Machine Learning Prediction Models of Beneficial and Toxicological Effects of Zinc Oxide Nanoparticles in Rat Feed

Abstract

Nanoparticles have found widespread application across diverse fields, including agriculture and animal husbandry. However, a persistent challenge in laboratory-based studies involving nanoparticle exposure is the limited availability of experimental data, which constrains the robustness and generalizability of findings. This study presents a comprehensive analysis of the impact of zinc oxide nanoparticles (ZnO NPs) in feed on elemental homeostasis in male Wistar rats. Using correlation-based network analysis, a correlation graph weight value of 15.44 and a newly proposed weighted importance score of 1.319 were calculated, indicating that a dose of 3.1 mg/kg represents an optimal balance between efficacy and physiological stability. To address the issue of limited sample size, synthetic data generation was performed using generative adversarial networks, enabling data augmentation while preserving the statistical characteristics of the original dataset. Machine learning models based on fully connected neural networks and kernel ridge regression, enhanced with a custom loss function, were developed and evaluated. These models demonstrated strong predictive performance across a ZnO NP concentration range of 1–150 mg/kg, accurately capturing the dependencies of essential element, protein, and enzyme levels in blood on nanoparticle dosage. Notably, the presence of toxic elements and some other elements at ultra-low concentrations exhibited non-random patterns, suggesting potential systemic responses or early indicators of nanoparticle-induced perturbations and probable inability of synthetic data to capture the true dynamics. The integration of machine learning with synthetic data expansion provides a promising approach for analyzing complex biological responses in data-scarce experimental settings, contributing to the safer and more effective application of nanoparticles in animal nutrition.

1. Introduction

Nanoparticles, defined as materials with dimensions measured in nanometers (typically between 1 and 100 nanometers), have revolutionized various fields, transforming the way scientists approach research and industrial applications. The unique properties of nanoparticles, such as their high surface area, reactivity, and ability to interact with biological systems, have made them increasingly valuable tools in multiple disciplines. In agriculture, nanoparticles have the potential to significantly impact animal husbandry, particularly in the areas of animal health and nutrition [1]. For example, nanoparticles can be used as feed additives to enhance the nutritional value of animal feed, promote animal health, and improve feed efficiency. Furthermore, nanoparticles can be employed in veterinary medicine [2] to develop targeted treatments for animal diseases, reducing the need for antibiotics and other harsh chemicals.

Remarkable progress was achieved in developing and implementing nanoparticle-based solutions to address challenges in livestock production systems [3]. With increased adoption of nanoparticles in animal husbandry, recent research has prioritized a comprehensive evaluation of their environmental impact. Kolesnikov et al. [4] conducted extensive microcosm experiments, assessing the effects of metal-based nanoparticles on soil microbial communities when introduced through animal waste. The study revealed that zinc oxide (ZnO) nanoparticles at concentrations exceeding 100 mg/kg significantly altered soil enzyme activities and microbial diversity in Cambisol soils. Despite their numerous benefits, the toxicity of nanoparticles, in practice, remains a significant concern [5]. As nanoparticles are increasingly used in various applications, it is essential to assess their potential risks and develop strategies for safe handling, use, and disposal. This requires a deeper understanding of the factors that influence nanoparticle toxicity, such as their size, shape, surface chemistry, and reactivity. Moreover, the development of standardized protocols for the assessment of nanoparticle toxicity is crucial for ensuring the safe use of these materials in agriculture and other fields. Machine learning (ML) algorithms can enhance and improve the simulation and modeling process for nanotoxicology [6]. By leveraging the power of ML, researchers can develop more accurate and reliable models to assess the harmful effects of nanoparticles.

This article explores the beneficial and toxicological effects of zinc oxide nanoparticles in the feed of laboratory animals and the use of machine learning models to address the small data challenge and to predict potential toxic doses. The rest of this article is organized as follows. Section 2 provides the literature review on the use of nanoparticles in animal husbandry and the problem of the limited availability of experimental data. Section 3 provides the materials and methods used to analyze experimental data, generate new data, and set up custom regression models for a prediction problem. Section 4 provides a comparison of implemented machine learning models for predicting the levels of elements, proteins, and ferments in blood, depending on the ZnO nanoparticle dose. Section 5 summarizes the discussion.

2. Literature Review

Nanoparticles in animal husbandry can exhibit varying levels of toxicity, which are crucial to assess. Saeed et al. [7] discussed the toxicity of different metal/metal oxide nanoparticles used as feed additives, emphasizing the need for careful evaluation of their safety in livestock. Naumenko et al. [8] noted that metal nanoparticles exhibit toxic parameters that limit their use in animal husbandry. The toxicokinetics vary, necessitating careful dosages to meet safety criteria while maximizing benefits like enhanced productivity and antioxidant properties in poultry farming. Rahman et al. [9] studied toxicological aspects of zinc oxide nanoparticles in animals. Zinc oxide nanoparticles (ZnO-NPs) can exhibit toxicity in animal husbandry, leading to adverse side effects. While they offer benefits such as improved absorption and antimicrobial properties, their use requires careful regulation to mitigate potential harmful consequences. Bąkowski et al. [10] reviewed the effects of silver and zinc nanoparticles in animal nutrition. The authors concluded that nanoparticles in animal husbandry can induce toxicity, causing pathological changes in tissues such as the pancreas, kidney, and liver. They may also lead to inflammatory responses, cell death, and potential nervous system malfunctions, necessitating caution in their use. Tsekhmistrenko et al. [11] studied the usage of nanoparticles of metals and non-metals in animal husbandry. The authors concluded that nanoparticles can exhibit toxicity in poultry farming, influenced by their form and source. Their interactions may affect bioavailability, metabolism, and excretion rates, necessitating further research to understand their safety and efficacy in livestock production. Hardy et al. [12] studied the application of nanoscience and nanotechnologies in the food and feed chain. The authors noted that nanoparticles may pose toxicity risks in animal husbandry, affecting reproduction, development, and immune responses. Toxicokinetics, local gastrointestinal effects, and specific testing for immunotoxicity and neurotoxicity are crucial for assessing their safety in feed applications. Elalfy et al. [13] studied the usefulness and adverse effects of nanoparticles in animal husbandry. Nanoparticles exhibit toxic effects, impacting the liver, lungs, skin, eyes, and reproductive health. Their toxicity arises from increased concentrations in non-target tissues, leading to genotoxicity, oxidative stress, and hemotoxic effects, adversely affecting healthy tissues. Lutkovskaya et al. [14] studied the impact of ultrafine trace elements in ruminant diets on productivity and health. The paper highlights that while ultrafine particles can enhance animal health and productivity, their accumulation may lead to cell death or pathological changes. The authors noted that further research is essential to assess the safety and potential toxicity of nanoparticles in animal husbandry. Vanivska et al. [15] studied the toxicity effects of nanoparticles on animal and human organisms. The review highlighted that nanoparticles can induce oxidative stress, inflammatory responses, and cell damage in animal organisms, with effects varying by nanoparticle size, shape, and composition. Shivaswamy et al. [16] studied the in vivo and in vitro toxicity of nanomaterials in animal systems. The authors noted that nanoparticle toxicity in animal husbandry is a growing concern due to the increasing environmental presence of nanomaterials. Assessing their short-term and long-term effects on animals is crucial, as existing toxicity assessment methods are inadequate for these smaller-sized materials. Sharma et al. [17] discussed nanotoxicity mechanisms, plausible mitigation strategies, and the effects on biological systems, including organs like the liver, brain, kidneys, and lungs. Pradhan et al. [18] noted that nanotoxicity affects animal behavior and development, with various factors like size and shape influencing toxicity levels. The authors concluded that reactive oxygen species are primary toxic agents. Parashar et al. [19] discussed nanoparticle toxicity, highlighting their adverse effects on various organisms, including cytotoxicity, embryotoxicity, and DNA damage in in vivo models like rats and rabbits, which could have implications for animal husbandry and livestock health. Bisla et al. [20] reviewed toxicological studies on metallic nanoparticles, highlighting their harmful effects on male germ cells in humans and animals, emphasizing the need to evaluate their impact on spermatozoa in animal husbandry due to increasing industrial applications. Dianová et al. [21] reviewed the toxicity of metal nanoparticles (Ag, ZnO, TiO₂) in animal studies, highlighting their adverse effects on male and female reproductive health, including decreased sperm motility, ovarian accumulation, and conditions like polycystic ovary syndrome and inflammation.

