*3.3. Influenza A virus*

LL-37 therapeutic activity against influenza type A virus has been demonstrated in vivo and in vitro. It is likely that in vivo, IAV encounters LL-37 in the respiratory tract following innate immune responses against the virus and is secreted from neutrophils, macrophages, and epithelial cells [44,49]. Early studies assessed the antiviral activity of LL-37 in vivo using a mouse IAV strain [50]. Mice were nebulized with LL-37 (500 μg/mL) a day prior to infection with a lethal dose of IVA PR/8 mouse strain and survival and weight loss were monitored for 14 days following infection [50]. Initially, all mice exhibited weight loss, but weight loss ceased at day seven in mice treated with LL-37 or the IAV antiviral zanamivir. Mice treated with LL-37 and zanamivir exhibited 60% survival compared to the untreated group which succumbed to infection by day nine suggesting that therapeutic use of LL-37 reduces IAV infection severity in a manner comparable to zanamivir [50]. LL-37 also decreased expression of inflammatory cytokines particularly IL-1β, granulocyte-macrophage colony-stimulating factor (GM-CSF), keratinocytes chemoattractant (KC), and the chemotactic cytokine known as regulated on activation normal t-cell expressed and secreted (RANTES), in bronchoalveolar lavage fluid in mice infected with PR/8 at two days following LL-37 treatment as determined by immunoassay demonstrating the immunomodulatory properties of LL-37 [50]. In vitro plaque assays demonstrated one log inhibition of PR/8 when virus was pre-incubated with LL-37 (50 μg/mL) in Madin-Darby canine kidney (MDCK) cells [50].

During IAV infection, in vitro LL-37 treatment did not prevent viral uptake, cause viral aggregation, and was not associated with blocking of hemagglutinin (HA). Interestingly LL-37 inhibits IAV replication at post-entry steps prior to viral RNA or protein synthesis [44]. A reduction in viral load, direct antiviral effects in epithelial cells, and inflammatory cytokine production have all been linked to LL-37 activity [49]. LL-37 inhibits the NY01 strain of IAV with a significant reduction in uptake of virus into cells, and in a manner dependent on dosage [44,49]. For optimal anti-IAV activity the central helix of LL-37 is required, as evident by fragments of LL-37 containing the complete central sequence of the peptide demonstrating more robust antiviral responses as compared to fragments with shorter central fragments. At a concentration of <2 μM, NY01 was only partially inhibited; however, this inhibition was surprisingly lost at higher concentrations of LL-37 [44]. A strain containing only the pandemic HA (Mex 1:7); however, was inhibited by LL-37 at all concentrations tested (up to 10 μM). Consistent with previous studies, these results suggest the antiviral effects of LL-37 are not determined by direct interaction of LL-37 with the viral HA [44].

Experimental data also demonstrates the participation of LL-37 in host defenses against IAV through modulation of innate immune cells, particularly neutrophils. IAV infection induces a respiratory burst response in neutrophils, and this response is noticeably up-regulated by pre-incubation of LL-37 with IAV [49]. LL-37 alone does not stimulate this respiratory burst response; however, optimal enhancement of this antiviral response is achieved only when the virus is pre-incubated with LL-37 [49]. Furthermore, there is growing evidence that NET formations play an important role during IAV infections [49]. Recently, in vivo studies have provided evidence of NET formation in the lungs of IAV-infected mice [51]. On the other hand, in vitro evidence of binding of IVA to NETs suggests LL-37 induces an increase in NET formation in response to IAV, which may promote viral clearance in vivo [49,51]. Data also suggest that significant protection against IAV may be provided by therapeutic treatment of influenza infected individuals with LL-37 or by increasing natural cathelicidin expression in the IAV-infected lung [11]. Hence, to maximize anti-IAV functions, approaches, such as therapeutic administration of naturally-occurring cathelicidins, as well as increasing vitamin D levels to boost endogenous cathelicidin have been proposed [11].


