Observation-Anchored Selective Assimilation for Longitudinal Tumor-State Proxy Forecasting in Post-Treatment Glioma

# Observation-Anchored Selective Assimilation for Longitudinal Tumor-State Proxy Forecasting in Post-Treatment Glioma
Source: [https://arxiv.org/html/2609.12435](https://arxiv.org/html/2609.12435)
Yeonjae JungAffiliation:Department of Software, Yonsei University, Wonju, 26493, Republic of KoreaE\-mail[mshin@yonsei\.ac\.kr](mailto:[email protected])Minwoo Shin††thanks:Corresponding author\.Affiliation:Department of Software, Yonsei University, Wonju, 26493, Republic of KoreaE\-mail[mshin@yonsei\.ac\.kr](mailto:[email protected])

###### Abstract

Post\-treatment MRI in patients with glioma provides serial observations for updating patient\-specific tumor\-state proxy estimates, but variable appearances and trajectories complicate forecasting\. We formulate forecasting as an observation\-aware digital\-twin update in which an intermediate observation anchors the patient\-specific state\. Among 203 patients and 594 follow\-up time points, a predefined no\-new\-treatment criterion retained 120 of 236 candidate triplets, split into 81/24/15 training/validation/test triplets at the patient level\. Each time point was represented by a continuous voxel\-wise tumor\-state proxy map in\[0,1\]\[0,1\]derived from MRI lesion labels\. A SegMamba\-based single\-step forecaster predicted update proposals from multimodal source\-state tensors\. Observation\-Anchored Selective Assimilation \(OASA\) retained the observed intermediate proxy as the state anchor and selectively applied updates through a validation\-selected tiered case\-level rule and voxel\-wise soft gate\. We compared initial\-scan forecasting, rollout without assimilation, latest\-observation persistence, direct prediction, OASA, OASA \+ calibration, and morphological dilation\. Checkpoints, OASA rules, and calibration thresholds were selected using validation data only\. Across three seeds on 15 held\-out test triplets, OASA maintained Dice atτ=0\.2\\tau=0\.2comparable to persistence \(0\.6071±0\.00250\.6071\\pm 0\.0025vs\.0\.60700\.6070\) while yielding numerically higher Dice atτ=0\.5\\tau=0\.5\(0\.4269±0\.00790\.4269\\pm 0\.0079vs\.0\.39810\.3981\), with a small RMSE increase\. Calibration increased Dice atτ=0\.2\\tau=0\.2to0\.6178±0\.00250\.6178\\pm 0\.0025, increased false\-positive \(FP\) support \(11,836→18,66311\{,\}836\\rightarrow 18\{,\}663\), and reduced false\-negative \(FN\) support \(22,107→17,53622\{,\}107\\rightarrow 17\{,\}536\)\. This reflects near\-threshold support calibration rather than improved biological predictive capability\. Code is publicly available at[https://github\.com/jsudg436/longitudinal\-proxy\-forecasting](https://github.com/jsudg436/longitudinal-proxy-forecasting)\.

###### Keywords:

Glioma Longitudinal MRI Digital Twin Tumor\-State Proxy Forecasting Observation\-aware Assimilation

## 1Introduction

Longitudinal post\-treatment MRI in patients with glioma provides repeated patient\-specific observations, but longitudinal tumor\-state proxy forecasting cannot be fully addressed by static lesion segmentation or one\-shot prediction alone\[[13](https://arxiv.org/html/2609.12435#bib.bib1),[17](https://arxiv.org/html/2609.12435#bib.bib2),[18](https://arxiv.org/html/2609.12435#bib.bib3),[8](https://arxiv.org/html/2609.12435#bib.bib4)\]\. Post\-treatment appearances and proxy trajectories may be stable, increasing, decreasing, or non\-monotonic, limiting a single fixed extrapolation rule\. We represent each time point by a continuous voxel\-wise tumor\-state proxy map derived from MRI lesion labels and address longitudinal forecasting of this proxy\.

Prior work on longitudinal tumor prediction, biophysical growth, reaction–diffusion modeling, and MRI synthesis motivates patient\-specific forecasting\[[16](https://arxiv.org/html/2609.12435#bib.bib13),[14](https://arxiv.org/html/2609.12435#bib.bib8),[4](https://arxiv.org/html/2609.12435#bib.bib9),[9](https://arxiv.org/html/2609.12435#bib.bib10),[5](https://arxiv.org/html/2609.12435#bib.bib11),[15](https://arxiv.org/html/2609.12435#bib.bib12),[21](https://arxiv.org/html/2609.12435#bib.bib14),[2](https://arxiv.org/html/2609.12435#bib.bib15)\]\. However, the newly acquired intermediate follow\-up observation has received less attention as an explicit state\-assimilation event in this setting\. Directly predictingt2t\_\{2\}fromt0t\_\{0\}, rolling forecasts forward, or imposing fixed growth or trend priors does not explicitly use the observedt1t\_\{1\}proxy as an updated patient\-specific state from which subsequent forecasting should proceed\.