Nanoparticles have the potential to revolutionize animal husbandry by improving productivity, enhancing health, and serving as effective feed additives. However, their use is not without risks, as they can exhibit toxicity that may harm animal health and the environment. To fully realize the benefits of nanoparticles, it is essential to carefully evaluate their safety and efficacy through comprehensive research and regulatory frameworks.

Table 1. Comparative analysis of nanoparticles in animal husbandry.

Nanoparticle Type	Effects on Animal Husbandry	Ref.
Zinc oxide (ZnO)	Improved growth, antioxidant properties, and enhanced immune function; potential liver and kidney damage	[8,9]
Silver (Ag), zinc (Zn)	Antimicrobial activity, improved productivity; potential neurotoxicity and reproductive toxicity	[10]
Zinc (Zn), silver (Ag), selenium (Se), cerium (Ce), iron (Fe)	Improved hemoglobin levels, enhanced productivity, potential oxidative stress, and tissue damage	[11]
Selenium (Se)	Enhanced antioxidant system, improved immune function; potential oxidative stress and inflammation	[14]
Silver (Ag), zinc oxide (ZnO), titanium dioxide (TiO2)	Improved productivity, antimicrobial activity, potential oxidative stress, and inflammation	[21]

aggregates the results obtained in the studies on the benefits and toxicity of nanoparticles in animal husbandry.

Sial et al. [22] reviewed the impact of ZnO nanoparticles on organ systems in rats. The authors concluded that ZnO nanoparticles induce toxicity in rats through various exposure routes, primarily affecting the liver, kidneys, and lungs. Sharif et al. [23] reviewed the toxic effects of metallic nanoparticles on the rat spleen. The authors noted that silver, copper, and gold nanoparticles induce toxicity in rats by generating reactive oxygen species, leading to oxidative stress, cell membrane damage, and histopathological changes in the spleen, including vacuolation, altered architecture, and cell necrosis. Shafiq et al. [24] studied the toxicity effects of magnesium oxide nanoparticles (MgO) on the liver in male rats. The study found that MgO nanoparticles caused significant liver toxicity in male rats, evidenced by increased liver enzymes (AST, ALT, ALP) and histopathological changes, including hepatocyte atrophy, necrosis, and inflammatory cell infiltration, indicating potential health risks. Verma et al. [25] studied the effects of iron oxide nanoparticles in Wistar rats. Iron oxide nanoparticles (IONPs) caused dose-dependent toxicity in Wistar rats, affecting the lungs, liver, and kidneys. Subchronic exposure led to significant body weight reduction, hepatic damage, altered serum creatinine, and blood urea nitrogen levels, indicating notable health implications. Ali et al. [26] studied the impact of silica and silica-based nanoparticles on serological parameters and genotoxicity in Rattus norvegicus rats. The study found that crystalline silica nanoparticles (C-SiO₂) caused severe histopathological alterations and significantly affected 95% of serological parameters, DNA damage, and oxidative stress parameters in rats, indicating high toxicity. Silver–silica and zinc–oxide–silica nanoparticles showed lesser effects. Yousef et al. [27] studied the toxic effects of aluminum oxide and zinc oxide nanoparticles in rats. The study revealed that aluminum oxide and zinc oxide nanoparticles induce neurotoxicity, cardiotoxicity, and lung toxicity in rats, as evidenced by increased oxidative stress, altered cytokine production, and significant changes in gene expression, particularly when nanoparticles are combined. Moshrefi et al. [28] studied the toxicological effects of zinc oxide nanoparticles on the brain and heart structures of male Wistar rats. Zinc oxide nanoparticles caused significant toxicity in male Wistar rats, leading to heart and brain lesions, increased bioaccumulation, elevated serum creatine phosphokinase levels, and behavioral impairments, particularly at doses exceeding 25 mg/kg. Rehman et al. [29] studied the toxicological effects of colloidal silver nanoparticles on rat health. The study evaluated colloidal silver nanoparticle toxicity in rats, revealing minimal effects on food intake, water consumption, and behavior. However, high-dose exposure (100 μg/kg/day) led to significant body weight reduction and potential liver enzyme alterations, necessitating further investigation. Jarrar et al. [30] studied the toxicity of metallic and metallic oxide nanoparticles in rats. The study found that metallic and metal oxide nanoparticles caused significant mitochondrial ultrastructural alterations in the hepatocytes and renal cells of rats, leading to cell injury. Key changes included cristolysis, swelling, and membrane disruption, indicating targeted toxicity of nanoparticles. Sutunkova et al. [31] studied the acute toxicity of lead oxide nanoparticles in rats. Inhalation exposure to lead oxide nanoparticles in rats resulted in increased granulocyte counts, elevated reticulocyte percentages, and a significant neutrophil response in bronchoalveolar lavage fluid, indicating both general toxic and cytotoxic effects, highlighting the need for further research on safe exposure levels.

While the studies highlight the significant toxic effects of some nanoparticles in rats, it is essential to consider that the biological responses may vary based on nanoparticle composition, size, and exposure duration, necessitating a nuanced understanding of their safety profiles in biomedical applications.

Table 2. Comparative analysis of nanoparticle toxicity in rats.

Nanoparticle Type	Rats Type	Main Outcomes	Ref.
Magnesium oxide nanoparticles (MgO)	Sprague–Dawley albino rats (Rattus norvegicus)	250 and 1000 mg/kg doses; a highly significant increase in AST, ALT, ALP, and total bilirubin	[24]
Iron oxide (IO)	Wistar rats	20, 40, and 80 mg/kg doses; significant changes in lungs, liver, and kidney; LDH increased significantly	[25]
Crystalline silica (C-SiO2) NPs, silver-silica (Ag-SiO2), zinc-oxide silica (ZnO-SiO2)	Rattus norvegicus	500 µg/kg doses; significantly altered 95% of serological, DNA damage, histopathological, and oxidative stress parameters	[26]
Aluminum oxide (Al2O3), zinc oxide (ZnO)	Male Wistar rats	70 mg/kg of Al2O3 and 100 mg/kg of ZnO NPs doses; increase in cytokines, p53, oxidative stress, creatine kinase, norepinephrine, acetylcholine, and lipid profile; significant decrease in the levels of antioxidant enzymes, total antioxidant capacity, and the activity of acetylcholine esterase in the brain, heart, and lung	[27]
Zinc oxide (ZnO)	Male Wistar rats	4, 8, 25, 50, 100, and 200 mg/kg doses; histopathologic lesions in the heart structures of 200 mg/kg; doses higher than 25 mg/kg are not recommended in terms of toxicity.	[28]
Colloidal silver nanoparticles (AgNPs)	Male Wistar rats	10 μg/kg/day and 100 μg/kg/day doses; a notable reduction in body weight and exhibited potential elevation in liver enzymes for the 100 μg/kg/day dose	[29]
Zinc oxide (ZnO)	Male Wistar rats	3.1 mg/kg dose is optimal in terms of balanced elemental homeostasis; good predictive results for essential elements, proteins, and enzymes in the range from 1 mg/kg to 150 mg/kg	Our research

aggregates the results obtained in the studies on the toxicological effects of various nanoparticles in rats.

