
==== Front
Heliyon
Heliyon
Heliyon
2405-8440
Elsevier

S2405-8440(24)12407-3
10.1016/j.heliyon.2024.e36376
e36376
Research Article
Quantitative MRI post-processing algorithm and visualization research based on moisture status detection of winter jujube
Li Yanan ab
Wang Yijin a
Teng Guifa tguifa@hebau.edu.cn
abc⁎
Yao Jingfa de
Luan Peng a
a College of Information Science & Technology, Hebei Agricultural University, Baoding, 071001, PR China
b Hebei Key Laboratory of Agricultural Big Data, Baoding, 071001, PR China
c Hebei Digital Agriculture Industrial Technology Research Institute, Shijiazhuang, 056400, PR China
d Software Engineering Department, Baoding, 071030, PR China
e Hebei College Intelligent Interconnection Equipment and Multi-modal Big Data Application Technology Research and Development Center, Baoding, 071030, PR China
⁎ Corresponding author. College of Information Science & Technology, Hebei Agricultural University, Baoding, 071001, PR China. tguifa@hebau.edu.cn
14 8 2024
30 8 2024
14 8 2024
10 16 e3637623 5 2024
9 8 2024
14 8 2024
© 2024 The Authors
2024
https://creativecommons.org/licenses/by-nc/4.0/ This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
Quantitative Magnetic Resonance Imaging (qMRI) offers precise measurements of the relaxation characteristics of microstructures, representing a cutting-edge method in non-destructive fruit analysis. This study aims to visualize information on changes in moisture status and distribution at the subcellular level of winter jujube. The 0.5 T nuclear magnetic imaging equipment was utilized to rapidly, non-invasively, and accurately capture the internal relaxation status of the sample with multiple-echo-imaging. By examining the signal and noise data, a simulated dataset was developed to tackle the optimization challenge of estimating parameters for the discrete relaxation model from the multiple-echo-imaging data, especially under conditions of low signal-to-noise ratio (SNR) and in the context of heteroscedastic noise. An optimal weighting factor and the T2NR truncation model have been identified to establish an effective experimental inversion strategy. Subsequently, multiple-echo-imaging can rapidly and stably yielded voxel-level maps under conditions of low signal-to-noise ratio. Utilizing this experimental approach, data from winter jujube was collected and analyzed, facilitating an exploration of water activity (T2 mapping) and associated water content (A2 mapping). Through analyzing winter jujube fruits across two maturity stages, this study elucidates the role of precise quantification and voxel-wise visualization in moisture status detection. The methodology presents an innovative approach for assessing internal moisture distribution in fruits.

Keywords

Quantitative MRI
Winter jujube
Moisture status
T2NR
T2-mapping
==== Body
pmc1 Introduction

Fruits are complex three-dimensional (3D) structures, and their structural and compositional features are the coordinated result of spatial and temporal processes of tissues growth and metabolism [1]. Traditional fruit phenotype imaging techniques, including visible light imaging, fluorescence imaging, thermal infrared imaging, and spectral imaging, greatly facilitate the mining of different fruit phenotypic data [2]. Among them, visible light imaging is mainly used to measure the surface, morphology, color, and texture, while fluorescence imaging technology is mainly used for disease detection of gene resistance. Thermal infrared imaging is used to detect temperature-related information, and spectral imaging technology can image internal components, but with low image accuracy and poor interpretability. Traditional detection techniques have insufficient understanding of fruits at the cellular and tissues levels, and lack the continuous, precise, and non-destructive monitoring ability of experimental data of structural, metabolite, and biophysical parameter changes that occur in fruit tissues during growth, maturation, and harvesting. Therefore, innovative experimental methods and phenotype analysis are needed.