We formulate this task as an observation\-aware digital\-twin update\. In contrast to broader healthcare digital\-twin work on patient\-specific simulation and treatment modeling\[[7](https://arxiv.org/html/2609.12435#bib.bib16),[12](https://arxiv.org/html/2609.12435#bib.bib19),[3](https://arxiv.org/html/2609.12435#bib.bib20)\], we use the term to denote a state\-estimation cycle that incorporates new follow\-up information, rather than clinical treatment simulation or direct biological tumor\-growth modeling\. We introduce Observation\-Anchored Selective Assimilation \(OASA\), which retains the observed intermediate proxy as the state anchor and selectively applies a model\-predicted update proposal through a validation\-selected tiered case\-level gating rule and a voxel\-wise soft change\-probability gate\. The single\-step forecaster is implemented with a SegMamba\-based 3D encoder–decoder\[[6](https://arxiv.org/html/2609.12435#bib.bib7),[19](https://arxiv.org/html/2609.12435#bib.bib17)\]; the contribution is the assimilation formulation rather than a claim of backbone superiority\.

Our contributions are: \(1\) an observation\-aware formulation for longitudinal tumor\-state proxy forecasting in which the intermediate observation anchors the subsequent forecast; \(2\) OASA, a selective assimilation rule for model\-predicted updates; and \(3\) an evaluation under patient\-level data partitioning using continuous proxy error and proxy\-support overlap atτ=0\.2\\tau=0\.2andτ=0\.5\\tau=0\.5, together with a descriptive characterization of heterogeneous proxy trajectories\. No checkpoint, OASA rule, calibration threshold, or final seed was selected based on held\-out test performance\.

## 2Method

![Refer to caption](https://arxiv.org/html/2609.12435v1/figures/figure1_oasa_pipeline_lr.png)Figure 1:OASA framework\. A shared single\-step forecaster predicts normalized velocity and voxel\-wise change probability from a source\-state tensor\. Thet0→t1t\_\{0\}\\\!\\rightarrow\\\!t\_\{1\}step estimates observation\-innovation MAE, while thet1→t2t\_\{1\}\\\!\\rightarrow\\\!t\_\{2\}step generates a direct update proposal\. OASA uses the predicted\-change fraction, innovation MAE, and voxel\-wise change probability to produce a gated update anchored to the observedt1t\_\{1\}proxy\. Optional validation\-selected calibration adjusts near\-threshold support\.Fig\.[1](https://arxiv.org/html/2609.12435#S2.F1)summarizes the proposed update cycle\. A shared forecaster first produces single\-step update proposals and change probabilities; OASA then uses the observedt1t\_\{1\}proxy, thet0→t1t\_\{0\}\\\!\\rightarrow\\\!t\_\{1\}innovation, and the predicted\-change burden to select a case\-level update tier and apply voxel\-wise gating, followed by optional near\-threshold calibration\.

### 2\.1Tumor\-State Proxy Forecasting

Each forecasting triplet contains observed time points\(t0,t1\)\(t\_\{0\},t\_\{1\}\)and future targett2t\_\{2\}\. A tumor\-state proxy mappt∈\[0,1\]D×H×Wp\_\{t\}\\in\[0,1\]^\{D\\times H\\times W\}, whereD,H,WD,H,Wdenote the three spatial dimensions, was generated at each time pointttfrom glioma labels\[[11](https://arxiv.org/html/2609.12435#bib.bib5),[1](https://arxiv.org/html/2609.12435#bib.bib6)\]\. We assigned weights 0\.7, 0\.4, and 1\.0 to non\-enhancing tumor core, surrounding non\-enhancing/FLAIR abnormality, and enhancing tumor labels, followed by Gaussian smoothing \(σ=1\.0\\sigma=1\.0\), rescaling if the maximum exceeded 1, and clipping to\[0,1\]\[0,1\]\. Cavity voxels were encoded as a separate binary channel\.

For a single forecast from source time pointssto destination time pointdd, the input is the 7\-channel source\-state tensorxs=\[ms,ps,cs,Δ​ts→d\]x\_\{s\}=\[m\_\{s\},p\_\{s\},c\_\{s\},\\Delta t\_\{s\\rightarrow d\}\], where brackets denote channel\-wise concatenation\. Here,msm\_\{s\}comprises four source MRI channels: contrast\-enhanced T1\-weighted \(T1c\), native T1\-weighted \(T1n\), T2\-weighted fluid\-attenuated inversion recovery \(T2F\), and T2\-weighted \(T2W\) MRI;psp\_\{s\}is the source tumor\-state proxy;csc\_\{s\}is the binary source cavity map; andΔ​ts→d\\Delta t\_\{s\\rightarrow d\}is a constant\-valued interval channel containing the elapsed days fromsstodd, normalized by 180\. The model predicts the destination proxypdp\_\{d\}fromxsx\_\{s\}, and does not receivet0t\_\{0\}andt1t\_\{1\}as a joint 14\-channel input\.

