*2.3. Structure of the Three Different Granularity of OIDFs*

#### 2.3.1. Particle Size Determination

In total, a 0.1% (*m*/*v*) OIDF-10, OIDF-50 and OIDF-100 suspension was prepared. The particle size and specific surface area were analyzed using a BT-9300HT laser particle sizer (Bettersize Instruments Ltd., Dandong, China).

#### 2.3.2. Scanning Electron Microscopy (SEM)

After spraying with gold-palladium alloy, the microscopic appearance of OIDF-10, OIDF-50 and OIDF-100 was studied using a scanning electron microscope (SEM; Zeiss Supra55VP, Carl Zeiss, Jena, Germany). The scanning pictures were taken at magnifications ranging from 1000 (scale bar 20 μm) to 8000 (scale bar 2 μm) at accelerating voltages of 20 kV.

#### 2.3.3. Fourier Infrared Spectrum (FT-IR)

The three distinct granularities of OIDF were evenly mixed with KBr at a 1/100 (*w*/*w*) ratio and pressed into tablets. Each sample was scanned using a Fourier-infrared spectrometer (IRTracer-100, Shimadzu, Kyoto, Japan) throughout a wave range of 4000 cm−<sup>1</sup> to 400 cm−<sup>1</sup> with a resolution of 4 cm<sup>−</sup>1.

#### 2.3.4. Determination of Thermogravimetry (TG)

Thermogravimetry (TG) is a technical method to measure the relationship between the mass of a substance and temperature under the condition of a program-controlled specific temperature. Thermogravimetric analysis of OIDF-10, OIDF-50, and OIDF-100 was carried out by the HCT-3 microcomputer differential thermal balance. A sample of weighed 3–4 mg was placed into a crucible, placed on a sling balance, and the parameters were set as follows: initial temperature: 25 ◦C; heating rate: 10 ◦C/min; termination temperature: 600 ◦C; nitrogen flow: 50 mL/min. Mass and temperature/time were recorded continuously to obtain thermogravimetric curves.

#### 2.3.5. Determination of X-ray Diffraction (XRD)

The structures of OIDF-10, OIDF-50 and OIDF-100 were determined using an X-ray diffractometer model XRD-7000. Using Cu-Kα radiation (λ = 0.15418 nm), the working voltage of 40.0 kV, and a working current of 30.0 mA, we took an appropriate amount of sample and placed it on the surface of the sample plate, flattened it with a flat and smooth glass sheet, put it into the diffractometer, and set the parameters as follows: measuring angle: 5◦~90◦; step size: 0.02◦; scanning speed: 4◦/min. The specific crystallinity (degree of crystallinity) calculation formula is as follows:

$$Dc(\%) = \frac{I\_{002} - I\_{am}}{I\_{002}} \times 100\tag{1}$$

where *Dc*—degree of crystallinity; *I*002—diffraction intensity of crystalline region (2θ = 20.78◦); *Iam*—diffraction intensity of amorphous region (2θ = 18.0◦).

#### *2.4. Physicochemical Properties of the Three OIDFs*

2.4.1. Water-Holding Capacity (WHC), Oil-Holding Capacity (OHC) and Water-Swelling Capacity (WSC)

Referring to the method of Zhang et al. [20] with a slight modification, we accurately weighed 0.5 g of OIDF-10, OIDF-50 and OIDF-100 samples into 50 mL centrifuge tubes, added 30 mL of distilled water, shook them evenly and placed them at room temperature for 24 h. They were then centrifuged at 4000 r/min for 20 min, supernatant was then removed, and the mass of the precipitate was weighed. The calculation formula is as follows:

$$\text{WHC(g/g)} = \frac{W\_2 - W\_1}{W\_1} \tag{2}$$

where *W*1—sample mass (g); *W*2—precipitate mass after centrifugation (g).

We accurately weighed 0.5 g of OIDF-10, OIDF-50 and OIDF-100 samples in three separate 50 mL centrifuge tubes, added 30 mL of soybean oil, and evenly shook them. They were then centrifuged at 4000 r/min for 20 min, the upper layer oil was then removed, and the mass of the sediment was weighed. The calculation formula is as follows:

$$\text{OHIC(g/g)} = \frac{W\_2 - W\_1}{W\_1} \tag{3}$$

where *W*1—sample mass (g); *W*2—precipitate mass after centrifugation (g).