**Author details**

Sara Mohamed Yonues1 \* and Abdou Saad El-Tabl2

1 Chemical Engineering Department, Borg El Arab Higher Institute Engineering and Technology, Alexandria, Egypt

2 Chemistry Department, Faculty of Science, Menoufia University, Shebin ElKom, Egypt

\*Address all correspondence to<EMAIL_ADDRESS>
© 2022 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*Perspective Chapter: Removal of Heavy Metals and Salmonella Pathogens from Sewage Sludge… DOI: http://dx.doi.org/10.5772/intechopen.109224*


**4.3 Hepatic protective effects of** *Citrus* **fruit**

The liver, the body's most significant digestive organ, is responsible for toxic compound metabolization via several routes, such as hydrolysis, oxidation, reduction, conjugation, and hydration [57]. Lipopolysaccharide (LPS) is a glycolipid of gram-negative bacteria's cell wall [16]. LPS raises total bilirubin levels, alkaline

phosphatase (ALP), aspartate aminotransferase (AST), and alanine aminotransferase (ALT). Tissue and serum nitrite levels, as well as thiobarbituric acid reactive substances (TBARS) levels, increased, whereas superoxide dismutase (SOD) and glutathione (GSH) content decreased. However, hesperidin injection restored all of these abnormalities, and the authors concluded that hesperidin might reduce nitric oxide and reactive oxygen species (ROS) formation and prevent LPS-induced hepatotoxicity [17].


**5.2 Prognostic**

The potential for MP as a prognostic tool is dependent on reliable, reproducible and easily available tools to measure microparticles. There is emerging data that MP may predict VTE in cancer patients and may be able to provide prognostic information in several other conditions.

## **5.3 Therapeutic**

An interesting dimension to this area is the approach to use or modify MP for therapeutic benefit. The possibility of bioengineered and/or harvested membrane microparticles in tissue repair or angiogenesis is being investigated (Soleti, 2009). The MP are also being studied as a drug delivery tool (Benameur, 2009). Microparticles could potentially be specifically targeted to reduce or prevent thrombotic complications or end organ damage (Myers, 2005). This is an promising and exciting new area for researchers and clinicians working in this area.

Microparticles have therefore emerged as key role players in vascular biology and pathophysiology of thrombosis. They remain an important research tool and their clinical applications are being actively investigated with potential to be applied in diagnostic, prognostic and therapeutic arenas. They are small yet powerful effectors for the pathophysiology of the endovascular system.

#### **6. References**

Pathophysiology and Clinical Aspects of 12 Venous Thromboembolism in Neonates, Renal Disease and Cancer Patients

however, the clinical utility of this approach is also as yet unkown (Howes ; Ramacciotti).

There are several outstanding issues such as standardization of preanalytical and analytical variables as well as integration of the various approaches in measuring MP. Several novel approaches are now being considered. 'Megamix beads' is novel approach to standardizing of gating of microparticles using flow cytometry. It uses a mix of a 0.9um and 0.3um sized beads to try and capture all events within the gate set by the beads (Robert, 2009 ;Robert, 2011). One of the problems of using this approach is the lack of linearity in the relationship between the size of beads and forward sctatter at that particle size. A recent commercially available nanoscale technology known as 'Nanosight' has incorporated antibody tagging of small particles for accurate identification and counting in this size range (Harrison, 2009).

Utility of Measuring MP in venous thromboembolism is yet to be fully established . The case for measuring MP in cancer related VTE is perhaps stronger. There are three areas within which the potential for detecting and measuring MP with respect to venous

The evidence for using measurement of MP in a diagnostic setting is limited. The studies so far have shown variable results depending on whether TF bearing MP, functional activity or total MP were measured. With respect to VTE MP have been assessed in the paradigm of VTE, diagnosis in a small pilot study where it was shown that D-dimer, P-selectin and total MP levels predicted thrombosis as demonstrated on Doppler ultrasound (Ramacciotti; Rectenwald, 2005). The role of MP in diagnosis of VTE warrants confirmation in prospective cohort studies. The standardization of measurement of MP will go a long way in ensuring

The potential for MP as a prognostic tool is dependent on reliable, reproducible and easily available tools to measure microparticles. There is emerging data that MP may predict VTE in cancer patients and may be able to provide prognostic information in several other

An interesting dimension to this area is the approach to use or modify MP for therapeutic benefit. The possibility of bioengineered and/or harvested membrane microparticles in tissue repair or angiogenesis is being investigated (Soleti, 2009). The MP are also being studied as a drug delivery tool (Benameur, 2009). Microparticles could potentially be specifically targeted to reduce or prevent thrombotic complications or end organ damage (Myers, 2005). This is an promising and exciting new area for researchers and clinicians

Automated devices to analyse MP are also being developed (Wagner, 2010).

**4.4 Measuring microparticles: Future directions**

**5. Conclusions**

**5.1 Diagnostic**

**5.2 Prognostic**

conditions.