### 2\.2Single\-Step Forecaster

Givenxsx\_\{s\}, the SegMamba\-based forecaster outputs a raw velocity channelrvr\_\{v\}and a change\-probability logit channelrqr\_\{q\}, converted to normalized velocityv=tanh⁡\(rv\)v=\\tanh\(r\_\{v\}\)and voxel\-wise change probabilityq=sigmoid⁡\(rq\)q=\\operatorname\{sigmoid\}\(r\_\{q\}\)\. The direct forecast is

p^d=clip⁡\(ps\+q⊙v⊙Δ​ts→d​λv,0,1\),λv=1\.0,\\hat\{p\}\_\{d\}=\\mathrm\{clip\}\\left\(p\_\{s\}\+q\\odot v\\odot\\Delta t\_\{s\\rightarrow d\}\\lambda\_\{v\},0,1\\right\),\\qquad\\lambda\_\{v\}=1\.0,\(1\)wherep^d\\hat\{p\}\_\{d\}is the predicted destination proxy,⊙\\odotdenotes element\-wise multiplication, andλv\\lambda\_\{v\}is the velocity scale\. Training used a forecast loss \(L1L\_\{1\}\+Dice\), velocity supervision on the effective velocityq⊙vq\\odot v, binary cross\-entropy for the change logit with binary targetyq=𝟏\{\|pd−ps\|≥0\.05\}y\_\{q\}=\\mathbf\{1\}\\\{\|p\_\{d\}\-p\_\{s\}\|\\geq 0\.05\\\}, and stable\-delta regularization in voxels with\|pd−ps\|<0\.05\|p\_\{d\}\-p\_\{s\}\|<0\.05, where𝟏​\{⋅\}\\mathbf\{1\}\\\{\\cdot\\\}denotes the indicator function\. The velocity target was the time\-normalized proxy change clipped to\[−1,1\]\[\-1,1\], and no auxiliary support head was active\. The final objective was

ℒ=ℒcwL1\+0\.5​ℒDice\+0\.5​ℒvel\+0\.1​ℒBCE\+ℒstable,\\mathcal\{L\}=\\mathcal\{L\}\_\{\\mathrm\{cwL1\}\}\+0\.5\\mathcal\{L\}\_\{\\mathrm\{Dice\}\}\+0\.5\\mathcal\{L\}\_\{\\mathrm\{vel\}\}\+0\.1\\mathcal\{L\}\_\{\\mathrm\{BCE\}\}\+\\mathcal\{L\}\_\{\\mathrm\{stable\}\},\(2\)whereℒ\\mathcal\{L\}is the total training loss, andℒcwL1\\mathcal\{L\}\_\{\\mathrm\{cwL1\}\},ℒDice\\mathcal\{L\}\_\{\\mathrm\{Dice\}\},ℒvel\\mathcal\{L\}\_\{\\mathrm\{vel\}\},ℒBCE\\mathcal\{L\}\_\{\\mathrm\{BCE\}\}, andℒstable\\mathcal\{L\}\_\{\\mathrm\{stable\}\}denote change\-weightedL1L\_\{1\}, soft Dice, velocity, change\-logit binary cross\-entropy, and stable\-delta losses, respectively\. The change\-weighted terms assign a weight of1\+2=31\+2=3to voxels with proxy change of at least 0\.05\.

### 2\.3Observation\-Anchored Selective Assimilation

OASA retains the observed intermediate proxypt1,obsp\_\{t\_\{1\},\\mathrm\{obs\}\}as the state anchor\. First, thet0→t1t\_\{0\}\\\!\\rightarrow\\\!t\_\{1\}forecast estimates observation\-innovation MAE,

I=mean​\|pt1,obs−p^t1\|t0\|\.I=\\mathrm\{mean\}\|p\_\{t\_\{1\},\\mathrm\{obs\}\}\-\\hat\{p\}\_\{t\_\{1\}\|t\_\{0\}\}\|\.\(3\)Here,p^t1\|t0\\hat\{p\}\_\{t\_\{1\}\|t\_\{0\}\}is thet1t\_\{1\}proxy forecast from thet0t\_\{0\}source state, and the mean is taken over all voxels\. Second, thet1→t2t\_\{1\}\\\!\\rightarrow\\\!t\_\{2\}step produces a direct proposalp^t2,direct\\hat\{p\}\_\{t\_\{2\},\\mathrm\{direct\}\}and change\-probability mapq12q\_\{12\}, where the subscript1212denotes thet1→t2t\_\{1\}\\\!\\rightarrow\\\!t\_\{2\}interval\. We define

u12=p^t2,direct−pt1,obs,B=\|Ω\|−1∑i∈Ω𝟏\{\|u12\(i\)\|≥0\.05\}\.u\_\{12\}=\\hat\{p\}\_\{t\_\{2\},\\mathrm\{direct\}\}\-p\_\{t\_\{1\},\\mathrm\{obs\}\},\\qquad B=\|\\Omega\|^\{\-1\}\\sum\_\{i\\in\\Omega\}\\mathbf\{1\}\\\{\|u\_\{12\}\(i\)\|\\geq 0\.05\\\}\.\(4\)whereu12u\_\{12\}is the proposed proxy update,Ω\\Omegais the voxel domain,\|Ω\|\|\\Omega\|is its voxel count,iiindexes voxels, andBBis the fraction of voxels with an absolute proposed update of at least 0\.05\. The validation\-selected rule evaluates high, mid, and low tiers in that order, using high whenB≥0\.01B\\geq 0\.01andI≥0\.03I\\geq 0\.03, mid whenB≥0\.01B\\geq 0\.01andI≥0\.015I\\geq 0\.015, low whenB≥0\.005B\\geq 0\.005, and persistence otherwise\. The tier\-specific factors\(βlow,βmid,βhigh\)=\(0\.1,0\.1,1\.0\)\(\\beta\_\{\\mathrm\{low\}\},\\beta\_\{\\mathrm\{mid\}\},\\beta\_\{\\mathrm\{high\}\}\)=\(0\.1,0\.1,1\.0\)control the fraction of the proposed update applied in the low, mid, and high update tiers, respectively; persistence applies no update\. The tier labels denote branches of the validation\-selected rule rather than calibrated confidence levels\. In compact notation,