The problem of small data in scientific research poses significant challenges for machine learning applications, as limited datasets often lead to poor model performance and hinder reproducibility. To address this issue, ML methods have emerged as powerful tools for generating synthetic data, thereby enhancing the training datasets available for model development. DaCosta et al. [32] presented a Python v3.7 package to generate complex nanoscale atomic structures for creating large, simulated datasets for training neural networks. The authors trained a series of neural networks on various subsets of simulated databases to segment nanoparticles. Danai Varsou et al. [33] highlighted the challenge of limited data availability in nanoparticle toxicity assessments. The authors addressed this challenge by employing synthetic data generation techniques (SMOTE and ADASYN) in the form of an automated machine learning (autoML) scheme. Kumari Khadka et al. [34] focused their research on synthetic data generation using combinatorial testing and a variational autoencoder (CT-VAE). The authors concluded that machine learning models trained with synthetic data could achieve performance similar to models trained with real data. Dou et al. [35] summarized and analyzed several potential solutions to small data challenges in chemical and biological sciences. The authors noted that ML methods, including generative adversarial networks (GANs), U-Net, and graph neural networks (GNNs), can generate synthetic data, enhance model training, and improve predictive performance in small datasets. Goyal et al. [36] reviewed synthetic data generation techniques using generative AI to address the data scarcity problem. The authors noted that GANs and VAEs can generate synthetic datasets, preserving original patterns while mitigating privacy concerns.

An analysis of state-of-the-art publications underscores the increasing relevance and application of nanoparticles in the field of animal husbandry, particularly for enhancing feed efficiency and improving disease resistance. However, a critical challenge associated with the application of nanoparticles in biological systems is the assessment of their potential toxicity, especially following chronic exposure. Furthermore, experimental investigations into nanoparticle effects are often constrained by the limited dimensionality of laboratory data, stemming from high costs, ethical constraints, and logistical limitations in animal experimentation. In this context, generative machine learning models present a promising avenue for synthesizing biologically plausible datasets, thereby enabling more robust statistical inference and predictive modeling. Unlike previous studies that primarily focused on histopathological or biochemical markers of toxicity, our research focused on the comprehensive assessment of elemental homeostasis in laboratory rats exposed to varying dietary concentrations of ZnO NPs. In this paper, we propose the development of concentration-dependent predictive models using advanced regression and machine learning techniques. These models integrate experimental data to forecast changes in elemental balance, offering insights into safe usage thresholds.

Our study is novel in several aspects, as follows:

• We developed a weighted importance score based on feature importance and element groups, and an integral indicator of efficiency and safety to assess the optimal dosage of zinc oxide nanoparticles in rat feed;
• We implemented a fully connected feedforward artificial neural network and kernel ridge regression model with a new custom loss function;
• We studied the possibility of generating reliable synthetic data for the problem of low-dimensional experimental data.

Our study makes several contributions to the field of nanoparticle safety in animal husbandry, as follows:

• We studied the effect of zinc oxide nanoparticles in feed on elemental homeostasis in rats;
• We determined the optimal dosage of zinc oxide nanoparticles in terms of beneficial and toxicological effects;
• We built predictions of the levels of essential and toxic elements, proteins, and enzymes, depending on the concentration of zinc oxide nanoparticles in the range from 1 mg/kg to 150 mg/kg.

3. Materials and Methods

3.1. Data Preprocessing

The experimental study was conducted in the biological clinic of the Federal Scientific Center for Biological Systems and Agrotechnology of the Russian Academy of Sciences (Orenburg) on male Wistar rats.

In total, 35 laboratory animals were randomly divided into 7 separate groups—the negative control group (C⁻) received a standard AIN-93M diet [37] and bottled drinking water; in the positive control group (C⁺), alimentary Zn deficiency was modeled by feeding animals with semi-synthetic zinc-deficient feed and drinking deionized water; experimental group I received zinc-deficient feed, deionized water, and intragastrically administered zinc oxide (ZnO) at a dose of 6.2 mg/kg body weight; experimental group II (100%) received zinc-deficient feed, deionized water, and intragastrically administered zinc oxide nanoparticles (ZnO NPs) at a dose of 6.2 mg/kg body weight; experimental group III (50%) received zinc-deficient feed, deionized water, and intragastrically administered NP-ZnO at a dose of 3.1 mg/kg body weight; experimental group IV (25%) received zinc-deficient feed, deionized water, and intragastrically administered NP-ZnO at a dose of 1.55 mg/kg body weight; experimental group V received zinc-deficient feed, deionized water, and intragastrically administered NP-ZnO at a dose of 150 mg/kg body weight. Zinc oxide nanoparticles had a size of 329 nm and a zeta potential of 87.8 ± 3.5 mV. The experiment was conducted for 28 days.

Blood was collected from the cardiac artery into VACUETTE vacuum tubes with a blood coagulation activator and gel for separating red blood cells (Greiner Bio-One International AG, Kremsmünster, Austria). The elemental composition of the obtained biosamples was studied for more than 20 parameters, including calcium (Ca), phosphorus (P), potassium (K), sodium (Na), magnesium (Mg), iron (Fe), zinc (Zn), copper (Cu), manganese (Mn), cobalt (Co), chromium (Cr), selenium (Se), iodine (I), nickel (Ni), arsenic (As), vanadium (V), lead (Pb), cadmium (Cd), tin (Sn), mercury (Hg), strontium (Sr), beryllium (Be), boron (B), silicon (Si), and lithium (Li). The levels of elements were determined by inductively coupled plasma mass spectrometry (ICP-MS) using a NexION 300D mass spectrometer (Perkin Elmer NexION 300D ICP Mass Spectrometer, Waltham, MA, USA). The elements have been widely studied [38,39] and can be divided into the following four groups:

• Essential microelements: Fe, Zn, Cu, Mn, Co, Se, I, Cr;
• Toxic microelements: Sn, Al, As, Hg, Pb, Be, Cd;
• Macroelements: Na, Ca, P, K, Mg;
• Partially essential elements: B, Si, V, Ni, Li.

Determination of alkaline phosphatase (ALP), carbonic anhydrase (CA4), alcohol dehydrogenase (ADH1B), alpha-2-zinc glycoprotein (ZAG), zinc-dependent superoxide dismutase (SOD-Zn), metallothionein-1 (MT-1), metallothionein-2 (MT-2), and metallothionein-3 (MT-3) in these biosubstrates was carried out by enzyme immunoassay using appropriate reagent kits (Cloud-Clone Corp., Wuhan, China).

The data received from the laboratory in XLSX format (size 35 × 147) contained information on samples, where the rows corresponded to the objects of study, and the columns reflected the levels of chemical elements in the blood, liver, kidneys, brain, and muscles, and the concentrations of zinc-dependent enzymes and proteins. The first stage of data preprocessing involved the analysis and filling of missing values; gaps were found in 25 columns associated with microelements in muscles (for the positive control group C⁺) and brain (for the negative control group C⁻). To fill them, we used the average values of the corresponding features within the experimental groups, which preserved the group specificity of the data. In 14 columns (Be, Cd, Hg, Sn in different tissues), we can observe categorical values “<0.0001”, denoting results below the sensitivity threshold of the laboratory equipment. These values were replaced by a numeric constant—the lower limit of sensitivity (0.0001)—in order to avoid data loss and preserve information about the presence of the element. After that, we searched for outliers using the interquartile range (IQR). For each feature, we calculated the 25th (Q1) and 75th (Q3) percentiles, defined the outlier boundaries as Q1—1.5 × IQR (lower) and Q3 + 1.5 × IQR (upper), and replaced the values outside these boundaries with the closest acceptable ones (for example, the upper or lower boundary). This helps minimize the impact of anomalies on subsequent analysis without completely deleting the data. Then, we standardized the features using the StandardScaler method, converting all numeric variables to a single scale (mean = 0, standard deviation = 1), which is necessary for the correct operation of machine learning algorithms. The categorical feature “Experimental group” is converted to a numeric format.

For clarity, we will use the following data annotations in the paper:

• EH_1—original data on element content;
• EH_2—original data on proteins and enzymes content;
• EH_Synt_1—synthetic data on element content;
• EH_Synt_2—synthetic data on proteins and enzymes content.

