Preamble

Machine Learning Prediction Radioactive Iodine Adsorption Metal-Organic Frameworks Nuclear Medicine Wastewater Ming-Jian Shu-Ting Ao-Tian

1 School

Environmental Biological Engineering, Nanjing University Science Technology, Nanjing, 210094, China These authors contributed equally work.

Correspondence:

Abstract

efficient removal radioactive iodine nuclear medicine wastewater great significance radiation protection.

Metal-organic frameworks (MOFs), owing their tunable structural characteristics, demonstrated considerable potential iodine adsorption. study, constructed published literature, machine learning

methods

applied predict iodine adsorption capacity identify influencing factors.

results

indicated XGBoost model exhibited predictive performance 0.96).

Feature importance analyses revealed metal exerted significant influence, while higher synthesis temperatures longer reaction times favored development crystalline structures channels. addition, higher drying temperatures effectively activated adsorption sites, thereby markedly enhancing adsorption capacity. study provides data-driven support rational design high-performance radioactive iodine adsorbents, offering valuable insights treatment nuclear medicine wastewater radiation protection.

Keywords

Adsorption capacit Machine learning; Metal-organic frameworks; Radioactive iodine;

1. Introduction

rapid development nuclear medicine, application radioactive isotopes disease diagnosis therapy become increasingly widespread Among them, iodine-131, short half-life strong tissue specificity, extensively radionuclide therapy thyroid cancer According nuclear medicine survey report Chinese Medical Association, approximately 197,766 cases radioactive iodine treatment conducted annually China, total annual usage about radioactive iodine During clinical application radiopharmaceuticals, wastewater containing radioactive iodine inevitably generated These effluents typically originate synthesis radiopharmaceuticals, laboratory operations, patient excretion solubility strong mobility aqueous environments, radioactive iodine easily diffuse wastewater bioaccumulate through chain, leading internal irradiation hazards Therefore, crucial ensure radiation exposure public exceed legal simple effective, though time-consuming,

method

reduce transfer

radioactive materials sewage system concentrate radioactive effluents dedicated storage tanks containers, allow decay half-lives, conduct radiation level testing before releasing national standards However, increasing radionuclide therapy, decay

method

costly, requires significant space resources, cannot avoid long-term environmental risks.

Furthermore, storage

method

depends human management, making susceptible equipment failures natural disasters, increasing radiation leakage 10,11 contrast, adsorption

methods

quickly remove radioactive iodine wastewater, reduce storage space requirements, lower management risks, decay process, making efficient sustainable wastewater treatment solution Traditional scrubbing solid adsorption technologies radioactive iodine treatment often suffer secondary waste generation potential pollution Conventional adsorbents activated carbon further limited adsorption capacity regeneration efficiency recent years, metal-organic frameworks (MOFs), their porosity, large surface area, tunable structures, emerged promising candidates radioactive iodine adsorption 5,15,16 assembled metal centers organic linkers, their structures functionally tailored through secondary building (SBU) design, enabling optimization adsorption, catalysis, other applications 17,18 varying organic ligands, metal ions, their ratios, nearly unlimited synthesized.

However, diversity presents challenge efficiently screening materials specific performance requirements Conventional trial-and-error experiments time-consuming labor-intensive, while systematic studies synthesis-structure-performance relationships remain limited September 2022, 110,000 deposited Cambridge Structural Database, exceeding capacity traditional experimental computational screening

methods

rapid artificial intelligence introduced approaches connect science chemistry.

Machine learning, particular, offers strong capabilities analyzing high-dimensional handling outliers, making efficient evaluating large, heterogeneous datasets, optimizing experimental workflows, establishing structure-property relationships already shown clear advantages pollutant adsorption prediction, materials design, parameter optimization.

Several studies demonstrated utility high-throughput screening, force field optimization, performance prediction, successfully guiding experimental synthesis validation.

Collectively, machine learning greatly accelerated development provides strong support efficient capture separation pollutants radioactive iodine 23,24

2.1 Data

collection preprocessing study,

Keywords

metal-organic frameworks iodide

adsorption search Science, yielding publications. After manual AI-assisted screening, publications selected construct containing adsorption capacity records, extracted directly original sources. included groups variables: synthesis parameters, physicochemical properties, adsorption conditions, adsorption capacity.

Synthesis parameters covered factors metal ligand type, ratio (M/O), solvent, modification, pyrolysis, reaction conditions, drying parameters, categorical continuous variables appropriately defined.