uOASA=βtier​g​\(q12\)⊙u12,p^t2,OASA=clip⁡\(pt1,obs\+uOASA,0,1\)\.u\_\{\\mathrm\{OASA\}\}=\\beta\_\{\\mathrm\{tier\}\}\\,g\(q\_\{12\}\)\\odot u\_\{12\},\\qquad\\hat\{p\}\_\{t\_\{2\},\\mathrm\{OASA\}\}=\\mathrm\{clip\}\(p\_\{t\_\{1\},\\mathrm\{obs\}\}\+u\_\{\\mathrm\{OASA\}\},0,1\)\.\(5\)Here,βtier\\beta\_\{\\mathrm\{tier\}\}is the factor for the selected tier,uOASAu\_\{\\mathrm\{OASA\}\}is the gated update, andp^t2,OASA\\hat\{p\}\_\{t\_\{2\},\\mathrm\{OASA\}\}is the assimilated future proxy\. The final voxel gate is soft,g⁡\(q12\)=q12g\(q\_\{12\}\)=q\_\{12\}; thus OASA applies additional voxel\-wise change\-score weighting to an already probability\-weighted update proposal rather than to the raw velocity field\.

### 2\.4Near\-Threshold Calibration

OASA \+ calibration applies a validation\-selected support adjustment:

p^cal​\(i\)=\{0\.201,θ02≤p^OASA​\(i\)<0\.2,p^OASA​\(i\),otherwise\.\\hat\{p\}\_\{\\mathrm\{cal\}\}\(i\)=\\begin\{cases\}0\.201,&\\theta\_\{02\}\\leq\\hat\{p\}\_\{\\mathrm\{OASA\}\}\(i\)<0\.2,\\\\ \\hat\{p\}\_\{\\mathrm\{OASA\}\}\(i\),&\\text\{otherwise\}\.\\end\{cases\}\(6\)Here,p^cal\\hat\{p\}\_\{\\mathrm\{cal\}\}is the calibrated proxy andθ02\\theta\_\{02\}is the validation\-selected lower eligibility threshold, set to 0\.075 for all three seeds\. Eligible voxels are raised to 0\.201, immediately above the evaluation threshold of 0\.2\. This is interpreted as near\-threshold support calibration, not evidence of improved biological predictive capability\.

## 3Experiments

### 3\.1Data, Splits, and Metrics

We used the de\-identified MU\-Glioma Post dataset, distributed through The Cancer Imaging Archive \(TCIA\) under a Creative Commons Attribution \(CC BY\) license\[[10](https://arxiv.org/html/2609.12435#bib.bib18),[20](https://arxiv.org/html/2609.12435#bib.bib21)\]\. The original retrospective collection was approved by the University of Missouri Institutional Review Board \(IRB \#2096253 MU\), which granted a waiver of informed consent for the collection and sharing of de\-identified data, as reported by the dataset authors\[[10](https://arxiv.org/html/2609.12435#bib.bib18)\]\. According to the dataset\-provided diagnosis labels, the source cohort comprised 203 patients, including 157 with glioblastoma and 46 with other glioma diagnoses\. We constructed 236 candidate triplets; the patient\-level training, validation, and test splits contained 142/30/31 patients and 164/43/29 candidate triplets\. A predefined no\-new\-treatment criterion excluded triplets with a recorded treatment start satisfyingsource​day<start​day≤destination​day\\mathrm\{source\\ day\}<\\mathrm\{start\\ day\}\\leq\\mathrm\{destination\\ day\}in either\(t0,t1\]\(t\_\{0\},t\_\{1\}\]or\(t1,t2\]\(t\_\{1\},t\_\{2\}\]\. The filter retained 120 triplets from 72 patients, distributed as 81/24/15 training/validation/test triplets, for modeling and trajectory characterization\. The retained cohort included 52 patients with glioblastoma and 20 with other glioma diagnoses; these groups contributed 90 and 30 triplets, respectively\. Diagnosis labels were used only for cohort characterization and were not provided to the forecasting model\. These filtered trajectories should not be interpreted as untreated biological trajectories\. MRI channels were standardized using nonzero voxels; training used foreground\-centered1283128^\{3\}crops with jitter, while validation and test used deterministic centered crops\.