To determine the optimal concentration of ZnO nanoparticles, we introduce a custom weighted importance score as follows: Let $C=\{c_1,c_2,\dots ,c_n\}$ be a set of chemical elements (columns in EH_1 data), and $R=\{r_1,r_2,\dots ,r_m\}$ be a set of rat objects (rows in EH_1 data). Let $G(c_i)$ be a group of elements $c_i$, where

$$\begin{array}{l}G(c_i)=1:\mathrm{Essential};\\ G(c_i)=0.5:\mathrm{Partially}\mathrm{essential};\\ G(c_i)=-1:\mathrm{Toxic}.\end{array}$$

(1)

Let $I(c_i)$ be an importance coefficient of element $c_i$, calculated using the random forest feature importance method. Let $W(c_i)$ be a final weight for element $c_i$, defined as follows:

$$W(c_i)=I(c_i)\cdot G(c_i).$$

(2)

Let $X(r_j,c_i)$ be a value of element $c_i$ in row (rat object) $r_j$. Let $S(r_j)$ be a weighted score for rat $r_j$, defined as follows:

$$S(r_j)={\displaystyle \sum _{i=1}^{n}X(r_j,c_i)\cdot W(c_i)}.$$

(3)

Let $E_k\subseteq R$ be the subset of rats in experimental group k. The average weighted importance score for group k is as follows:

$$\overline{S}(k)={\displaystyle \frac{1}{\left|E_k\right|}}{\displaystyle \sum _{r_j\in E_k}S(r_j)}.$$

(4)

Let us formulate a problem of multicriteria optimization to select an optimal experimental group based on ZnO nanoparticle dosage. Let $Z_d$ denote the zinc level in the blood in group d, ${\mathrm{Balance}}_d$ denote the microelement balance index in group d, and ${\mathrm{Toxicity}}_d$ denote the toxicity index in group d. For each group d, we calculate the following values:

• 1. Zinc recovery efficacy (relative to the norm), defined as follows:

  $${\mathrm{Efficacy}}_d={\displaystyle \frac{Z_d-Z_{C^{+}}}{Z_{C^{-}}-Z_{C^{+}}}}.$$

  (5)
• 2. Balance of elemental composition (average deviation from the norm), defined as follows:

  $${\mathrm{Balance}}_d={\displaystyle \frac{1}{L}}{\displaystyle \sum _{l=1}^L\exp \left(-\frac{{({\mu }_{l,d}-{\mu }_{l,C^{-}})}^2}{2{(c\cdot {\sigma }_{j,C^{-}})}^2}\right)},{\mathrm{Balance}}_d\in (0,1],$$

  (6)

  where L is the number of elements, ${\mu }_{l,d}$ is the average level of the l-th element in group d, ${\mu }_{l,C^{-}}$ and ${\sigma }_{j,C^{-}}$ denote the average level and standard deviation of the l-th element in the negative control group C⁻.
• 3. Toxicity (deviation of toxic elements) is defined as follows:

  $${\mathrm{Toxicity}}_d=\max \left(0,{\displaystyle \frac{1}{P}}{\displaystyle \sum _{p=1}^P\frac{{\mu }_{p,d}-{\mu }_{p,C^{-}}}{2{\sigma }_{p,C^{-}}}}\right),$$

  (7)

  where P is the number of toxic microelements, ${\mu }_{p,d}$ is the average level of the p-th toxic element in group d, and ${\mu }_{p,C^{-}}$ and ${\sigma }_{p,C^{-}}$ are the average level and standard deviation of the p-th toxic element in the negative control group C⁻.

The integral indicator of efficiency and safety score is defined as follows:

$${\mathrm{IIES}}_d=w_e\cdot {\mathrm{Efficacy}}_d+w_b\cdot {\mathrm{Balance}}_d-w_t\cdot {\mathrm{Toxicity}}_d,$$

(8)

where the w_e, w_b, and w_t weights reflect the importance of each criterion. The assigned weights are as follows: w_t = 2, w_b = 1, and w_e = 2. This weighting scheme is justified by the prioritization of environmental safety—emphasizing toxicity minimization—and process efficiency in zinc recovery, which are considered more critical than functional performance indicators in the context of the present analysis.

The optimal dose of nanoparticles is defined as follows:

$$d^{*}=\underset{d\in \left\{\mathrm{GI},\mathrm{GII},\mathrm{GIII},\mathrm{GIV},\mathrm{GV}\right\}}{\arg \max }{\mathrm{IIES}}_d.$$

(9)

The proposed approach is robust since it is resistant to outliers and does not require the assumption of normal distribution; the approach is biologically relevant, since elements with small σ make a greater contribution, and natural variability is automatically considered; it is comparable, since a single scale is used for different elements and an integral balance assessment is applied.

3.2. Synthetic Data Generation and Evaluation

With an EH_1 dataset of only 35 records, the sample size is extremely limited, which can lead to biased and underrepresented results. This scarcity of data can result in a lack of generalizability, making it challenging to draw meaningful conclusions about the effects of different doses of zinc oxide nanoparticles. GANs can help alleviate this issue by generating new, synthetic data that can augment the existing dataset, thereby increasing its size and improving its representativeness. CTGAN [40] was used for data augmentation to generate new records for each of the four experimental groups with doses of 1.55/3.1/6.2/150 mg/kg, respectively. The use of GANs for data augmentation can be validated through various metrics, including the SDMetrics library (https://github.com/sdv-dev/SDMetrics (accessed on 15 May 2025)).

Table 3. Evaluation of augmented data.

Number of Records	Total Score	Column Shapes Score	Column Pair Trends Score
EH_Synt_1 data
100	0.8069	0.7217	0.8922
200	0.8059	0.7213	0.8904
300	0.8132	0.7302	0.8961
500	0.8120	0.7288	0.8953
EH_Synt_2 data
100	0.8270	0.7729	0.8811
200	0.8285	0.7724	0.8845
300	0.8254	0.7715	0.8793
500	0.8269	0.7730	0.8807

aggregates the metrics obtained by the report of the SDMetrics library on synthesized data. The shape of a column describes its overall distribution. The higher the Column Shapes score, the more similar the distributions of real and synthetic data. The trend between the two columns describes how they vary in relation to each other. The higher the Column Pair Trends score, the more the trends are alike. The Total Score reflects the average of all the scores. Figure 1 and Figure 2 show KDE plots of the distribution of observations of real and synthetic data. It can be concluded that the size of the generated data sample does not affect the quality metrics of synthetic data. More than half of the chemical elements in the synthetic data have distributions close to the real ones, and elements As, B, Be, Cd, Co, Cr, Hg, Li, Mn, Pb, Sn, and V have wider distribution patterns. All proteins and enzymes in the synthetic data have distributions close to the real ones.

3.3. Non-Linear Regression Models

The nonlinear nature of the dependence of the element content on the dose of ZnO nanoparticles is due to the fact that the biochemistry of chemical elements is determined by various competitive chemical processes and specific cellular responses. Therefore, in this study, we created a custom loss function that penalizes models that predict negative values, zero values, and values close to each other by the threshold.

Let $y_{\mathrm{true}}\in {\mathbb{R}}_n$ denote true target values (ground truth), $y_{\mathrm{pred}}\in {\mathbb{R}}_n$ denote predicted values from the model, and n denote the number of predictions in the batch. We define the following components:

1. The mean squared error is defined as follows:

$$\mathrm{MSE}(y_{\mathrm{true}},y_{\mathrm{pred}})={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n{(y_{\mathrm{true},\mathrm{i}}-y_{\mathrm{pred},\mathrm{i}})}^2}.$$

(10)

2. The penalty for negative predictions is defined as follows:

$$\mathrm{NegPenalty}(y_{\mathrm{pred}})={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n\max (-y_{\mathrm{pred},\mathrm{i}},0)}.$$

(11)

3. The penalty for zero predictions is defined as follows:

$$\mathrm{ZeroPenalty}(y_{\mathrm{pred}})={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n{1}_{\{y_{\mathrm{pred},\mathrm{i}}=0\}}},.$$

(12)

where $1_{\{\cdot \}}$ is the indicator function (1 if the condition is true, else 0).

