2022; 3:1026-38.

[5]	Kather JN, Pearson AT, Halama N, Jäger D, Krause J, Loosen SH, et al. Deep learning can predict microsatellite instability directly from histology in gastrointestinal cancer. Nat Med 2019; 25:1054-6.

[6]	Yamashita R, Long J, Longacre T, Peng L, Berry G, Martin B, et al. Deep learning model for the prediction of microsatellite instability in colorectal cancer: a diagnostic study. Lancet Oncol 2021; 22:132-41.

[7]	Sirinukunwattana K, Domingo E, Richman SD, Redmond KL, Blake A, Verrill C, et al. Image-based consensus molecular subtype (imCMS) classiﬁcation of colorectal cancer using deep learning. Gut 2021; 70:544-54.

[8]	Wagner SJ, Reisenbüchler D, West NP, Niehues JM, Zhu J, Foersch S, et al. Transformer-based biomarker prediction from colorectal cancer histology: a large-scale multicentric study. Cancer Cell 2023; 41:1650-61.

[9]	Song AH, Jaume G, Williamson DFK, Lu MY, Vaidya A, Miller TR, et al. Artiﬁcial intelligence for digital and computational pathology. Nat Rev Bioeng 2023; 1:930-49.

[10]	Xu H, Usuyama N, Bagga J, Zhang S, Rao R, Naumann T, et al. A whole-slide foundation model for digital pathology from real-world data. Nature 2024; 630:181-8.

[11]	Vorontsov E, Bozkurt A, Casson A, Shaikovski G, Zelechowski M, Severson K, et al. A foundation model for clinical-grade computational pathology and rare cancers detection. Nat Med 2024; 30:2924-35.

[12]	Wang X, Yang S, Zhang J, Wang M, Zhang J, Yang W, et al. Transformer-based unsupervised contrastive learning for histopathological image classiﬁcation. Med Image Anal 2022; 81:102559.

[13]	Lu MY, Williamson DFK, Chen TY, Chen RJ, Barbieri M, Mahmood F. Data-efﬁcient and weakly supervised computational pathology on whole-slide images. Nat Biomed Eng 2021; 5:555-70.

[14]

Macenko M, Niethammer M, Marron JS, Borland D, Woosley JT, Guan X, et al. A method for normalizing histology slides for quantitative analysis. In: Proceedings of the 2009 IEEE International Symposium on Biomedical Imaging: From Nano to Macro; 2009 Jun 28-Jul 1; Boston, MA USA. Piscataway, NJ: IEEE; 2009. p. 1107-10.

[15]	Vahadane A, Peng T, Sethi A, Albarqouni S, Wang L, Baust M, et al. Structure-preserving color normalization and sparse stain separation for histological images. IEEE Trans Med Imaging 2016; 35:1962-71.

[16]	Reasat T, Sushmit A, Smith DS. Data efﬁcient contrastive learning in histopathology using active sampling. MLWA 2024; 17:100577.

[17]	Fujii M, Shimokawa M, Date S, Takano A, Matano M, Nanki K, et al. A colorectal tumor organoid library demonstrates progressive loss of niche factor requirements during tumorigenesis. Cell Stem Cell 2016; 18:827-38.

[18]	Yueh MH, Lin WW, Wu CT, Yau ST. An efﬁcient energy minimization for conformal parameterizations. J Sci Comput 2017; 73:203-27.

[19]	Yueh MH, Lin WW, Wu CT, Yau ST. A novel stretch energy minimization algorithm for equiareal parameterizations. J Sci Comput 2019; 78:1353-86.

[20]	Floater MS, Hormann K. Surface parameterization:a tutorial and survey. In: Dodgson NA, Floater MS, Sabin MA, Berlin, Heidelberg: Springer; 2005. p. 157-86.

[21]	Lin WW, Juang C, Yueh MH, Huang TM, Li T, Wang S, et al. 3D brain tumor segmentation using a two-stage optimal mass transport algorithm. Sci Rep 2021; 11:1-19.

[22]	Guinney J, Dienstmann R, Wang X, de Reyniès A, Schlicker A, Soneson C, et al. The consensus molecular subtypes of colorectal cancer. Nat Med 2015; 21:1350-6.

[23]	Kuo YC, Lin WW, Yueh MH, Yau ST. Convergent conformal energy minimization for the computation of disk parameterizations. SIAM J Imaging Sci 2021; 14:1790-815.

[24]	Tan ZH, Li T, Lin WW, Yau ST. n-Dimensional volumetric stretch energy minimization for volume-/mass-preserving parameterizations. arXiv:2402.00380.

[25]	Colling R, Pitman H, Oien K, Rajpoot N, Macklin P, Group C-PA in HW, et al. Artiﬁcial intelligence in digital pathology: a roadmap to routine use in clinical practice. J Pathol 2019; 249:143-50.