We report RMSE for continuous proxy error and Dice atτ=0\.2\\tau=0\.2andτ=0\.5\\tau=0\.5for lower\- and higher\-threshold proxy\-support overlap, respectively\. The lower threshold captures broader proxy support, whereas the higher threshold evaluates a more restrictive region of the continuous proxy map\. Metrics were computed over all voxels in the centered1283128^\{3\}evaluation patch without an additional brain mask; FP@0\.2 and FN@0\.2 are voxel counts\. Main learned results are mean±\\pmpopulation standard deviation over three training seeds\. For paired uncertainty analysis, metrics were first averaged across seeds within each triplet, followed by 10,000 paired triplet\-level bootstrap resamples\.

### 3\.2Baselines and Validation Protocol

We compared initial\-scan forecasting, rollout without assimilation, persistence, direct prediction, OASA, OASA \+ calibration, and validation\-selected radius\-1 morphological dilation\. Initial forecasting predictst2t\_\{2\}directly fromt0t\_\{0\}; rollout predictst1t\_\{1\}fromt0t\_\{0\}and then propagates that prediction tot2t\_\{2\}; persistence copies the observedt1t\_\{1\}proxy; and direct prediction forecastst2t\_\{2\}from the observedt1t\_\{1\}state without OASA gating\. Checkpoints, OASA gating rules, calibration threshold, and baseline parameters were selected on validation data only\. The fixed patient\-level split was shared across seeds; only initialization, training order, and sampling varied\. The selected checkpoints corresponded to epochs 40, 25, and 45 for seeds 42, 43, and 44\. Each validation\-selected configuration was applied once to the 15 held\-out test triplets, with no test\-based seed or method selection\. The public SegMamba implementation was trained for 60 epochs on two NVIDIA RTX A6000 GPUs using AdamW \(learning rate1\.1844×10−41\.1844\{\\times\}10^\{\-4\}, weight decay7\.1145×10−47\.1145\{\\times\}10^\{\-4\}\), cosine scheduling without warmup, gradient clipping at 0\.5, mixed precision, and batch size 2 per GPU\. Online augmentation, dropout/drop path, and auxiliary support heads were disabled\.

## 4Results

### 4\.1Main Comparison

Table 1:Performance on 15 held\-out test triplets from the fixed patient\-level test split\. Learned results are mean±\\pmpopulation standard deviation over three seeds; deterministic baselines omit their zero seed standard deviations\. FP/FN are support voxel counts atτ=0\.2\\tau=0\.2, reported in10310^\{3\}voxels\. Bold indicates best\.Table[1](https://arxiv.org/html/2609.12435#S4.T1)shows that initial\-scan forecasting and rollout without assimilation had substantially lower overlap than methods using the intermediate observation\. Latest\-observation persistence was a strong conservative baseline\. OASA maintained Dice atτ=0\.2\\tau=0\.2comparable to persistence \(0\.6071±0\.00250\.6071\\pm 0\.0025vs\.0\.60700\.6070\) while yielding numerically higher Dice atτ=0\.5\\tau=0\.5\(0\.4269±0\.00790\.4269\\pm 0\.0079vs\.0\.39810\.3981\), with a small RMSE increase\. Direct prediction had Dice atτ=0\.2\\tau=0\.2similar to OASA and persistence, but lower Dice atτ=0\.5\\tau=0\.5and higher RMSE, indicating that unconditional model\-predicted updates were less favorable for proxy\-support overlap atτ=0\.5\\tau=0\.5\. OASA \+ calibration increased Dice atτ=0\.2\\tau=0\.2to0\.6178±0\.00250\.6178\\pm 0\.0025without changing aggregate Dice atτ=0\.5\\tau=0\.5, but increased FP@0\.2 from 11,836 to 18,663 while reducing FN@0\.2 from 22,107 to 17,536\. Morphological dilation was competitive in RMSE and Dice atτ=0\.2\\tau=0\.2, but had lower Dice atτ=0\.5\\tau=0\.5and a higher FP voxel count atτ=0\.2\\tau=0\.2\.

A paired triplet\-level bootstrap supported the main direct\-update contrast: OASA increased Dice atτ=0\.5\\tau=0\.5over direct prediction by 0\.1493 \(95% CI 0\.0291–0\.3055\) and reduced RMSE by 0\.0202 \(95% CI 0\.0113–0\.0294\)\. Confidence intervals \(CIs\) for OASA versus persistence and morphological dilation included zero for Dice metrics; calibration increased mean Dice atτ=0\.2\\tau=0\.2by 0\.0108 over OASA, but its CI included zero\.

### 4\.2Trade\-off, Trajectories, and Qualitative Update

\(a\)Proxy\-support overlap atτ=0\.2\\tau=0\.2vs\.τ=0\.5\\tau=0\.5\.![Refer to caption](https://arxiv.org/html/2609.12435v1/figure2b_proxy_trajectory_heterogeneity.png)\(b\)Descriptive proxy\-trajectory heterogeneity\.