Physicochemical properties included volume, size, specific surface area, while adsorption conditions included concentration, dosage, temperature, time. output variable Langmuir maximum adsorption capacity balance integrity representativeness, features missing values retained imputed using combination simple

methods

mean, median, imputation advanced techniques random forest, hot-deck thereby improv quality, enhancing stability, supporting reliable machine learning modeling 26,27

Methods

Feature Engineering Feature selection critical improving predictive performance generalization machine learning models.

Strong correlations among features cause redundancy, importance assessment, reduce interpretability. address issues Spearman correlation coefficients hierarchical clustering applied analyze feature relationships study Spearman correlation, non-parametric measure, effectively captures monotonic relationships nonlinear non-normal data. correlation matrix constructed identify strongly related features, hierarchical clustering average linkage merge similar ones, preserving information while reducing feature numbers mitigating multicollinearity Subsequently additional screening combined correlation strength physicochemical relevance remove redundant weakly explanatory variables. final feature accurately represented target variable enhanced model stability generalizability, providing reliable support subsequent modeling

1. 3

Methods

for constructing machine learning models

machine learning workflow study involved reading dataset, specifying categorical continuous variables, defining input output features, splitting dataset, configuring models, setting hyperparameters, performing five-fold cross-validation, training final model, evaluating accuracy generalization hyperparameters strongly influence predictive performance, joint optimization conducted ensure comparison prevent overfitting underfitting. ensemble learning models tested:

LightGBM, XGBoost, CatBoost, Random Forest Random Forest, optimized hyperparameters included minimum samples split, maximum depth, number estimators, while CatBoost, LightGBM, XGBoost, included learning rate, maximum depth,

number estimators. Model performance assessed using coefficient determination square error (RMSE) reflects explanatory power, values closer indicating better whereas measures average deviation between predicted actual values, smaller values indicating higher accuracy.

During tuning, maximizing minimizing optimization objectives, optimal hyperparameter configurations model determined 37,38

methods

of machine learning models

machine learning algorithms traditionally regarded black-box models, meaning inputs outputs observable, while internal operations components remain unknown. internal structure working principles systems often fully understood.

However, study, uncovering potential relationships between prediction

results

different input features primary objectives. Mainstream machine learning interpretation

methods

broadly categorized global local approaches addition feature importance analysis, which quantifies relative weight input feature iodine adsorption capacity MOFs, study employed several advanced interpretability techniques.

Shapley additive explanation (SHAP) method, based theory, assign contribution feature individual predictions.

Individual conditional expectation (ICE)

analysis

applied visualize effect varying single feature while holding others constant.

Furthermore, partial dependence plots (PDPs) utilized quantitatively analyze influence trends different features adsorption capacity further explore mechanisms adsorption process

analysis

optimization process During collection, adsorption capacity records obtained, comprising input features output feature. features pyrolysis atmosphere, heating rate, pyrolysis time, pyrolysis temperature missing values removed avoid noise.

Using threshold, average feature eliminated. shown Table input features categorical variables, metal type, ligand type, solvent type, modified heated features.

Proportion

Classification Input features Minimum M aximum

missing values Preparation conditions Physical properties Adsorption reaction temperature conditions react dosage( compares imputation

methods

handling missing values: mean, median, mode, hot-deck, random forest. violin plots, height width represent range distribution density, respectively; white indicates median, thick represents interquartile range, shows confidence interval.

Missing values imputed effects evaluated using violin plots.

Results

showed that, except total volume, distributions after imputation

methods

consistent original data. Consequently, hot-deck imputation applied total volume, while imputation other continuous variables. original distributions indicated process parameters, reaction temperature, reaction time, relatively concentrated, whereas ratio, drying time, synthesis temperature exhibited greater dispersion categorical variables, metal type, organic ligand, solvent

encoded using label encoding limited sample size, pyrolysis modification conditions binarized indicating presence absence After applying imputation, hot-deck imputation, label encoding, fully cleaned prepared subsequent modeling. (A-L) Compare original violin plots average, median, mode, deck, random forest interpolation

Analysis

feature engineering processing

results

study, Spearman correlation matrices hierarchical clustering applied analyze filter input features MOFs. shown ratio metal organic ligands significantly positively correlated specific surface (0.37, 0.001) total volume (0.45, 0.001), indicating higher metal ratio favors formation well-ordered structures Synthesis reaction negatively correlated specific surface 0.29, 0.001), which attributed excessive crystal growth reducing surface area.