4. The penalty for similar predictions is applied when adjacent predictions are too close to each other, based on a threshold. Let $\tau$ be the threshold value. The penalty for similar predictions is defined as follows:

$$\left\{\begin{array}{c}\mathrm{SamePenalty}(y_{\mathrm{pred}})={\displaystyle \frac{1}{n-1}}{\displaystyle \sum _{i=1}^{n-1}\max (\tau -\left|y_{\mathrm{pred},\mathrm{i}+1}-y_{\mathrm{pred},\mathrm{i}}\right|,0),\mathrm{if}\mathrm{n}>1}\\ \mathrm{SamePenalty}(y_{\mathrm{pred}})=0,\mathrm{otherwise}\end{array}\right.,$$

(13)

Then, the general custom loss function is defined as follows:

$$\begin{array}{l}L(y_{\mathrm{true}},y_{\mathrm{pred}})=\mathrm{MSE}(y_{\mathrm{true}},y_{\mathrm{pred}})+\\ +5.0\cdot \mathrm{NegPenalty}(y_{\mathrm{pred}})+2.5\cdot \mathrm{ZeroPenalty}(y_{\mathrm{pred}})+2.5\cdot \mathrm{SamePenalty}(y_{\mathrm{pred}}).\end{array}$$

(14)

Due to the extreme sparsity of experimentally validated concentrations (only 35 data points across a range of 1–150 mg), we used the 2:1 ratio, which reflects a hierarchical severity in terms of scientific interpretability and model utility. This aligns with principles in constrained regression and physical modeling, where violating physical constraints is prioritized over other forms of inaccuracy.

Non-linear regression algorithms can be used to predict non-linear relationships between the concentration of ZnO nanoparticles and the levels of each element in blood. Since we want to make predictions for concentration values that were not included in the original laboratory experiment, decision tree-based regression models are not appropriate for this task. Therefore, in this study, to build a single-feature regression model, we will focus on the use of artificial neural networks and the Kernel Ridge regression algorithm with varying activation functions and kernels. Both MLPRegressor and Kernel Ridge from the Scikit-learn library (https://scikit-learn.org/ (accessed on 5 June 2025)) do not support custom loss functions; therefore, we implemented custom regression models based on TensorFlow and PyTorch solutions:

1. We define a fully connected feedforward artificial neural network model. A linear stack of layers is defined using Sequential(), where each layer feeds directly into the next without any branching or skipping connections. The input shape is dynamically determined by training data. Two fully connected (dense) hidden layers, each consisting of 64 artificial neurons, are used. Each neuron applies a linear transformation followed by an activation function (‘tanh’, ‘sigmoid’, ‘softmax’, or ‘swish’). As an output layer, a single neuron with linear activation is used, producing a scalar output value. The Adam optimizer is used, which is an adaptive learning rate optimization algorithm based on estimates of the first and second moments of the gradients. The model is trained for 100 epochs. Mini-batch gradient descent is applied with a batch size of 32, balancing computational efficiency and convergence stability. Moreover, 20% of the training data is reserved for validation during training, enabling early detection of overfitting or underfitting.

2. We define a nonlinear regression model formulated specifically within the dual formulation of kernel ridge regression. The model learns a set of coefficients α associated with training samples in a reproducing kernel Hilbert space. The objective function optimized during training consists of the MSE metric, L2 regularization on dual coefficients, and a custom loss function $ℒ$ Equation (14). The model parameters α are initialized randomly and optimized using the Adam optimizer. Training is performed over 2500 epochs using full-batch gradient descent since all samples are used at each step. Gradients are computed explicitly through automatic differentiation in PyTorch. The model uses one of the kernels (RBF, Chi-squared, or Laplacian) to capture nonlinear relationships between inputs and outputs.

We will focus our predictive studies on the levels of elements in the blood due to the fact that blood functions as a multifunctional transport system, essential for sustaining cellular metabolism, coordinating physiological responses, and maintaining systemic homeostasis in multicellular organisms.

4. Results

4.1. Data Analysis of Elemental Homeostasis of Wistar Rats

Chord diagrams from HoloViews v1.21.0 library allow us to visualize the weighted relationships between features in data. Figure 3 shows the chord diagrams of the EH_1 dataset in general and for each organ separately, with a threshold of 0.5. The size of the arc is proportional to the importance of each feature. The thickness of the connection between features is the magnitude of the correlation (the higher the correlation, the thicker the connection). As for color, blue is a positive correlation, and red is a negative one. Notably, the kidneys, liver, and brain exhibited strong inter-element correlations, indicating a high level of elemental homeostasis regulation and possible susceptibility to systemic disruption upon exposure. In contrast, the weaker correlations observed in the heart, muscles, and the overall dataset suggest either more localized or less synchronized elemental responses in these tissues. Specifically, I, Na, and Sn emerged as key interacting elements in the global dataset, while organ-specific analyses identified sets of influential elements—Na, Fe, Cu, Se, I, V in blood; Zn, Fe, Mg, Si, Mn in brain; and Na, Se, I, V in muscles. These findings imply that zinc oxide nanoparticles may influence specific elemental networks in an organ-dependent manner, potentially affecting physiological functions related to those elements, such as neurotransmission, oxygen transport, and redox balance.

To assess the strength of the correlation between chemical elements, proteins, and enzymes for different experimental groups of the Wistar rats, the integral indicator correlation graph weight (CGW) can be used [41]. The results of the calculations of the CGW are presented in

Table 4. Correlation graph weight calculations.

№	Experimental Group	CGW	CGW, α = 0.5
Both EH_1 and EH_2 datasets
1	C+	457.35	293.23
2	C−	470.82	315.21
3	I group (6.2 mg/kg ZnO)	461.12	300.87
4	II group (6.2 mg/kg ZnO NPs)	440.52	279.65
5	III group (3.1 mg/kg ZnO NPs)	474.28	302.99
6	IV group (1.55 mg/kg ZnO NPs)	455.50	294.54
7	V group (150 mg/kg ZnO NPs)	466.35	299.43
Blood data
1	C+	23.93	15.82
2	C−	25.18	17.52
3	I group (6.2 mg/kg ZnO)	24.18	15.56
4	II group (6.2 mg/kg ZnO NPs)	25.04	16.74
5	III group (3.1 mg/kg ZnO NPs)	23.40	15.44
6	IV group (1.55 mg/kg ZnO NPs)	25.44	17.26
7	V group (150 mg/kg ZnO NPs)	27.27	19.70
Brain data
1	C+	48.77	34.56
2	C−	52.12	41.30
3	I group (6.2 mg/kg ZnO)	45.41	33.43
4	II group (6.2 mg/kg ZnO NPs)	47.69	34.02
5	III group (3.1 mg/kg ZnO NPs)	44.50	30.73
6	IV group (1.55 mg/kg ZnO NPs)	47.75	36.21
7	V group (150 mg/kg ZnO NPs)	51.54	37.71
Kidney data
1	C+	14.79	10.47
2	C−	19.62	17.20
3	I group (6.2 mg/kg ZnO)	13.90	9.83
4	II group (6.2 mg/kg ZnO NPs)	15.91	11.48
5	III group (3.1 mg/kg ZnO NPs)	12.69	8.56
6	IV group (1.55 mg/kg ZnO NPs)	16.43	12.64
7	V group (150 mg/kg ZnO NPs)	15.53	11.40
Liver data
1	C+	24.29	19.18
2	C−	23.76	17.65
3	I group (6.2 mg/kg ZnO)	25.25	18.48
4	II group (6.2 mg/kg ZnO NPs)	21.33	14.16
5	III group (3.1 mg/kg ZnO NPs)	21.19	15.25
6	IV group (1.55 mg/kg ZnO NPs)	24.55	18.74
7	V group (150 mg/kg ZnO NPs)	21.54	14.95
Muscle data
1	C+	26.70	20.00
2	C−	13.78	8.70
3	I group (6.2 mg/kg ZnO)	14.38	10.93
4	II group (6.2 mg/kg ZnO NPs)	13.41	8.21
5	III group (3.1 mg/kg ZnO NPs)	15.37	10.77
6	IV group (1.55 mg/kg ZnO NPs)	13.43	8.58
7	V group (150 mg/kg ZnO NPs)	15.21	10.78