Low-Field Magnetic Resonance Imaging (LF-MRI) equipment has developed rapidly in recent years, with the advantages of low cost, easy maintenance and easy operation, marking that NMR has moved from medical inspection services to a broader field, playing an increasingly important role in agriculture research [[3], [4], [5], [6], [7], [8]], food science [[8], [9], [10], [11]], civil engineering [[12], [13], [14], [15]] and other fields. Weighted images (T2-weighted imaging, T2WI, T1-weighted imaging T1WI) obtained by MRI reflect the relative signal intensity of per-pixel (voxel). Although they reflect the strength of T2 or T1 of the sample, they are not direct T2 or T1 data, resulting in difficulties in quantitatively comparing and analyzing [16]. It mainly relies on visual cognition, where different tissues structures produce different luminance levels, thereby performing qualitative analysis of the images. QMRI, known as nuclear magnetic mapping, is an imaging technique used to presents the most basic and intrinsic relaxation parameters (T2 relaxation or T1 relaxation) of each voxel. Based on the physical principles of nuclear magnetic imaging, a series of weighted nuclear magnetic images are mathematically modeled to calculate the T2 or T1 relaxation of per-voxel. The resulting new images called T2-maping or T1-maping, providing quantifiable information about tissues microstructure and composition. The information is closely related to tissues conditions, and can detect differences between different tissues as well as different status of the same tissues, even in tissues without apparent morphological changes. The strict characteristics of relaxation and the advantages of continuous non-destructive observation can be used to monitor relaxation status and changes, and have high potential application value in tissues component analysis, structural analysis, and quantitative diagnosis [17,18].

Nuclear magnetic resonance (NMR) relaxation data have shown great potential in fruit evaluation. The relaxation data detects hydrogen (H) protons in different status in the sample, and the large number of H protons in fruit cells is an inherent parameter value of fruit texture. The behavior of H protons is contingent upon cellular morphology, arrangement, and intrinsic properties, exhibiting sensitivity to subcellular compartmentalization and the permeability or integrity of cellular membranes. It is influenced by the distribution of water, carbohydrates, gases, and nutrients in the fruit, as well as the mechanical properties of the fruit. Many experts have conducted extensive research to analyze these data. Interactions between water molecules in fruits result in mutual coupling of magnetic moments causing T2 signal attenuation. T2 can be used as an indicator of how active the water is, with shorter T2 values usually indicating lower proton degrees of freedom. T2 relaxation is generally thought to depend on the diffusion of water molecules between adjacent cell compartments separated by cell membranes, influenced by differences in water self-diffusion coefficients, compartment sizes, and membrane permeability, to a large extent depending on the composition of water in the tissues (type and concentration of solutes). It is usually considered to correspond to different water status in the tissues (free water, bound water, or partially bound water), or to vesicles containing water in different subcellular compartments (vacuoles, cytoplasm, cell walls, and extracellular spaces), or to vesicles of cell groups with different volume distributions.

Studies have shown that the different structures, metabolite contents, hardness, texture, defects, growth stages, and processing methods of fruits can cause regular changes in T2, and interpretative models have been established [[19], [20], [21], [22], [23], [24]]. Weighted images are used for texture analysis to observe changes in structure [25], moisture [26], defects [6,27], and to study the changes in structure and quality of fruit tissues during maturation [7,[28], [29], [30], [31]], and processing (drying [32], thermal processes [33]). QMRI of fruits provides spatial information on sample relaxation data, and T2 relaxation maps have been attempted to evaluate microstructural changes [17,18,34,35], the contents of fruit metabolites (such as sugars, starch, etc.) [36,37], defects [38], porosity [26,39], water dynamics [7,40] etc.

The study took the late-maturing variety of fresh-eating jujube (Ziziphus jujuba 'Dongzao') as an experimental and analytical object. Winter jujube, owing to its crisp texture, unique flavor, and high nutrition value, is popular among consumers [41]. China is the main producing area of winter jujube, with the production accounting for about 90 % of the world's output, which is mainly distributed in Shaanxi, Shanxi, Shandong and Hebei provinces [42]. In recent years, the market demand for jujube has been growing steadily, and significant economic benefits have been achieved. In this research, based on the precise expression of T2 relaxation on water, multi-echo magnetic resonance images were used to obtain the T2 relaxation information of the samples under the spatial information of tissues, and quantitatively present the active status, content and distribution of water in winter jujube.