We accurately weighed 0.5 g of OIDF-10, OIDF-50 and OIDF-100 samples in triplicate and placed them in a 25 mL graduated cylinder, and read the dry product volume V1. Then, we added 20 mL of distilled water to the graduated cylinder and mixed well. After standing at room temperature for 24 h, we recorded the volume of the fully swollen sample. The calculation formula is as follows:

$$\text{SW(mL/g)} = \frac{V\_2 - V\_1}{W} \tag{4}$$

where *V*1—sample volume (mL); *V*2—swollen volume (mL); *W*—sample mass (g).

2.4.2. Adsorption Capacity of the Three Particle Sizes of OIDF Cholesterol-Adsorption Capacity (CAC)

A total of 1 mg/mL cholesterol in ethanol was made. Then, 0.2 g OIDF-10/OIDF-50/OIDF-100 was mixed with 10 mL cholesterol solution, adjusted to pH = 2/7 (adding water phase would precipitate cholesterol), incubated at 37 ◦C for 2 h (pH = 2/4) or 4 h (pH = 7), centrifuged at 4000 rpm for 20 min, and supernatant obtained to test cholesterol concentration using the OPA technique [21].

#### Sodium Cholate-Adsorption Capacity (SCAC)

A total of 0.1 g OIDF-10/OIDF-50/OIDF-100 was mixed with 10 mL sodium cholate standard solution (0.2 g sodium cholate + 15 mmol/L NaCl aq 100 mL), adjusted to pH = 2, 4, 7, incubated at 37 ◦C for 2 h (pH = 2, 4) or 4 h (pH = 7), centrifuged at 4000 rpm for 20 min, and the permeate was taken to determine the exact concentration of sodium cholate using this method [22].

#### *2.5. Animals and Experimental Diets*

The experiment was conducted in compliance with Jilin Agricultural University's Laboratory Animals Guidelines and was authorized by Jilin Agricultural University's Laboratory Animal Welfare and Ethics Committee (no. 20210422001). SD rats were kept in a temperature-controlled (20–25 ◦C) environment with a 12-h light/dark cycle. SD rats were randomly separated into five groups (*n* = 10) after a week of adaption, with the average weight in each group being comparable. The diet for each of the five groups of SD rats was divided into a normal diet (NC), HD, HD-OIDF-10, HD-OIDF-50, HD-OIDf-100. NC: Normal diet rats; HD: high-fat diet rats; HD-OIDF-10: High-fat diet + OIDF-10 (1000 mg/kg); HD-OIDF-50: High-fat diet + OIDF-50 (1000 mg/kg); HD-OIDF-100: Highfat diet + OIDF-100 (1000 mg/kg); After eight weeks of feeding, all rats were starved for 12 h and then anesthetized at the end of the experiment. For the serum preparation, blood samples were obtained and kept at −80 ◦C for future use. The liver and cecal contents were kept at a temperature of −80 ◦C. The composition of diets for each group is shown in Table 1.


**Table 1.** Composition of experimental diets.

#### *2.6. Lipid Analysis*

The blood concentrations of TC, TG, LDL-C, HDL-C, were measured using commercial test kits employing an enzymatic technique. A microplate reader was used to measure all of the data.

#### *2.7. Histological Analysis*

Liver tissues were fixed in four percent paraformaldehyde, embedded in paraffin for tissue slice preparation (5 m thickness), and stained with hematoxylin and eosin for histological investigation (H&E).

#### *2.8. RNA Extraction and Quantitative Real-Time PCR Analysis*

Total RNA was extracted from the frozen liver using Trizol reagent according to the manufacturer's instructions for quantitative real-time PCR analysis. A spectrophotometer (Thermo Fisher Scientific, Waltham, MA, USA) was used to determine the RNA content and purity at 260 and 280 nm. The cDNA Synthesis Kit was used to reverse-transcribe the total RNA (1 g) into cDNA. Then, using a Biometra TProfessional PCR, mRNA expression was measured using quantitative real-time PCR with the SYBR Premix Ex Taq TM mix (Takara, Shiga, Japan). The manufacturers' websites include the sequences of the primers that were used to amplify the target genes. The subsequent PCR amplification protocol was used: 95 ◦C for 30 s, followed by 40 cycles of 95 ◦C for 10 s, 56 ◦C for 30 s, and 72 ◦C for 30 s. The 2-ΔΔCT technique was used to calculate relative quantification.