Figure 2:Performance trade\-off and descriptive support changes in the 120 no\-new\-treatment triplets\. In \(b\),VaV\_\{a\}andVbV\_\{b\}are low\-threshold support voxel counts at successive time pointsaaandbb, andΔ​Va​b=\(Vb−Va\)/max⁡\(Va,Vb,1\)\\Delta V\_\{ab\}=\(V\_\{b\}\-V\_\{a\}\)/\\max\(V\_\{a\},V\_\{b\},1\); color denotest1t\_\{1\}–t2t\_\{2\}Dice atτ=0\.2\\tau=0\.2\. Trajectory categories were not used for model selection\.Fig\.[2](https://arxiv.org/html/2609.12435#S4.F2)\(a\) shows that direct prediction and morphological dilation can be competitive in Dice atτ=0\.2\\tau=0\.2while showing lower Dice atτ=0\.5\\tau=0\.5\. OASA and OASA \+ calibration shared the highest numerical Dice atτ=0\.5\\tau=0\.5, whereas calibration shifted OASA toward higher Dice atτ=0\.2\\tau=0\.2through near\-threshold support adjustment\. Fig\.[2](https://arxiv.org/html/2609.12435#S4.F2)\(b\) shows heterogeneous proxy trajectories\. Patterns were non\-monotonic \(54/120, 45\.0%\), mixed/mild \(26/120, 21\.7%\), increase\-like \(24/120, 20\.0%\), stable\-like \(10/120, 8\.3%\), or decrease\-like \(6/120, 5\.0%\)\. This descriptive analysis motivates observation\-aware updating rather than a single monotonic extrapolation rule\.

![Refer to caption](https://arxiv.org/html/2609.12435v1/figure3_representative_oasa_visual_panel.png)Figure 3:Illustrative observation\-anchored update for a held\-out triplet\. Among the six visualization candidates, the displayed case was selected because its Dice atτ=0\.2\\tau=0\.2for OASA with calibration under seed 42 was closest to the median across the candidate set\. The case was selected only for visualization after all model, checkpoint, rule, threshold, and seed choices had been fixed\. Cyan contours denote future target support atτ=0\.2\\tau=0\.2\. The support\-comparison map uses green, red, and blue to denote true\-positive \(TP\), false\-positive \(FP\), and false\-negative \(FN\) voxels, respectively, at the same threshold\.Fig\.[3](https://arxiv.org/html/2609.12435#S4.F3)illustrates that direct prediction, OASA, and OASA \+ calibration produce different support patterns for the same future target proxy\. OASA retains the observed intermediate proxy as the state anchor and applies a conservative gated update rather than unconditionally applying the model\-predicted update proposal\. Near\-threshold calibration is shown as a secondary support adjustment\.

## 5Discussion and Conclusion

Our results support observation anchoring as a conservative alternative to unconditional direct prediction\. OASA was comparable to persistence in Dice atτ=0\.2\\tau=0\.2while showing numerically higher Dice atτ=0\.5\\tau=0\.5, with a small RMSE increase relative to persistence\. Direct prediction showed greater across\-seed variability than OASA for all reported metrics\. Morphological dilation occupied a different operating point: compared with OASA, it showed numerically higher Dice and a higher FP voxel count atτ=0\.2\\tau=0\.2, but lower Dice atτ=0\.5\\tau=0\.5\.

OASA \+ calibration reduced FN and increased Dice atτ=0\.2\\tau=0\.2, but also increased FP\. By construction, it left Dice atτ=0\.5\\tau=0\.5unchanged\. This operation should be interpreted as a near\-threshold support adjustment rather than improved biological prediction; uncalibrated OASA remains the primary method\.

No\-new\-treatment proxy trajectories were frequently non\-monotonic, motivating the use of intermediate observations\. Although recorded treatment starts were excluded, these should not be considered untreated biological trajectories\. Growth and reaction–diffusion frameworks\[[21](https://arxiv.org/html/2609.12435#bib.bib14),[2](https://arxiv.org/html/2609.12435#bib.bib15)\]motivate extrapolation, but we neither reproduce them nor claim superiority\. SegMamba provides the 3D backbone; the contribution is observation\-anchored assimilation\.

This study forecasts a label\-derived proxy rather than clinical progression, recurrence, treatment response, or biological tumor burden\. Results from one institution and 15 held\-out test triplets should be interpreted descriptively\. Future work should evaluate larger cohorts from multiple institutions and clinical endpoints\. Overall, OASA provides a conservative strategy for observation\-aware forecasting\.

#### Acknowledgements

This work was supported by the Korea Medical Device Development Foundation grant funded by the Korean government \(the Ministry of Science and ICT, the Ministry of Trade, Industry and Energy, the Ministry of Health and Welfare, and the Ministry of Food and Drug Safety\) \(Grant No\. RS\-2026\-25543484\)\.

This research was also supported by the ANCHOR Program through the Gangwon ANCHOR Center, funded by the Ministry of Education \(MOE\) and Gangwon State \(G\.S\.\), Republic of Korea \(Grant No\. 2026\-ANCHOR\-10\-006\)\.

This research was further supported by the Ministry of Science and ICT \(MSIT\), Korea, under the National Program in Medical AI Semiconductor \(Grant No\. 2024\-0\-00096\), supervised by the Institute of Information & Communications Technology Planning & Evaluation \(IITP\) in 2026\.

#### Disclosure of Interests\.

The authors have no competing interests to declare that are relevant to the content of this article\.