. A dose of 6.2 mg/kg ZnO nanoparticles in feed, according to the CGW value with a threshold α = 0.5, reduces the strength of the correlation of elemental homeostasis for the general dataset, liver, and muscle data. A dose of 3.1 mg/kg ZnO nanoparticles in feed, according to the CGW value with a threshold α = 0.5, reduces the strength of the correlation of elemental homeostasis for the blood, brain, and kidney data. The maximum correlation between the indicators of chemical elements, proteins, and enzymes is observed for experimental group V (150 mg/kg ZnO NPs) in the blood; in the negative control group C⁻ in the brain and kidneys; and in the positive control group C⁺ with zinc deficiency in the liver and muscles.

The ranked results of the weighted importance score calculations (Equation (4)) are presented in

Table 5. Weighted importance score comparison.

№	Experimental Group	Weighted Importance Score
1	III group (3.1 mg/kg ZnO NPs)	1.319
2	C−	1.224
3	II group (6.2 mg/kg ZnO NPs)	1.095
4	I group (6.2 mg/kg ZnO)	1.063
5	V group (150 mg/kg ZnO NPs)	1.061
6	IV group (1.55 mg/kg ZnO NPs)	1.011
7	C+	0.58

. A dosage of 3.1 mg/kg ZnO nanoparticles in rat feed, according to the weighted importance score value, is the best one based on feature importance and element group factors; Equations (1) and (2).

Figure 4a shows the results of calculating the IIES score (Equation (8)) for each experimental group; Figure 4b shows the results of calculating the IIES score for zinc recovery efficacy (Equation (5)), microelement balance (Equation (6)), and toxicity (Equation (7)). Figure 5 shows the results of calculating the IIES score for blood and organs separately.

In Figure 5, we observed a significant decrease in the microelement balance in the liver in all experimental groups compared to other organs. This indicates that the liver, as a central organ of metabolism and detoxification, is most sensitive to the introduction of zinc oxide nanoparticles. Violation of the balance of elements in the liver indicates the potential hepatotoxicity of nanoparticles, which requires special attention when assessing the safety of therapeutic doses.

4.2. Predictive Models of Toxic and Essential Elements in the Blood of Laboratory Animals Based on the Dosage of Zinc Oxide Nanoparticles

Predictive models for forecasting the levels of a group of essential elements (Fe, Zn, Cu, Mn, Co, Se, I, Cr) were constructed. We compared two regression models for forecasting, with varying activation functions and kernels, based on a custom loss function (Equation (14)), RMSE and MAE metrics values, and residual distribution analysis. The metric values are averaged over 15 model runs with different splits of data into training and test sets.

Table 6. Comparison of regression models and their parameters for predicting the levels of essential elements in the EH_Synt_1 dataset.

№	Element	Model	Parameters	RMSE	MAE	Residuals Distribution	Predicted Max Content
1	Fe	Kernel Ridge	kernel = ‘rbf’	0.2787	0.3995	Asymmetrical	2.9512
			kernel = ‘chi2’	0.3195	0.4205	Asymmetrical	2.7698
			kernel = ‘laplacian’	0.3515	0.4443	Asymmetrical	2.6436
		FCNN	activation = ‘tanh’	0.2619	0.3905	Asymmetrical	3.2968
			activation = ‘sigmoid’	0.3102	0.4442	Asymmetrical	2.9483
			activation = ‘softmax’	0.2841	0.4203	Asymmetrical	2.7619
			activation = ‘swish’	0.3498	0.4237	Asymmetrical	3.5429
2	Zn	Kernel Ridge	kernel = ‘rbf’	0.2621	0.3988	Asymmetrical	2.0894
			kernel = ‘chi2’	0.2246	0.3739	Multimodal	2.4197
			kernel = ‘laplacian’	0.2591	0.4104	Asymmetrical	2.5861
		FCNN	activation = ‘tanh’	0.1029	0.2556	Asymmetrical	2.3542
			activation = ‘sigmoid’	0.1644	0.3198	Asymmetrical	2.0265
			activation = ‘softmax’	0.1016	0.2531	Asymmetrical	2.2347
			activation = ‘swish’	0.1797	0.3071	Asymmetrical	2.1959
3	Cu	Kernel Ridge	kernel = ‘rbf’	0.6491	0.6345	Asymmetrical	3.0081
			kernel = ‘chi2’	0.6063	0.6091	Asymmetrical	2.7348
			kernel= ‘laplacian’	0.6079	0.6043	Asymmetrical	2.7927
		FCNN	activation = ‘tanh’	0.5197	0.5419	Asymmetrical	2.7821
			activation = ‘sigmoid’	0.5959	0.5853	Asymmetrical	2.2453
			activation = ‘softmax’	0.6274	0.5906	Asymmetrical	2.3305
			activation = ’swish’	0.6028	0.5955	Asymmetrical	2.5059
4	Mn	Kernel Ridge	kernel = ‘rbf’	0.3409	0.4838	Multimodal	1.2808
			kernel = ‘chi2’	0.2695	0.4232	Multimodal	0.6692
			kernel = ‘laplacian’	0.3207	0.4336	Multimodal	0.5349
		FCNN	activation = ‘tanh’	0.0309	0.1412	Multimodal	0.2166
			activation = ‘sigmoid’	0.0323	0.1461	Multimodal	0.2598
			activation = ‘softmax’	0.0301	0.1368	Multimodal	0.3187
			activation = ’swish’	0.0413	0.1470	Multimodal	0.2062
5	Co	Kernel Ridge	kernel = ‘rbf’	0.3930	0.4909	Multimodal	0.3964
			kernel = ‘chi2’	0.2161	0.3426	Multimodal	0.6996
			kernel = ‘laplacian’	0.3082	0.4400	Multimodal	0.8097
		FCNN	activation = ‘tanh’	0.0336	0.1484	Multimodal	0.2830
			activation = ‘sigmoid’	0.0363	0.1584	Multimodal	0.3190
			activation = ‘softmax’	0.0305	0.1298	Multimodal	0.3104
			activation = ’swish’	0.1126	0.2129	Multimodal	0.5359
6	Se	Kernel Ridge	kernel = ‘rbf’	0.1816	0.3158	Multimodal	1.6265
			kernel = ‘chi2’	0.3138	0.4278	Multimodal	2.0551
			kernel = ‘laplacian’	0.3660	0.4779	Multimodal	1.1546
		FCNN	activation = ‘tanh’	0.0224	0.1242	Asymmetrical	0.5166
			activation = ‘sigmoid’	0.0243	0.1283	Asymmetrical	0.4496
			activation = ‘softmax’	0.0193	0.1164	Asymmetrical	0.4557
			activation = ’swish’	0.0636	0.1474	Asymmetrical	0.5595
7	I	Kernel Ridge	kernel = ‘rbf’	0.3719	0.4487	Multimodal	1.1298
			kernel = ‘chi2’	0.3036	0.4342	Multimodal	0.7566
			kernel = ‘laplacian’	0.2773	0.4258	Multimodal	1.2144
		FCNN	activation = ‘tanh’	0.0210	0.1134	Multimodal	0.3210
			activation = ‘sigmoid’	0.0209	0.11511	Multimodal	0.4038
			activation = ‘softmax’	0.0161	0.1030	Multimodal	0.3103
			activation = ’swish’	0.0582	0.1437	Multimodal	0.3563
8	Cr	Kernel Ridge	kernel = ‘rbf’	0.4244	0.5110	Multimodal	0.3600
			kernel = ‘chi2’	0.1800	0.3301	Multimodal	1.0060
			kernel = ‘laplacian’	0.2813	0.4280	Multimodal	0.8072
		FCNN	activation = ‘tanh’	0.0291	0.1362	Multimodal	0.2161
			activation = ‘sigmoid’	0.0340	0.1504	Multimodal	0.3866
			activation = ‘softmax’	0.0297	0.1378	Multimodal	0.2245
			activation = ’swish’	0.0648	0.1715	Multimodal	0.4179

presents the results of the comparison of regression models; Figure 6a shows graphs of the best models with minimal RMSE metric values.