Drying temperature positively correlated total

volume specific surface 0.001), higher temperatures facilitate solvent evaporation opening Pyrolysis negatively correlated total volume 0.35, 0.001), suggesting pyrolysis cause structural collapse.

Modification excluded because showed significant correlation physicochemical properties limited organic ligand strongly correlated solvent (rank correlation coefficient 0.8). avoid multicollinearity, decisive variable, organic ligand type, retained, while solvent removed 44,45 Hierarchical clustering further indicated drying conveyed similar information solvent type.

Combined literature findings drying minimal influence, excluded Ultimately, features retained: metal type, ligand type, ratio, hydrothermal reaction temperature, drying temperature, heated, total volume, specific surface area, concentration, dosage, reaction temperature.

Input characteristics spearman correlation

analysis

0.001, 0.01, 0.05)

Input feature hierarchical clustering Model construction hyperparameter optimization machine learning model constructed study carried Jutai parallel computing server, specific hardware software configuration summarized Table Table Hardware software configuration training model Module Model/Version Experimental System Ubuntu System Environment Manager Anaconda Integrated Development Environment PyCharm Programming Language Python

Machine Learning Library Scikit - learn 0.24.2

Central Processing Intel Platinum 8375C optimal hyperparameter settings varied across models differences distribution, feature dimensionality, algorithm mechanisms ensure reproducibility rigor, study referred parameter-setting approaches reported literature combined characteristics present establish appropriate search ranges Table summarizes optimal hyperparameter values model under their best-performing conditions.

samples Catboost Learning Learning XGBoost Learning Random Forest model, search conducted maximum depths trees, minimum split sizes esults (Fig.4.A-B) showed strong parameter dependence: greater depth steadily improved reduced RMSE, while increasing number trees enhanced model stability accuracy.

Minimum split limited influence, though smaller values provided slight gains, suggesting relaxed splitting constraints capture finer details.

CatBoost, search tested learning rates 0.005-0.025, depths 1-10, iterations. depth iterations increased, improved decreased (Fig.4.C-D).

Performance gains strongest learning rates, where additional iterations compensated individual learners, highlighting CatBoost reliance careful learning adjustment iterative training.

LightGBM (Fig.4.E-F) XGBoost (Fig.4.G-H) shared hyperparameter ranges.

LightGBM performed learning rates, deeper trees, iterations, showing steady accuracy gains.

XGBoost showed sharpest improvement: initially negative, reflecting underfitting, rapidly iterations, while dropped.

These

results

confirm deeper longer training significantly improves generalization fitting performance.

Four-dimensional based hyperparameter optimization (A-B) Random forest (C-D) Category feature enhancement (E-F) LightGBM; (G-H) XGBoost.

3.4 The

training effect of machine learning models

MOFs. points represent predictions training points represent predictions dashed denotes ideal prediction (predicted value actual value), marginal curves illustrate distribution densities sets.

Overall, models demonstrated strong fitting ability, though there notable differences performance.

XGBoost model (Fig.5D) achieved outstanding accuracy, training reflecting excellent generalization capability. contrast, CatBoost model (Fig.5B) performed training 0.9802, 29.7509),

performance decreased 0.8701, 38.5160), suggesting overfitting.

Random Forest LightGBM (Fig.5C) achieved values around training However, LightGBM outperformed Random Forest 0.8811) showed slightly lower (41.8123 40.5665). indicates LightGBM adaptable data. summary, XGBoost achieved lowest error highest training maintained stable performance surpassing other three models.

Therefore, XGBoost identified suitable model predicting adsorption capacity MOFs, offering balance accuracy generalization. omparison between predicted actual adsorption capacities Random Forest CatBoost LightGBM XGBoost

3.5 Analysis

of Optimal Machine Learning models

3.5.1 Input

feature importance

analysis

presents

results

feature importance analysis, showing different categories input variables contributed unequally model.