**5.3 Therapeutic**

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**2**

*Slovenia*

**Hyperhomocysteinemia: Relation to**

Homocysteine is a sulphur-containing amino acid, which structurally is closely related to the essential amino acids methionine and cysteine. The cellular methylation cycle performs the metabolism of methionine and since homocysteine is an intermediate within this cycle, the body in this way is provided with all organic homocysteine. The term homocysteine is used to define the combined pool of homocysteine, homocystine, and mixed disulfide compounds (Fig. 1) even involving homocysteine thiolactone a cyclic form which is often

Homocysteine was first isolated by Butz and du Vigneaud in 1932. However, the relation of homocysteine to human disease was first suggested in 1962, in the classical paper of Carson and Neil, reporting an elevated homocysteine level in the urine of mentally retarded children. Nowadays, it has long been known that homocystinuria—also known as severe hyperhomocysteinemia, a genetic disorder in which blood levels of homocysteine are about 20-fold higher than the normal concentration—is associated with greatly increased risk for

found in the plasma of patients with hyperhomocisteinemia.

Fig. 1. Structural formulae of homocysteine

**1. Introduction**

**Cardiovascular Disease and**

**Venous Thromboembolism**

*University of Primorska, College of Health Care Izola,*

Nadja Plazar and Mihaela Jurdana


**5. Conclusions**

Underutilized fruit crops play an important role for their therapeutic properties due to their significant medicinal and nutritional value and can be considered as future horticultural assets to help nations assuring nutrition and food security, besides providing recreational, social and environmental significance. Being hardy and adapted locally, these species may serve the purpose of enhancing sustainable farm income under the harsh arid and semi-arid environments, such as waste lands (jharber, kair, pilu), marginal or saline soil and water conditions (ber, aonla, bael, karonda, etc.), rocky terrains (custard apple, timroo, jamun, etc.) and also in the backyard or kitchen gardening (karonda, custard apple, khejri, mulberry, etc.) and avenue plantation (tamarind, lasora, khirni, jamun, mulberry, khejri, etc.). Some fruit crops possess high significance in food processing industries (aonla, bael, karonda, tamarind, etc.). Their horticultural development is moving quite fast, and in the future, there will be greater technological adoption, extension and policy planning, both in traditional horticultural enterprises as well as in the commercial sectors. Special efforts are needed in terms of research and development of suitable specific packaging practices and of superior varieties. Considering the potential of the underutilized fruit crops, the emphasis shall be made to substantiate the efforts being made towards eradicating global malnutrition by their direct introduction in other arid and semi-arid regions of the world so as to achieve the goal of sustainable development (1 to 3) of the United Nations.

**Author Contributions:** Conceptualization, V.S.M., P.K., J.S.G. and A.S.; methodology, V.S.M., C.R., N.K.M., J.S.G., A.S. and P.; writing—original draft preparation, V.S.M., J.S.G., N.K.M., A.S., P. and P.K.; visualization and illustration of Tables, J.S.G., P.K., C.R., A.S., Y.R., B.B. and P.; writing—review and editing, P.K., A.S., Y.R. and B.B.; draft finalization, A.S., P.K., Y.R. and B.B. All authors have read and agreed to the published version of the manuscript.

**Funding:** There was no external funding involved in the study.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** The authors thankfully acknowledge A.K. Singh, Principal Scientist, ICAR-Central Institute for Arid Horticulture, CHES, Godhra, Gujarat, for providing some of the pictures of fruit crops, and the Director, ICAR-NBPGR, New Delhi, ICAR-CAZRI, Jodhpur, for extending logistic support for conducting the study.

**Conflicts of Interest:** The authors declare no conflict of interest.


*5.2.5 Binge-watching leads to respiratory function issues*

The position of the body can affect the function and strength of respiratory muscles in both healthy individuals and those with cardiopulmonary dysfunction. For instance, young adults have less respiratory pressure and dyspnoea in the semi recumbent or supine position. On the other hand, the strength of their respiratory muscles is decreased in the supine position [77–81].

The length of a muscle fibres relationship with its surrounding tissues is biomechanically related to its ability to develop tension. It is believed that rib changes can affect the length-tension relationship of certain respiratory muscles, such as those in the diaphragm. This could cause these muscles to develop less tension and reduce respiratory rate [77, 82].