Predictive models for forecasting the levels of a group of toxic elements (Sn, Al, As, Hg, Pb, Be, Cd) were constructed.

Table 7. Comparison of regression models and their parameters for predicting the levels of toxic elements in the EH_Synt_1 dataset.

№	Element	Model	Parameters	RMSE	MAE	Residuals Distribution	Predicted Max content
1	Sn	Kernel Ridge	kernel = ‘rbf’	0.3273	0.4493	Multimodal	0.6358
			kernel = ‘chi2’	0.3228	0.4881	Multimodal	0.5155
			kernel = ‘laplacian’	0.2566	0.4080	Multimodal	0.8477
		FCNN	activation = ‘tanh’	0.0325	0.1469	Multimodal	0.2775
			activation = ‘sigmoid’	0.0315	0.1438	Multimodal	0.2979
			activation = ‘softmax’	0.0299	0.1368	Multimodal	0.3272
			activation = ‘swish’	0.0761	0.1931	Multimodal	0.5563
2	Al	Kernel Ridge	kernel = ‘rbf’	0.2435	0.4112	Multimodal	0.8085
			kernel = ‘chi2’	0.4254	0.4732	Asymmetrical	0.3071
			kernel = ‘laplacian’	0.3558	0.4688	Multimodal	0.3434
		FCNN	activation = ‘tanh’	0.0248	0.1264	Asymmetrical	0.3146
			activation = ‘sigmoid’	0.0308	0.1452	Asymmetrical	0.3201
			activation = ‘softmax’	0.0325	0.1494	Asymmetrical	0.3039
			activation = ‘swish’	0.1629	0.2027	Multimodal	0.6211
3	As	Kernel Ridge	kernel = ‘rbf’	0.3767	0.4672	Multimodal	1.8047
			kernel = ‘chi2’	0.3368	0.4689	Multimodal	0.5911
			kernel = ‘laplacian’	0.2887	0.4435	Multimodal	0.7845
		FCNN	activation = ‘tanh’	0.0288	0.1367	Multimodal	0.2441
			activation = ‘sigmoid’	0.0349	0.1538	Multimodal	0.2718
			activation = ‘softmax’	0.0272	0.1314	Multimodal	0.2665
			activation = ’swish’	0.1043	0.1979	Multimodal	0.5054
4	Hg	Kernel Ridge	kernel = ‘rbf’	0.3155	0.4647	Multimodal	0.6869
			kernel = ‘chi2’	0.3728	0.4747	Multimodal	1.0555
			kernel = ‘laplacian’	0.3018	0.4151	Multimodal	0.4964
		FCNN	activation = ‘tanh’	0.0342	0.1497	Multimodal	0.3177
			activation = ‘sigmoid’	0.0353	0.1552	Multimodal	0.3263
			activation = ‘softmax’	0.0292	0.1337	Multimodal	0.3183
			activation = ’swish’	0.0679	0.1671	Multimodal	0.1973
5	Pb	Kernel Ridge	kernel = ‘rbf’	0.2680	0.4015	Multimodal	1.3640
			kernel = ‘chi2’	0.2704	0.4107	Multimodal	0.6657
			kernel = ‘laplacian’	0.3206	0.4354	Multimodal	0.9522
		FCNN	activation = ‘tanh’	0.0322	0.1455	Multimodal	0.3568
			activation = ‘sigmoid’	0.0330	0.1484	Multimodal	0.3164
			activation = ‘softmax’	0.0294	0.1350	Multimodal	0.3146
			activation = ’swish’	0.1638	0.2251	Multimodal	0.3828
6	Be	Kernel Ridge	kernel = ‘rbf’	0.3186	0.4307	Multimodal	0.8344
			kernel = ‘chi2’	0.4514	0.5470	Multimodal	0.9656
			kernel = ‘laplacian’	0.3062	0.4377	Multimodal	0.1190
		FCNN	activation = ‘tanh’	0.0382	0.1597	Multimodal	0.2436
			activation = ‘sigmoid’	0.0328	0.1487	Multimodal	0.3366
			activation = ‘softmax’	0.0313	0.1340	Multimodal	0.2603
			activation = ’swish’	0.1704	0.2423	Multimodal	0.3919
7	Cd	Kernel Ridge	kernel = ‘rbf’	0.2955	0.4306	Multimodal	0.4646
			kernel = ‘chi2’	0.2932	0.4290	Multimodal	0.8920
			kernel = ‘laplacian’	0.3988	0.4934	Multimodal	0.8130
		FCNN	activation = ‘tanh’	0.0322	0.1434	Multimodal	0.4029
			activation = ‘sigmoid’	0.0335	0.1493	Multimodal	0.2838
			activation = ‘softmax’	0.0268	0.1269	Multimodal	0.3301
			activation = ’swish’	0.1734	0.2314	Multimodal	0.4846

presents the results of the comparison of regression models; Figure 6b shows graphs for the best models with minimal RMSE metric values.

Predictive models for forecasting the levels of a group of proteins and ferments (CA4, ADH1B, ALP, ZAG, SOD-Zn, MT1, MT2, MT3) were constructed.

Table 8. Comparison of regression models and their parameters for predicting the levels of proteins and ferments in the EH_Synt_2 dataset.