2 Materials and methods

2.1 Experimental trials

The experimental samples for this analysis were picked from Hebei Agricultural University's Winter Jujube Planting Base in Cangzhou. Fresh jujubes of uniform size, without mechanical damage on the surface, with smooth and clean fruit surface, and free of pests and diseases were selected as the experimental samples. After collection, the samples were instantly delivered to the laboratory. Multi-echo MRI images were acquired using the LF-MRI equipment of the Chinese Academy of Sciences. A permanent magnet with a magnetic field strength of 0.5 T and a radio frequency coil that can accommodate samples with an outer diameter of 45 mm, were used to non-destructively obtain mid-plane (cross-sectional) multi-echo MRI images. In the experiment, the MEMS pulse sequence was used to collect 4-layer (Layer) space slice information of the target sample, and the equipment sequence parameters were set to Repetition Time (TR) = 4000 ms (long TR time), Echo Time (TE) = 30, 60, 90, …, collect the SI (magnetization signal intensity) of each slice voxel by different TE, and generate a 4-position slice multi-echo 256 × 256 voxel image set.

In the experiment, T1 relaxation and T2 relaxation are two simultaneous and independent processes. T1 relaxation (longitudinal relaxation, spin-lattice relaxation) is a process in which the excited high-energy level magnetic nucleus transfers energy to the surrounding medium particles and restores itself to the low-energy magnetic nucleus. After the RF pulse is turned off, the time constant T1 of the longitudinal magnetization vector AZ along the direction of the main magnetic field from 0 to the maximum is called the longitudinal relaxation time. T2 relaxation (transverse relaxation, spin-spin relaxation) is the process in which the excited high-energy-level magnetic nucleus transfers energy to the same low-energy-level magnetic nucleus and returns to the low-energy magnetic nucleus itself. After the RF pulse is turned off, the time constant T2 for the disappearance of the Axy transverse magnetization component is called the transverse relaxation time.(1) SI∝N(H)(e−TET2)(1−e−TRT1)

MRI uses the gradient field to spatially encode the signal. By setting TR (repetition time) and TE (echo time), the SI (magnetization signal intensity) of each voxel under the sample space information is obtained. The magnetization signal intensity SI represents the signal intensity, and N (H) is the hydrogen proton density. The signal intensity Signal of a single voxel is denoted by SI.

Analysis of Formula (1) shows that the MRI signal intensity is not only related to tissues properties (T1, T2), but also related to acquisition parameters (TE, TR). Set the device sequence parameter TR = 4000 ms (long TR time), so that the longitudinal magnetization vector in each signal is restored to 100 %, and the influence of T1 relaxation on the image is filtered out. Under the premise that the proton content is basically the same, the voxel-wise brightness of the image obtained at this time reflects the difference in T2 of the sample tissues. Fig. 1 shows the T2 weighted image (T2WI) at the four slices (Layer). The SI (magnetization signal intensity) of the sample under different TEs is recorded voxel-by-voxel according to the spatial information.Fig. 1 SI acquisition process under the attenuation and recovery curve of a certain voxel.

Fig. 1

It can be seen in Fig. 2 that there is a lack of signals from the seeds and endocarp, and the echo images of different tissues of the mesocarp and exocarp under the same TE show different signal intensities, showing that the long T2 tissue is brighter, and the short T2 tissue is brighter dark. At the same slice position, the evolution of signal intensity with increasing TE varies among tissues. Tissues with short T2 exhibit a rapid signal decay, resulting in a darker appearance, whereas those with long T2 display a more gradual change, maintaining a higher signal intensity and a brighter appearance. On the whole, as TE increases, the signal weakens, the noise gradually increases, and consequently, the SNR of the image also decreases.Fig. 2 MEMS pulse sequence image set of jujube equatorial plane.

Fig. 2

The image is processed by using the texture analysis method based on the gray matrix. The mean and standard deviation of the entropy and gradient of each layer's ROI signal are shown in Fig. 3. The texture details of the third slice are clearer, and the third slice is selected as the sample for subsequent quantitative analysis.Fig. 3 ROI signal entropy and signal gradient data table for each layer.

Fig. 3

2.2 Models and methods

2.2.1 Signal model

The relaxation signal of each voxel in qMRI, establishes from an inversion model through exponential decay [42]. Assuming that the voxel in the MRI image represents a single tissue of the sample, the voxel usually contains several types of components or multiple water status with specific characteristics, and the signals of various components or water status are superimposed to in the current voxel. A mono exponential decay model will capture the relaxation times and corresponding amplitudes for an ensemble of all constituents or water status of the tissues.