Reaction condition variables accounted 91.0% total importance, exceeding physicochemical properties (6.1%) adsorption conditions (2.9%).

results

highlight decisive synthesis parameters determining structural functional attributes metal influential feature

59.8%, which consistent fundamental metal nodes defining framework topology, surface charge distribution, active types, thermal stability instance, Zr-based exhibit strong affinity anionic pollutants Cr(VI), whereas Fe-based readily cationic pollutants. ifferent valence states metal alter strength coordination which affect framework flexibility adsorption selectivity Reaction (15.5%) drying temperature (5.8%) ranked highly because reaction influences crystal development defect density, drying temperature impact structures functional group stability These factors indirectly regulat adsorption activating Among variables adsorption, initial concentration contributed 5.2%, which higher contributions (0.5%) reaction temperature (2.3%).

results

suggest pollutant concentration gradients significantly impact loading capacity adsorption saturation, which consistent previous experimental findings adsorption driving forces physicochemical properties, contributed specific surface suggesting adsorption capacity solely determined surface rather accessibility distribution functional groups. example, studies Zr-MOFs As(V) adsorption shown higher surface necessarily yield greater adsorption, whereas number active sites electronic density distribution decisive

Analysis

Feature Importance,

Analysis

further understand positive negative influence trends variable prediction results, value

analysis

conducted shown value distribution across samples, indicating strong impact model outputs.

Generally, igher values generally associated greater predicted adsorption capacities corroborat feature importance ranking confirm different metal cause either positive negative shifts model outputs. addition, synthesis reaction time, drying temperature, solution concentration demonstrated clear influence directions onger reaction times moderate drying temperatures favorable

improving adsorption capacity. Conversely, variables adsorbent dosage displayed relatively narrow distributions, suggesting weaker explanatory power samples localized effects within specific subsets

Analysis

individual conditional expectations partial dependencies Individual Conditional Expectation (ICE)

method

applied continuous variables order analyze sample-level responses further interpret mechanisms influence adsorption performance represents dependency single sample, indicates average trend.

Continuous variable input feature individual conditional expectation

analysis

Consistent

results

feature importance analyses, plots revealed heterogeneity direction effects across samples, reflecting nonlinear complex behavior MOFs. metal-to-ligand ratio showed sharp increase ~2.0, suggesting sufficient metal sites necessary promoting framework integrity generating active sites.

Reaction temperature showed stable overall effects, though positive responses observed around 57,58 Reaction stronger effects below hours weakened later, highlighting importance early crystal

formation. Drying temperature total volume enhanced adsorption certain ranges: drying volume, suggesting structural sensitivity zones.

Specific surface initial concentration showed dispersed patterns, indicating heterogeneous effects influenced microstructure diffusion.

Below adsorption increased sharply, gains plateaued higher values, reflecting diminishing returns Adsorption temperature improved performance above consistent endothermic adsorption. promoted adsorption enhancing surface protonation, while adsorbent dosage adsorption showed minimal influence 60,61 Bivariate partial dependence

analysis

input features adsorption capacity partial dependence

analysis

continuous features adsorption capacity shown highlighted interaction between drying temperature specific surface Adsorption capacity increased significantly drying temperature below after which gains saturated. effect drying temperature showed rise-then-fall trend, suggesting appropriate drying improved utilization. indicated strong synergy between drying temperature metal-to-ligand ratio, where higher ratios allowed temperature increases enhance adsorption providing coordination centers improving stability. showed adsorption markedly reaction exceeded drying around demonstrating crystal development required matched drying conditions. showed specific surface responsive within synthesis temperatures, while higher synthesis temperatures (>180

combined drying further improved stability adsorption.

Figures revealed boundary effects. exceeded longer synthesis times higher temperatures produced saturated gains, suggesting structural limits.

Overall, interactions among metal-to-ligand ratio, drying temperature, synthesis temperature, specific surface dominant regulating adsorption capacity, establishing mechanistic basis multiparameter optimization.

Conclusions

study machine learning optimize synthesis removing radioactive iodine nuclear medicine wastewater. constructed, cleaning feature engineering effectively addressed multicollinearity. models developed tuned search,

results

showing XGBoost achieved performance 0.962, 20.83).

Model interpretation further revealed relationships between input features adsorption capacity, providing strong decision support design optimization.

However, study limitations. relatively small, which could fully capture structural diversity MOFs.

Additionally, microscopic factors influencing adsorption, functional distribution crystal orientation, included input variables.

Future should expand experimental

results

improve model depth generalization, integrate learning

methods

capture nonlinear structure performance relationships.

Combining these approaches quantum chemical calculations high-throughput screening enable closed-loop framework modeling, prediction, optimization, thereby accelerating engineering application nuclear medicine wastewater treatment contributing radiation protection public health.

Availability support findings study available reasonable request.

Conflict interest statement authors disclosed relevant relationships.

Acknowledgements acknowledge National Natural Science Foundation China (No.52470120 No.12475310); China Postdoctoral Science Foundation, (2024M764228); Fundamental Research Funds Central Universities (30925010402) partially funding work.

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