№	Element	Model	Parameters	RMSE	MAE	Residuals Distribution	Predicted Max Content
1	CA4	Kernel Ridge	kernel = ‘rbf’	14.6207	2.5678	Multimodal	26.9611
			kernel = ‘chi2’	15.6488	2.6430	Asymmetrical	26.0791
			kernel = ‘laplacian’	13.8650	2.4912	Multimodal	24.5711
		FCNN	activation = ‘tanh’	40.6357	4.6784	Asymmetrical	19.3162
			activation = ‘sigmoid’	40.8586	4.7742	Asymmetrical	19.1345
			activation = ‘softmax’	263.2020	14.917	Asymmetrical	4.0573
			activation = ‘swish’	15.0017	2.5964	Asymmetrical	26.8949
2	ADH1B	Kernel Ridge	kernel = ‘rbf’	3.5569	1.2353	Multimodal	54.9218
			kernel = ‘chi2’	4.1477	1.3417	Multimodal	57.6527
			kernel = ‘laplacian’	3.8703	1.2907	Multimodal	47.6248
		FCNN	activation = ‘tanh’	30.7518	4.7432	Multimodal	48.5105
			activation = ‘sigmoid’	37.8307	4.5278	Multimodal	45.5706
			activation = ‘softmax’	2001.93	44.3947	Multimodal	4.1230
			activation = ‘swish’	6.0534	1.8218	Asymmetrical	59.6373
3	ALP	Kernel Ridge	kernel = ‘rbf’	9.9965	1.9220	Multimodal	26.6896
			kernel = ‘chi2’	9.4867	1.8509	Multimodal	26.8992
			kernel = ‘laplacian’	10.3592	1.9001	Multimodal	21.3801
		FCNN	activation = ‘tanh’	22.8733	3.2491	Asymmetrical	22.3343
			activation = ‘sigmoid’	22.2092	3.1820	Multimodal	22.7722
			activation = ‘softmax’	357.2593	18.2905	Asymmetrical	3.9571
			activation = ’swish’	10.1903	2.1047	Asymmetrical	26.9728
4	ZAG	Kernel Ridge	kernel = ‘rbf’	0.0772	0.1955	Multimodal	12.0935
			kernel = ‘chi2’	0.0917	0.2112	Multimodal	12.2758
			kernel = ‘laplacian’	0.0824	0.1989	Multimodal	11.5086
		FCNN	activation = ‘tanh’	0.2983	0.4494	Multimodal	11.6732
			activation = ‘sigmoid’	0.3957	0.5246	Multimodal	11.4666
			activation = ‘softmax’	55.9166	7.4532	Multimodal	3.9647
			activation = ’swish’	0.2390	0.3785	Multimodal	12.1311
5	SOD-Zn	Kernel Ridge	kernel = ‘rbf’	1.4288	0.6696	Multimodal	10.2444
			kernel= ‘chi2’	1.5202	0.6944	Multimodal	10.5237
			kernel = ‘laplacian’	1.4431	0.6727	Multimodal	9.1893
		FCNN	activation = ‘tanh’	1.5072	0.7509	Asymmetrical	10.1673
			activation = ‘sigmoid’	1.6879	0.8332	Asymmetrical	10.0199
			activation = ‘softmax’	28.4987	5.0826	Asymmetrical	3.7381
			activation = ’swish’	1.4718	0.6924	Asymmetrical	10.1762
6	MT1	Kernel Ridge	kernel = ‘rbf’	18.6226	2.6608	Asymmetrical	79.6881
			kernel = ‘chi2’	20.9568	2.8212	Asymmetrical	83.6053
			kernel = ‘laplacian’	20.3503	2.8068	Asymmetrical	75.3316
		FCNN	activation = ‘tanh’	67.1140	7.3396	Multimodal	72.1062
			activation = ‘sigmoid’	395.9441	19.1312	Asymmetrical	64.6869
			activation = ‘softmax’	5555.85	74.3725	Asymmetrical	4.0292
			activation = ’swish’	25.1968	3.9657	Asymmetrical	83.0218
7	MT2	Kernel Ridge	kernel = ‘rbf’	0.9364	0.6131	Asymmetrical	6.3687
			kernel = ‘chi2’	0.9325	0.6285	Asymmetrical	7.1156
			kernel = ‘laplacian’	0.8081	0.5622	Asymmetrical	5.5452
		FCNN	activation = ‘tanh’	1.0611	0.7543	Asymmetrical	6.7182
			activation = ‘sigmoid’	1.0325	0.7113	Asymmetrical	6.4843
			activation = ‘softmax’	6.9113	2.4723	Asymmetrical	3.6365
			activation = ‘swish’	1.0315	0.7060	Asymmetrical	7.2760
8	MT3	Kernel Ridge	kernel = ‘rbf’	0.3527	0.4698	Multimodal	1.0865
			kernel = ‘chi2’	0.3199	0.4196	Multimodal	0.9241
			kernel = ‘laplacian’	0.2291	0.3630	Multimodal	0.9298
		FCNN	activation = ‘tanh’	0.0211	0.1125	Multimodal	0.4658
			activation = ‘sigmoid’	0.0242	0.1233	Multimodal	0.3263
			activation = ‘softmax’	0.0182	0.1104	Multimodal	0.2827
			activation = ‘swish’	0.0895	0.1798	Multimodal	0.4480

presents the results of the comparison of regression models; Figure 7a shows graphs for the best Kernel Ridge models with minimal RMSE metric values, and Figure 7b shows graphs for the best FCNN models with minimal RMSE metric values.

5. Discussion

Essential elements are tightly regulated in biological systems. Their concentrations are expected to remain within narrow physiological ranges. Best prediction results (see Figure 6a) were obtained for softmax and tanh activation functions. These results suggest that the changes in essential element concentrations in response to ZnO NPs exposure are predictable and follow a relatively stable functional relationship, likely due to regulatory mechanisms in the body. Toxic elements typically do not have active physiological roles and may accumulate under certain conditions, especially when barrier functions are overwhelmed. The low concentrations and possibly sporadic or non-linear increases make prediction difficult. FCNN with the softmax activation function shows the best results for the RMSE metric (see Figure 6b), but the forecasts turn out to be template-like for most elements (the forecast either tends to zero or to the maximum threshold value of the element). Such poor performance suggests that toxic element dynamics are not well-captured by probabilistic normalization across classes or outputs. For the Al element with sufficiently high concentration values, the model shows better predictive results compared to elements whose concentration is close to zero.

Enzyme activity reflects metabolic and physiological responses to stress or toxicity. ZnO NPs can induce oxidative stress, inflammation, or cellular damage, altering enzyme release into the bloodstream. Best prediction results are obtained for Kerner Ridge regression models and FCNN with swish activation function. Kernel Ridge regression performs well, suggesting that enzyme responses may be modeled effectively using smooth, regularized nonlinear mappings. It should be noted that Kernel Ridge regression (see Figure 7a) poorly predicts the levels of elements in the blood outside the initial experimental dosages (1.55/3.1/6.2/150 mg/kg) of nanoparticles. The swish activation function may better capture the complex, dose-dependent nonlinear enzyme kinetics induced by ZnO NPs compared to other functions (see Figure 7b). Based on the weighted importance score and the IIES score values, a ZnO nanoparticle dose of 3.1 mg/kg represents an optimal balance between efficacy and physiological stability. The optimal doses of ZnO nanoparticles in rat feed achieved in other studies [27,28] are consistent with the results obtained in this study.

The distribution of certain elements in the synthetic dataset deviates from that in the original dataset, attributable to the sensitivity threshold of the laboratory instrumentation. Comparative analysis of two predictive modeling approaches—FCNN and Kernel Ridge regression—reveals that accurate forecasting is particularly challenging for elements predominantly belonging to the toxic group (whose values are very close to zero), likely due to measurement limitations and, as a consequence, the inability of synthetic data to capture the true dynamics. However, using the proposed methodology, robust predictive models were successfully developed for most other elements whose concentrations were measured with higher precision.

Differential sensitivity of blood components to ZnO NP exposure implies that each category (essential elements, toxic elements, ferments, and enzymes) responds through distinct biological pathways. These findings support the use of hybrid modeling strategies, where different subsets of biomarkers are predicted using tailored algorithms based on their dynamic range and biological context.

6. Conclusions

This study had several limitations that should be acknowledged. This study was conducted on male Wistar rats. Elemental homeostasis was studied after adding zinc oxide nanoparticles to rat feed. Generation of new synthetic data was conducted for each of the four experimental groups with doses of 1.55/3.1/6.2/150 mg/kg, respectively. We are aware of the potential limitations of GAN-based synthetic data generation in preserving biological plausibility, particularly when trained on small datasets.

To mitigate this risk and enhance the biological credibility of the generated data:

• We rigorously evaluated the similarity between the original and synthetic datasets using the SDMetrics tool and KDE plots;
• During training, we incorporated domain-informed constraints to prevent the generation of physiologically implausible values with a custom loss function;
• The utility of the augmented dataset was assessed through the performance of two predictive models (FCNN and Kernel Ridge).

Therefore, we position the synthetic data as a tool for statistical augmentation under the assumption of distributional stability, not as a substitute for mechanistic modeling.

This study demonstrates that the effects of ZnO nanoparticles on rat blood composition are complex and group-specific. Predictive accuracy depends not only on data quality and quantity, but also on aligning the model’s architecture with the biological and physicochemical characteristics of the target variables. Future work should consider multi-model ensembles, adaptive activation functions, and interpretability tools to further elucidate the mechanisms of nanoparticle–biological interactions. In conclusion, nanoparticles have the potential to transform various fields, from animal husbandry to agriculture, and their use has significant implications for animal nutrition and animal health. However, it is essential to address the concerns surrounding nanoparticle toxicity and develop strategies for safe handling and use.