Without considering the influence of noise, the effective measurement signal of each voxel j at time t is represented by a multiple exponential decay models j and t of transverse relaxation signals.(2) Sjt(θ,t)=∑1eA(e,j)etT2(e,j)t=TE1,……,TEN

In the equation, e represents the total number of exponential components. A(n,j) and T2(n,j) are the amplitude and relaxation time of each exponential component e in voxel j, and t is the echo time for the acquisition of the weighted image. In the present experimental environment, t(n) = 30 ms, 60 ms, ….The parameter θj = {A(1,j),T2(1,j), …,A(e,j),T2(e,j)} characterizes the T2 characteristics of voxel j of the sample. In this experiment, θj can be obtained by inverting the exponential decay model according to Formula (2) for each voxel using the weighted images obtained at multiple echo times. The mono exponential decay model obtains the sum of the relaxation time and corresponding amplitude of all components or water status in the tissues. In this experiment, a mono exponential decay model was used.

The average power of MRI image signals under eight TE times for quantitative analysis of the sample, as shown in Signal_Power in Fig. 3 presented the exponential decay characteristics in the model Formula (2), confirming the validity of the experimental data.

2.2.2 Signal acquisition model

Deffer from high-field devices with high SNR, LF devices have higher noise levels and need to be considered in data processing. The main noise carried during the process of acquiring the real and imaginary channel signals by the equipment's receiving coils is generally considered to be independent additive white Gaussian noise with mean 0 and variance σ2 [1,42]. In the process of image reconstruction, the discrete Fourier transform is used to obtain the MRI image domain data. Due to the linearity and orthogonality of Fourier transforms, the reconstructed MRI image data remains as complex Gaussian white noise. In order to meet the requirements of subsequent image processing and visual display, the modulus operation is applied to the reconstructed real and imaginary data to obtain the final visual MRI image data.

Respectively, ε1 and ε2 are independent additive Gaussian white noise Sjt with mean value 0 and variance σ2. Sjt and ɸjt are the amplitude and phase of the original signal at voxel j of the MRI image and acquisition time t. The observed image is the amplitude image obtained by the reconstruction data through the modulo operation, see Formula (3).(3) yjt=(Sjtcosφjt+ξ1)2+(Sjtsinφjt+ξ2)2

The modulus operation transforms the complex Gaussian noise from a Gaussian distribution to a Rician distribution [1,42], related to the image data, and its probability density function is in Formula (4), with I0 represents the zero-order modified Bessel function.(4) p(yjt/Sjt,σj)=(yjt/σj2)eyjt2+Sjt22σj2I0(yjtSjtσj2)

2.2.3 Signal-noise-ratio (SNR)

The stationarity of the quantitatively analyzed sample signals was tested, and the data of each image were estimated and analyzed. Fig. 4 presents the probability density plots of noise for each image layer (Fig. 4a) and their power spectral density (PSD) plots (Fig. 4b), in addition to the probability density plots (Fig. 4c) of the region of interest (ROI) within the acquisition signals, and their corresponding power spectral density plots (Fig. 4d). The noise signal degraded from the Rayleigh distribution to the Rician distribution, with the noise power increasing layer by layer. The ROI in each layer exhibited high signal-noise-ratio, represented by Gaussian distribution under the Rayleigh distribution, and the ROI power decreased layer by layer. The characteristics of ROI and noise data are shown in Fig. 5. As TE increases, the ROI power signal decreases, and the overall noise power signal increases layer by layer, while the signal-noise-ratio of the ROI decreases layer by layer.Fig. 4 Data analysis in the third slice layers. a: Noise probability density, showing amplitude distribution; b: Noise PSD, displaying frequency distribution; c: Acquisition signal probability density, indicating amplitude distribution; d: Acquisition signal PSD, revealing frequency composition.

Fig. 4

Fig. 5 Analysis of signal and noise data in each layer of weighted MRI image.