[26]	Kingma DP, Ba J. Adam: a method for stochastic optimization. arXiv:1412.6980.

[27]	Lu MY, Chen B, Williamson DFK, Chen RJ, Liang I, Ding T, et al. A visual-language foundation model for computational pathology. Nat Med 2024; 30:863-74.

[28]	Chen RJ, Ding T, Lu MY, Williamson DFK, Jaume G, Song AH, et al. Towards a general-purpose foundation model for computational pathology. Nat Med 2024; 30:850-62.

[29]	Kather JN, Krisam J, Charoentong P, Luedde T, Herpel E, Weis CA, et al. Predicting survival from colorectal cancer histology slides using deep learning: a retrospective multicenter study. PLoS Med 2019; 16:e1002730.

[30]	He K, Zhang X, Ren S, Sun J. Deep residual learning for image recognition. arXiv:1512.03385.

[31]	Farin HF, Mosa MH, Ndreshkjana B, Grebbin BM, Ritter B, Menche C, et al. Colorectal cancer organoid-stroma biobank allows subtype-speciﬁc assessment of individualized therapy responses. Cancer Discov 2023; 13:2192-211.

[32]	Kim SC, Park JW, Seo HY, Kim M, Park JH, Kim GH, et al. Multifocal organoid capturing of colon cancer reveals pervasive intratumoral heterogenous drug responses. Adv Sci 2022; 9:e2103360.

[33]	Cho EJ, Kim M, Jo D, Kim J, Oh JH, Chung HC, et al. Immuno-genomic classiﬁcation of colorectal cancer organoids reveals cancer cells with intrinsic immunogenic properties associated with patient survival. J Exp Clin Cancer Res 2021; 40:230.

[34]	Huang K, Li M, Li Q, Chen Z, Zhang Y, Gu Z. Image-based proﬁling and deep learning reveal morphological heterogeneity of colorectal cancer organoids. Comput Biol Med 2024; 173:108322.

[35]	Ilse M, Tomczak JM, Welling M.Attention-based deep multiple instance learning. In: Proceedings of the 35th International Conference on Machine Learning; Stockholm, Sweden; 2018 Jul 10-15. Berkly, CA: International Machine Learning Society; 2018. p. 3376-91.

[36]	Lin WW, Lin JW, Huang TM, Li T, Yueh MH, Yau ST. A novel 2-phase residual U-net algorithm combined with optimal mass transportation for 3D brain tumor detection and segmentation. Sci Rep 2022; 12:1-16.

[37]	Tsai PC, Lee TH, Kuo KC, Su FY, Lee TLM, Marostica E, et al. Histopathology images predict multi-omics aberrations and prognoses in colorectal cancer patients. Nat Commun 2023; 14:2102.

[38]	Toyota M, Ahuja N, Ohe-Toyota M, Herman JG, Baylin SB, Issa JP. CpG island methylator phenotype in colorectal cancer. Proc Natl Acad Sci USA 1999; 96:8681-6.

[39]	Carroll KJ. On the use and utility of the Weibull model in the analysis of survival data. Control Clin Trials 2003; 24:682-701.

[40]	Shaban MT, Baur C, Navab N, Albarqouni S. Staingan: stain style transfer for digital histological images 2018. In:Proceedings of the 2019 IEEE 16th International Symposium on Biomedical Imaging (ISBI 2019); Venice, Italy; 2019 Apr 8-11. Piscataway, NJ: IEEE; 2019. p. 953-6.

[41]	Lafarge MW, Domingo E, Sirinukunwattana K, Wood R, Samuel L, Murray G, et al. Image-based consensus molecular subtyping in rectal cancer biopsies and response to neoadjuvant chemoradiotherapy. npj Precis Oncol 2024; 8:1-11.

[42]	Raghavan S, Winter PS, Navia AW, Williams HL, DenAdel A, Lowder KE, et al. Microenvironment drives cell state, plasticity, and drug response in pancreatic cancer. Cell 2021; 184:6119-37.

[43]	Kawasaki K, Toshimitsu K, Matano M, Fujita M, Fujii M, Togasaki K, et al. An organoid biobank of neuroendocrine neoplasms enables genotype-phenotype mapping. Cell 2020; 183:1420-35.

[44]	Fessler E, Medema JP. Colorectal cancer subtypes: developmental origin and microenvironmental regulation. Trends Cancer 2016; 2:505-18.

[45]	Sato T, Stange DE, Ferrante M, Vries RGJ, Van Es JH, Van den Brink S, et al. Long-term expansion of epithelial organoids from human colon, adenoma, adenocarcinoma, and Barrett’s epithelium. Gastroenterology 2011; 141:1762-72.