## References

- \[1\]\(2017\)Advancing the cancer genome atlas glioma MRI collections with expert segmentation labels and radiomic features\.Scientific Data4,pp\. 170117\.External Links:[Document](https://dx.doi.org/10.1038/sdata.2017.117)Cited by:[§2\.1](https://arxiv.org/html/2609.12435#S2.SS1.p1.1)\.
- \[2\]V\. Biller, N\. Bubeck, L\. Zimmer,et al\.\(2026\)TumorFlow: physics\-guided longitudinal MRI synthesis of glioblastoma growth\.arXiv preprint arXiv:2603\.04058\.External Links:2603\.04058,[Document](https://dx.doi.org/10.48550/arXiv.2603.04058)Cited by:[§1](https://arxiv.org/html/2609.12435#S1.p2.1),[§5](https://arxiv.org/html/2609.12435#S5.p3.1)\.
- \[3\]S\. Cho, M\. Seo, M\. Shin, and K\. Yoon\(2026\)Towards digital twin of RF ablation: real\-time prediction of time\-dependent thermal effects using Transformer\.InDigital Twin for Healthcare,L\. Li, V\. Jirsa, J\. Feng, J\. Deng, L\. Dede’, S\. An, Y\. Lyu, and X\. Liu \(Eds\.\),Cham,pp\. 69–78\.External Links:ISBN 978\-3\-032\-07694\-6,[Document](https://dx.doi.org/10.1007/978-3-032-07694-6%5F7)Cited by:[§1](https://arxiv.org/html/2609.12435#S1.p3.1)\.
- \[4\]O\. Clatz, M\. Sermesant, P\. Bondiau,et al\.\(2005\)Realistic simulation of the 3\-d growth of brain tumors in MR images coupling diffusion with biomechanical deformation\.IEEE Transactions on Medical Imaging24\(10\),pp\. 1334–1346\.External Links:[Document](https://dx.doi.org/10.1109/TMI.2005.857217)Cited by:[§1](https://arxiv.org/html/2609.12435#S1.p2.1)\.
- \[5\]I\. Ezhov, K\. Scibilia, K\. Franitza,et al\.\(2023\)Learn\-morph\-infer: a new way of solving the inverse problem for brain tumor modeling\.Medical Image Analysis83,pp\. 102672\.External Links:[Document](https://dx.doi.org/10.1016/j.media.2022.102672)Cited by:[§1](https://arxiv.org/html/2609.12435#S1.p2.1)\.
- \[6\]A\. Gu and T\. Dao\(2023\)Mamba: linear\-time sequence modeling with selective state spaces\.arXiv preprint arXiv:2312\.00752\.External Links:2312\.00752,[Document](https://dx.doi.org/10.48550/arXiv.2312.00752)Cited by:[§1](https://arxiv.org/html/2609.12435#S1.p3.1)\.
- \[7\]T\. Hernandez\-Boussard, P\. Macklin, E\. J\. Greenspan,et al\.\(2021\)Digital twins for predictive oncology will be a paradigm shift for precision cancer care\.Nature Medicine27\(12\),pp\. 2065–2066\.External Links:[Document](https://dx.doi.org/10.1038/s41591-021-01558-5)Cited by:[§1](https://arxiv.org/html/2609.12435#S1.p3.1)\.
- \[8\]L\. C\. Hygino da Cruz, I\. Rodriguez, R\. C\. Domingues, E\. L\. Gasparetto, and A\. G\. Sorensen\(2011\)Pseudoprogression and pseudoresponse: imaging challenges in the assessment of posttreatment glioma\.American Journal of Neuroradiology32\(11\),pp\. 1978–1985\.External Links:[Document](https://dx.doi.org/10.3174/ajnr.A2397)Cited by:[§1](https://arxiv.org/html/2609.12435#S1.p1.1)\.
- \[9\]E\. Konukoglu, O\. Clatz, B\. H\. Menze,et al\.\(2010\)Image guided personalization of reaction\-diffusion type tumor growth models using modified anisotropic eikonal equations\.IEEE Transactions on Medical Imaging29\(1\),pp\. 77–95\.External Links:[Document](https://dx.doi.org/10.1109/TMI.2009.2026413)Cited by:[§1](https://arxiv.org/html/2609.12435#S1.p2.1)\.
- \[10\]E\. Mahmoud, J\. Gass, Y\. Dhemesh,et al\.\(2025\)MU\-Glioma Post: a comprehensive dataset of automated MR multi\-sequence segmentation and clinical features\.Scientific Data12,pp\. 1847\.External Links:[Document](https://dx.doi.org/10.1038/s41597-025-06011-7)Cited by:[§3\.1](https://arxiv.org/html/2609.12435#S3.SS1.p1.1)\.
- \[11\]B\. H\. Menze, A\. Jakab, S\. Bauer,et al\.\(2015\)The multimodal brain tumor image segmentation benchmark \(BRATS\)\.IEEE Transactions on Medical Imaging34\(10\),pp\. 1993–2024\.External Links:[Document](https://dx.doi.org/10.1109/TMI.2014.2377694)Cited by:[§2\.1](https://arxiv.org/html/2609.12435#S2.SS1.p1.1)\.