Fig. 5

2.2.4 T2 signal-noise-ratio (T2NR)

The signal-noise-ratio in the simulated experimental environment is plotted by the exponential decay relaxation process of a single voxel point at two different T2 times under multiple echoes. The process is shown in Fig. 6. Based on noise in low field equipment cannot be ignored, as the number of echoes (or TE) increases, the useful signal in the collected signal decreases and the noise gradually increases. As a result, the signal-noise-ratio at the back end of the echo chain gradually deteriorates, and the disturbance of the noise to the signal increases layer by layer, and this disturbance is affected by the value of T2, and the data with a large disturbance of T2 affects the fitting results of the parameters. In order to effectively describe the degree to which the target parameter T2 is disturbed by noise during the acquisition process, the T2 signal-noise-ratio (T2NR) [16] is introduced.Fig. 6 Example of disturbance effects of different T2 component attenuation processes in rician noise environments. The red dot represents the signal values obtained at each layer during the multi echo acquisition process for voxels with T2 = 50 ms, while the blue dot represents the signal values obtained at each layer during the multi echo acquisition process for voxels with T2 = 100 ms

Fig. 6

Taking the single index as an example, the signals S1 and Sn detected by the 1st echo and the nth echo can be obtained from Formula (5).(5) T2=TEn−TE1ln(S1/Sn)

The influence of noise in the acquisition environment leads to T2 measurement error, and the standard deviation σT2 of T2 measurement error is an important parameter that characterizes noise propagation. According to the basic error analysis principle, σT2 can be expressed as a function of S1 and Sn, see Formula (6).σT22=σ12(∂T2∂S1)2+σn2(∂T2∂Sn)2=σ12(ΔTES1)2+σn2(ΔTESn)2

σT2=T22ΔTE−1S1−1(σ12+σn2e2ΔTET2)1/2

T2NR is defined as the ratio of the T2 measured mean value to the standard deviation σT2, deduced, see Formula (7).(7) T2NR=T2σT2=ΔTES1T2−1(σ12+σn2e2ΔTET2)−1/2

In Fig. 7, it can be seen intuitively that different T2 are affected by noise in different echo layers, the noise of the same echo layer has different disturbance degrees for different T2, and the same T2 voxels are affected by noise in different echo layers. T2NR reflects the degree of noise disturbance at each T2 time of each layer, which can be used as the echo data screening standard for model parameter evaluation.Fig. 7 Relationship between T2NR with TE and T2.

Fig. 7

2.3 Method for inverting and calculating T2 graph

2.3.1 Evaluation function based on heteroscedasticity

According to the signal relaxation model (Formula (2)), solving the relaxation model parameters (relaxation time and amplitude) boils down to an exponential inversion problem using the measured signals under multiple echoes at each voxel point. The evaluation function is given by Formula (8).(8) CLS(θjˆ)=∑n=1NWn×(yjt−sjt(θjˆ,t))2

The yjt represents the acquisition data of voxel j at the t echo time. Sjt is the echo signal data of voxel j calculated according to model 1 at time t. Parameter j is the estimated relaxation parameter, with e = 1 for the mono exponential decay model, and e = 3 for the triple-exponential decay model.

Wn, the weighting factor, determines the weight of each echo sampling data in the fitting process, which is mostly chosen as 1, 1/σ2 (Variance), and 1/σ (Standard Deviation) [43]. According to the analysis above, the weighted image acquired by the echo sequence has heteroskedasticity. And as TE increases, the noise perturbation of the signal increases layer by layer.

N, the number of sampling points used in the evaluation process, is the length of the echo chain used for model estimation. Truncation models in inversion have been widely studied to select a reasonable N and to resolve noise-induced T2 overestimation. The Subjective Analysis by Experts Method [44,45], in which N is determined by experts based on observations, yielded reproducible and accurate T2 measurements [46], but was subjective. The Automated Truncation Method has feasibility and good reproducibility properties. Studies have proposed effective region-of-interest (ROI) based echo truncation methods [47,48]. However, the insensitivity of parameter metrics in low SNR hinders the application of these methods to voxel-wise truncation. Voxel-wise inverse truncation models often use schemes that determine N based on SNR thresholding [49] or fixed-value [43].

Considering that varying T2 relaxation times exhibit distinct sensitivities to noise perturbation, a T2NR-guided truncation model is introduced to quantify the impact of SNR across diverse T2 inversions. Simulation-based experiments are conducted to identify the optimal values of Wn and N for voxel-wise inversion in MRI scenarios characterized by low SNR.