[46]	Zhan T, Ambrosi G, Wandmacher AM, Rauscher B, Betge J, Rindtorff N, et al. MEK inhibitors activate Wnt signalling and induce stem cell plasticity in colorectal cancer. Nat Commun 2019; 10:1-17.

[47]	Betge J, Rindtorff N, Sauer J, Rauscher B, Dingert C, Gaitantzi H, The drug-induced phenotypic landscape of colorectal cancer organoids. Na t Commun 2022; 13:1-15.

[48]	Ayyaz A, Kumar S, Sangiorgi B, Ghoshal B, Gosio J, Ouladan S, et al. Single-cell transcriptomes of the regenerating intestine reveal a revival stem cell. Nature 2019; 569:121-5.

[49]	Nusse YM, Savage AK, Marangoni P, Rosendahl-Huber AKM, Landman TA, De Sauvage FJ, et al. Parasitic helminths induce fetal-like reversion in the intestinal stem cell niche. Nature 2018; 559:109-13.

[50]	Roulis M, Kaklamanos A, Schernthanner M, Bielecki P, Zhao J, Kaffe E, et al. Paracrine orchestration of intestinal tumorigenesis by a mesenchymal niche. Nature 2020; 580:524-9.

[51]	Chen L, Qiu X, Dupre A, Pellon-Cardenas O, Fan X, Xu X, et al. TGFB1 induces fetal reprogramming and enhances intestinal regeneration. Cell Stem Cell 2023; 30:1520-37.

[52]	Qin X, Cardoso Rodriguez F, Suﬁ J, Vlckova P, Claus J, Tape CJ. An oncogenic phenoscape of colonic stem cell polarization. Cell 2023; 186:5554-68.

[53]	Geurts MH, Gandhi S, Boretto MG, Akkerman N, Derks LLM, van Son G, et al. One-step generation of tumor models by base editor multiplexing in adult stem cell-derived organoids. Nat Commun 2023; 14:4998.

[54]	Michels BE, Mosa MH, Grebbin BM, Yepes D, Darvishi T, Hausmann J, et al. Human colon organoids reveal distinct physiologic and oncogenic Wnt responses. J Exp Med 2019; 216:704-20.

[55]	Jänne PA, Mayer RJ. Chemoprevention of colorectal cancer. N Engl J Med 2000; 342:1960-8.

[56]	Zhang Y, Tang C, Span PN, Rowan AE, Aalders TW, Schalken JA, et al. Polyisocyanide hydrogels as a tunable platform for mammary gland organoid formation. Adv Sci 2020; 7:2001797.

[57]	Joanito I, Wirapati P, Zhao N, Nawaz Z, Yeo G, Lee F, et al. Single-cell and bulk transcriptome sequencing identiﬁes two epithelial tumor cell states and reﬁnes the consensus molecular classiﬁcation of colorectal cancer. Nat Genet 2022; 54:963-75.

[58]	Malla SB, Byrne RM, Lafarge MW, Corry SM, Fisher NC, Tsantoulis PK, et al. Pathway level subtyping identiﬁes a slow-cycling biological phenotype associated with poor clinical outcomes in colorectal cancer. Nat Genet 2024; 56:458-72.

[59]	Nunes L, Li F, Wu M, Luo T, Hammarström K, Torell E, et al. Prognostic genome and transcriptome signatures in colorectal cancers. Nature 2024; 633:137-46.

[60]	Yan M, Xie L, Tang J, Liang K, Mei Y, Kong B. Recent advances in heterosilica-based micro/nanomotors: designs, biomedical applications, and future perspectives. Chem Mater 2021; 33:3022-46.

[61]	Yan M, Chen Q, Liu T, Li X, Pei P, Zhou L, et al. Site-selective superassembly of biomimetic nanorobots enabling deep penetration into tumor with stiff stroma. Nat Commun 2023; 14:4628.

[62]	Liu T, Xie L, Price CAH, Liu J, He Q, Kong B. Controlled propulsion of micro/nanomotors: operational mechanisms, motion manipulation and potential biomedical applications. Chem Soc Rev 2022; 51:10083-119.

[63]	Liu Y, Xie L, Gao M, Zhang R, Gao J, Sun J, et al. Super-assembled periodic mesoporous organosilica frameworks for real-time hypoxia-triggered drug release and monitoring. ACS Appl Mater Interfaces 2021; 13:50246-57.

[64]	Zeng J, Xie L, Liu T, He Y, Liu W, Zhang Q, et al. Super-assembl ed multilayered mesoporous TiO 2 nanorockets for light-powered space-conﬁned microflu idic catalysis. ACS Appl Mater Interfaces 2024; 16:23484-96.