- \[12\]M\. Seo, M\. Shin, G\. Noh, S\. Yoo, and K\. Yoon\(2026\)Acoustic simulation with deep learning for low\-intensity transcranial focused ultrasound digital twins\.InDigital Twin for Healthcare,L\. Li, V\. Jirsa, J\. Feng, J\. Deng, L\. Dede’, S\. An, Y\. Lyu, and X\. Liu \(Eds\.\),Cham,pp\. 58–68\.External Links:ISBN 978\-3\-032\-07694\-6,[Document](https://dx.doi.org/10.1007/978-3-032-07694-6%5F6)Cited by:[§1](https://arxiv.org/html/2609.12435#S1.p3.1)\.
- \[13\]R\. Stupp, W\. P\. Mason, M\. J\. van den Bent,et al\.\(2005\)Radiotherapy plus concomitant and adjuvant temozolomide for glioblastoma\.New England Journal of Medicine352\(10\),pp\. 987–996\.External Links:[Document](https://dx.doi.org/10.1056/NEJMoa043330)Cited by:[§1](https://arxiv.org/html/2609.12435#S1.p1.1)\.
- \[14\]K\. R\. Swanson, C\. Bridge, J\. D\. Murray, and E\. C\. Alvord\(2003\)Virtual and real brain tumors: using mathematical modeling to quantify glioma growth and invasion\.Journal of the Neurological Sciences216\(1\),pp\. 1–10\.External Links:[Document](https://dx.doi.org/10.1016/j.jns.2003.06.001)Cited by:[§1](https://arxiv.org/html/2609.12435#S1.p2.1)\.
- \[15\]J\. Weidner, I\. Ezhov, M\. Balcerak,et al\.\(2025\)A learnable prior improves inverse tumor growth modeling\.IEEE Transactions on Medical Imaging44\(3\),pp\. 1297–1307\.External Links:[Document](https://dx.doi.org/10.1109/TMI.2024.3494022)Cited by:[§1](https://arxiv.org/html/2609.12435#S1.p2.1)\.
- \[16\]L\. Weizman, L\. Ben\-Sira, L\. Joskowicz, O\. Aizenstein, B\. Shofty, S\. Constantini, and D\. Ben\-Bashat\(2012\)Prediction of brain MR scans in longitudinal tumor follow\-up studies\.InMedical Image Computing and Computer\-Assisted Intervention – MICCAI 2012,Lecture Notes in Computer Science, Vol\.7511,pp\. 179–187\.External Links:[Document](https://dx.doi.org/10.1007/978-3-642-33418-4%5F23)Cited by:[§1](https://arxiv.org/html/2609.12435#S1.p2.1)\.
- \[17\]P\. Y\. Wen, D\. R\. Macdonald, D\. A\. Reardon,et al\.\(2010\)Updated response assessment criteria for high\-grade gliomas: response assessment in neuro\-oncology working group\.Journal of Clinical Oncology28\(11\),pp\. 1963–1972\.External Links:[Document](https://dx.doi.org/10.1200/JCO.2009.26.3541)Cited by:[§1](https://arxiv.org/html/2609.12435#S1.p1.1)\.
- \[18\]P\. Y\. Wen, M\. van den Bent, G\. Youssef,et al\.\(2023\)RANO 2\.0: update to the response assessment in neuro\-oncology criteria for high\- and low\-grade gliomas in adults\.Journal of Clinical Oncology41\(33\),pp\. 5187–5199\.External Links:[Document](https://dx.doi.org/10.1200/JCO.23.01059)Cited by:[§1](https://arxiv.org/html/2609.12435#S1.p1.1)\.
- \[19\]Z\. Xing, T\. Ye, Y\. Yang, G\. Liu, and L\. Zhu\(2024\)SegMamba: long\-range sequential modeling Mamba for 3D medical image segmentation\.InMedical Image Computing and Computer Assisted Intervention – MICCAI 2024,pp\. 578–588\.External Links:[Document](https://dx.doi.org/10.1007/978-3-031-72111-3%5F54)Cited by:[§1](https://arxiv.org/html/2609.12435#S1.p3.1)\.
- \[20\]D\. Yaseen, F\. Garrett, J\. Gass, J\. Greaser, E\. Isufi, L\. J\. Layfield, A\. Nada, K\. Pogorzelski, J\. Sinclair, N\. H\. M\. Tahon, and J\. Thacker\(2025\)University of Missouri post\-operative glioma dataset \(MU\-Glioma\-Post\) \(version 1\) \[Data set\]\.Note:The Cancer Imaging ArchiveExternal Links:[Document](https://dx.doi.org/10.7937/7K9K-3C83)Cited by:[§3\.1](https://arxiv.org/html/2609.12435#S3.SS1.p1.1)\.
- \[21\]L\. Zimmer, J\. Weidner, M\. Balcerak,et al\.\(2025\)PREDICT\-GBM: a multi\-center platform to advance personalized glioblastoma radiotherapy planning\.arXiv preprint arXiv:2509\.13360\.External Links:2509\.13360,[Document](https://dx.doi.org/10.48550/arXiv.2509.13360)Cited by:[§1](https://arxiv.org/html/2609.12435#S1.p2.1),[§5](https://arxiv.org/html/2609.12435#S5.p3.1)\.