2.3.2 Evaluation algorithm and initial value estimation strategy

The Levenberg-Marquardt algorithm is one of the optimization algorithms. It has the advantages of the gradient method and the Newton method at the same time. It is fast and accurate, and is suitable for the real-time and accurate calculation requirements of this project for batch algorithms. The LM initialization scheme affects the effectiveness of the algorithm. Unlike setting the initial value based on a priori experience [43], this study, taking into account the physical characteristics, sets the mono exponential inversion initial value as follows (9), (10), (11).(9) θj0={A0(1,j),T20(i,j)}

(10) A20(1,j)=yj(t=30)/(e_30T2(1,j))≈yj(t=30)

(11) T2(1,j)=30/ln(yj(t=30)/yj(t=60))

The initial value of voxel point j under the mono exponential decay model θj0, with the estimated value. Due to the influence of noise, the logarithmic calculation will have a large deviation in some cases, so the data range of (50–250) is used to correct the relaxation time.

3 Results and discussion

3.1 Simulated data experiment

Simulate the experimental noise environment based on the signal and noise models and Formulas shown in Fig. 2, Fig. 3, Fig. 4. In the simulation experiment, three-layered structured data were constructed using three typical T2 times (short, medium, and long) as examples to simulate a noisy environment, resulting in 45 layers of scanned image matrices (as shown in Fig. 8). Weight factors Wn were chosen as 1, 1/σ2 and 1/σ to construct LM VAR_LM and SD_LM. Exponential fitting experiments were conducted on the simulated data with different fitting weights and echo chain lengths to verify the impact of weighting factors and echo selection data on the inversion results.Fig. 8 256x256x45 Simulated data graph. Central signal absent; loop 1: A = 250, T2 = 80 ms; loop 2: A = 250, T2 = 200 ms; loop 3: A = 250, T2 = 600 ms (mono exponential).

Fig. 8

Fig. 9 displays the inversion results for the first, second, and third loops of the simulated data graph, corresponding to three typical T2 times: short, medium, and long, respectively. Fig. 9a, b, and 9c illustrate the results for the short, medium, and long T2 times, respectively. The comparison of these experimental results indicates that the inversion performance of SD_LM and VAR_LM is superior to that of the unweighted classical LM. The symbol ★ denotes the optimal echoes for LM, SD_LM, and VAR_LM.Fig. 9 T2 relaxation by weight and echo. a: Loop 1: Short Relaxation, Varying Weight & Echo; b: Loop 2: Medium Relaxation, Varying Weight & Echo; c: Loop 3: Long Relaxation, Varying Weight & Echo.

Fig. 9

With unweighted classical LM, as the echo chain length increases, the SNR gradually decreases, and the signal at the end of the echo chain is increasingly disturbed by noise, resulting in worse inversion effects. SD_LM and VAR_LM can effectively utilize the high-perturbation noise signal at the end of the echo chain under heteroscedastic environments, achieving better inversion effects, with SD_LM having the best effect. However, increasing the number of echoes after a certain value does not significantly improve the inversion effect. From Fig. 10, it can be seen that the longer the T2 time, the longer the optimal echo chain length required for fitting, and the optimal truncation echo number is related to T2 and its SNR. Formula (7) establishes the mathematical relationship between T2NR signal-noise-ratio and echo chain length and T2. By analyzing the simulated experimental results under typical T2 times, the T2 and T2NR for each echo for this voxel were calculated. At the optimal inversion effect of the classical LM, the short, medium, and long T2 correspond to the 7th, 15th, and 28th echoes respectively, with T2NR less than 0.027. At the optimal inversion effect of SD_LM and VAR_LM, the short, medium, and long T2 correspond to the 9th, 19th, and 39th echoes respectively, with T2NR less than 0.016. To achieve the best fitting effect with the shortest echo chain length, from the perspectives of fitting effect and execution efficiency, T2NR is used as a criterion for selecting the echo chain for inversion, truncating the echo chain in a timely manner, and dynamically adjusting the echo chain length used for parameter estimation for each voxel, which can effectively improve the inversion effect.Fig. 10 T2NR under three types of T2 echoes: short, medium, and long.

Note: marked with ★ for the optimal echo of LM, ▲ for the optimal echo of SD_LM and VAR_LM.

Fig. 10

3.2 Comparison of algorithm results

Inversion experiments of 40-echo, 20-echo, SNR-truncated, and T2NR-truncated (ADA) models under the three fitting algorithms of LM, VAR_LM, and SD_LM are performed on the simulated plots (216*216). After comparing with the standard data, the obtained Amplitude (A) vs. relaxation time (T2) error map (Fig. 11) and data results (Table 1) show that the weighting algorithm and the number of echoes affect the inversion effect of different T2 layers. The weighted VAR_LM and SD_LM show better fitting results than the classical LM, and the SD_LM error spectrum is the smallest, which once again proves that the SD weight factor can obtain better inversion result. The greater the number of echoes, the greater the fitting disturbance for short T2, and the better the inversion effect for long T2. At the same time, the more echoes are used, the more obvious the improvement effect after weighted fitting is. The T2NR adaptive truncation (ADA) provides a consistent and precise estimation of A versus Ttu across the full spectrum of T2 values in simulated datasets, outperforming fixed-value and SNR threshold truncation methods in terms of accuracy and computational efficiency. Collectively, the image outcomes align with the data analysis findings, affirming that the ADA_SD_LM approach utilized in this study generates maps that are both smoother and more detailed, offering superior accuracy and robustness.Fig. 11 Error map of amplitude (A) and relaxation time (T2) of simulated data (256 * 256). From left to right: LM, VAR_LM, SD_LM, from top to bottom: 40 echoes, 20 echoes, SNR truncation, T2NR truncation. There is no signal at the center of the circle. From inside out, the first loop: mono exponential model A = 250, T2 = 80 ms; the second loop: mono exponential model A = 250, T2 = 200 ms; the third loop: mono exponential model A = 250, T2 = 600 ms

Fig. 11

Table 1 Comparison of experimental results using simulated images (216 * 216).

Table 1Echo chain length	LM	VAR_LM	SD_LM	
NRMSE	TIME (s)	NRMSE	TIME (s)	NRMSE	TIME (s)	
40	0.0467	78.5726	0.0254	79.3091	0.0245	79.1982	
20	0.0370	73.8819	0.0263	75.2414	0.0239	74.0375	
SNR	0.0276	73.2598	0.0247	73.5420	0.0232	72.7965	
T2NR	0.0266	73.8452	0.0239	76.4598	0.0222	77.1220	

3.3 Application and discussion

The development of jujube fruit can usually be divided into four stages: young fruit stage, enlargement stage, stone hardening stage, and ripening stage, with the ripening stage including the white ripe stage and the crispy ripe stage. Multiple-echo-imaging was used to image the fruit during the two ripening stages of winter jujube. The ADA_SD_LM method was used for qMRI analysis to obtain the relaxation amplitude A mapping and relaxation time T2 mapping (Fig. 12), which can visually observe the internal voxel-by-voxel water content and water activity of the fruit, and the inversion results were analyzed to obtain the T2 average amplitude maps and T2 histograms (Fig. 12), which present the overall water activity content distribution and water activity distribution.Fig. 12 Quantitative map and data analysis of the equatorial plane in two mature stages of winter jujube.

Fig. 12

The imaging results clearly differentiated physiological changes between different tissues and between different ripening periods. The lack of T2 signal in the middle seed and endocarp of the fruit stems from the low water (H) content and weak MRI signal in this part of the fruit. The total amount of H increased in mature red fruits, where water with short relaxation times is localized in the exocarp. The mesocarp has a shorter T2 below about 120 ms in a part of the region close to the endocarp and exocarp portions, indicating that there is enhanced interaction between H at this location, a higher content of bound water, and poor mobility. Contrasting the appearance of the samples, the exocarp is redder here, and it can be seen that the difference stems from the fact that part of the region is exposed to more sunlight and therefore ripens faster.

Comparison of the average T2 amplitude maps and different T2 histograms in the two ripening stages of winter jujube shows that the T2 in the white ripening stage is centered on 185 ms and mainly concentrated near 100–250 ms, while that in the crisp ripening stage is centered on 160 ms, with the main area concentrated near 85–200 ms. By comparing the quantitative mapping and data analysis of the white ripening stage and crisp ripening stage, it can be seen that from the white ripening stage to the crisp ripening stage, the overall T2 time of the fruits became shorter, and the growth of short T2 tissue signals was obvious, indicating that with the gradual ripening of fruits, the tissue moisture status within the fruits became more bounded. This may be due to the formation of a stronger bond between water molecules and macromolecules (e.g., proteins, polysaccharides, etc.) in the tissues of winter jujube, which restricts the movement of water molecules.

This study employs an advanced T2-mapping technique to precisely delineate the active internal moisture status within winter jujube. This method offers comprehensive data, which enabling precise quantification and voxel-wise visualization of winter jujube's moisture status. Furthermore, the approach's scientific rigor and practical applicability furnish robust data support for moisture analysis in agriculture, food science, and related disciplines.

4 Conclusion

Based on the precise expression of T2 relaxation on the water active status of fruits, this study acquires mid-plane multi-echo MRI images of the sample and analyzes the signal and noise data of the multi-echo MRI images to establish a simulated image dataset, corresponding to the experimental study. Utilizing a mono exponential discrete model, this study has optimized the weighting factor and implemented a T2NR-guided echo truncation strategy within the inversion assessment model, specifically tailored for low SNR scenarios. Proceed, an experimental method has been developed to rapidly and reliably extract T2 relaxation data, including T2 and A2 maps, from multi-echo MRI images, even in low SNR scenarios. The discussion focuses on the precise interpretation of voxel-wise quantitative mapping in fruits. Employing the jujube as a model, the study delineates the water active status within each voxel of the scanned surface through T2 mapping and concurrently visualizes the associated water content via A2 mapping. Through the scanning and processing of jujube fruits across various ripening stages, this study examines the variations in water activity across tissues and their progression throughout the jujube's ripening process. The study introduces an innovative method for fruit phenotyping research, facilitating the precise and visual assessment of the internal water activity and content within samples based on voxel-wise relaxation data. This method is advantageous as it is independent of the sample's appearance and facilitates continuous, non-destructive monitoring.

Nonetheless, certain aspects require additional investigation and refinement for future studies.

Initially, the T2 relaxation in fruit tissues typically follows a triple-exponential decay pattern, distinguishing between free, semi-bound, and bound water active status. With Enhanced SNR and increased echo images, voxel-wise tri-exponential inversion can be performed to generate more informative maps.

Subsequently, spatial information can be incorporated into the evaluation function. The current model lacks spatial dimension consideration, leading to coarse image granularity. Importantly, voxel points are not isolated; they exhibit structural correlations with surrounding voxels. Spatial regularization in inversion, which accounts for the interdependencies among voxels, leverages the image's structural context, albeit at the cost of increased computational demands.

Furthermore, insights from large-scale intelligent algorithms suggest potential enhancements. Rational adjustments to the parameters of these algorithms could improve their search capabilities and convergence rates, thereby enhancing both the efficiency and accuracy of the inversion outcomes.

Moreover, building on voxel-wise water expression, subsequent image segmentation can delineate the water distribution across fruit structures, facilitating a comprehensive assessment of the fruit's multiscale water activity and content.

With the growth, storage and transportation, the internal structure and moisture status of the fruit change throughout the development process. QMRI of fruits such as winter jujube provides a means to study its subcellular water regulation characteristics and regulatory mechanisms. This has significant implications for in-depth research into respiration type, maturation regulation, and storage quality, as well as for advancing technologies in timely harvesting, storage, preservation, and cold chain logistics.

Funding

This work was supported in part by 10.13039/501100001809 National Natural Science Foundation of China (U20A20180 ), Innovation Support Project for Graduate Students of Hebei (No. CXZZBS2022047 ), Basic Business Expenses Research Project of Provincial Higher Education Institutions in Hebei Province (KY2021052 ), Hebei Province Key Research Program Project (No. 21327405D ), and China University Industry University Research Innovation Fund (No. 2021LDA10005 ).

Data availability statement

Data will be made available on request.

Ethics declaration

Review and/or approval by an ethics committee was not needed for this study.

CRediT authorship contribution statement

Yanan Li: Writing – original draft. Yijin Wang: Data curation. Guifa Teng: Formal analysis. Jingfa Yao: Software. Peng Luan: Writing – review & editing.

Declaration of competing interest

The authors declare no conflict of interest.
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