*Article* **Monitoring Wheat Powdery Mildew Based on Hyperspectral, Thermal Infrared, and RGB Image Data Fusion**

**Ziheng Feng 1,2, Li Song 1, Jianzhao Duan 1, Li He 1, Yanyan Zhang 1, Yongkang Wei 1 and Wei Feng 1,\***

**Abstract:** Powdery mildew severely affects wheat growth and yield; therefore, its effective monitoring is essential for the prevention and control of the disease and global food security. In the present study, a spectroradiometer and thermal infrared cameras were used to obtain hyperspectral signature and thermal infrared images data, and thermal infrared temperature parameters (TP) and texture features (TF) were extracted from the thermal infrared images and RGB images of wheat with powdery mildew, during the wheat flowering and filling periods. Based on the ten vegetation indices from the hyperspectral data (VI), TF and TP were integrated, and partial least square regression, random forest regression (RFR), and support vector machine regression (SVR) algorithms were used to construct a prediction model for a wheat powdery mildew disease index. According to the results, the prediction accuracy of RFR was higher than in other models, under both single data source modeling and multisource data modeling; among the three data sources, VI was the most suitable for powdery mildew monitoring, followed by TP, and finally TF. The RFR model had stable performance in multi-source data fusion modeling (VI&TP&TF), and had the optimal estimation performance with 0.872 and 0.862 of R2 for calibration and validation, respectively. The application of multi-source data collaborative modeling could improve the accuracy of remote sensing monitoring of wheat powdery mildew, and facilitate the achievement of high-precision remote sensing monitoring of crop disease status.

**Keywords:** wheat powdery mildew; machine learning; information fusion; remote sensing monitoring

#### **1. Introduction**

In recent years, multiple crop diseases and insect pests have emerged, with considerable impacts on yield and productivity following local outbreaks. According to the United Nations Food and Agriculture Organization (FAO), 20%–40% of crops globally are damaged by disease and insect pests annually [1]. Powdery mildew is the major wheat disease; it causes considerable yield reductions or even no harvest, posing a major threat to wheat production and global food security. Conventional methods of monitoring wheat disease are time-consuming and laborious, and are associated with mechanical damage to crops. Therefore, it is essential to identify and develop approaches of carrying out rapid and damage-free wheat disease monitoring.

Plant disease and insect pest infestations lead to biomass reductions, leaf structure destruction, and chlorophyll and water content reductions. Shifts in chlorophyll, water, and other biochemical components in plant tissues would inevitably yield diverse absorption and reflectance characteristics on the plant reflectance spectrum curve, which provides a theoretical basis and facilitates the real-time monitoring of wheat diseases using remote sensing technologies [2]. In recent years, with continuous advancements in remote sensing technologies, numerous scholars have applied technologies to monitor wheat diseases. Generally, different crops, varieties, and diseases exhibit diverse spectral characteristics, which

**Citation:** Feng, Z.; Song, L.; Duan, J.; He, L.; Zhang, Y.; Wei, Y.; Feng, W. Monitoring Wheat Powdery Mildew Based on Hyperspectral, Thermal Infrared, and RGB Image Data Fusion. *Sensors* **2022**, *22*, 31. https://doi.org/10.3390/s22010031

Academic Editors: Jiyul Chang and Sigfredo Fuentes

Received: 11 November 2021 Accepted: 19 December 2021 Published: 22 December 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

leads to varying reflectance sensitivities at different bands following disease infestation [3]. Consequently, the identification of crop diseases and crop disease incidence estimation can be achieved based on changes in spectral responses and reflectance characteristics [4–6]. Researchers have previously developed disease monitoring indices following the extraction of disease-sensitive bands for monitoring the infestation of crops by bacterial diseases, such as powdery mildew index (PMI) [7], double green vegetation index [8], and red edge vegetation stress index (RVSI) [9].

The modeling algorithms applied in remote sensing influence the accuracy of remote sensing technologies. Today, the algorithms applied in disease and pest monitoring with remote sensing technologies are mainly empirical models and machine learning algorithms [10,11]. Among them, the empirical models are relatively simple; however, the data are easily influenced by external conditions and have poor universality. In recent years, machine learning methods have emerged, with rapid development. Crop disease monitoring models established based on machine learning methods consider training error and generalization ability, and address the challenges associated with slight changes in reflection coefficient during crop disease detection [12,13]. Gu et al. [14] used hyperspectral imaging technologies to monitor tobacco infected by tomato spotted wilt virus and reported that the combination of a successive projections algorithm (SPA) and boosted regression tree was the optimal modeling approach. In addition, Liu et al. [15] established a wheat wilt monitoring model using an improved backward propagation neural network. Wheat is a crop planted in dense rows; if only a single spectral data type is applied in disease monitoring activities, the model is often insensitive to changes in canopy spectrum reflectance, and the reflectance data can be saturated, leading to significant model prediction errors [16,17].

Texture information obtained using imaging spectroscopy tools can reflect disease spot sizes and infestation levels of bacterial diseases [18], in addition to integrating plant morphology and canopy structure information in the spectral data, which enhances the accuracy of remote sensing tools in crop disease monitoring activities [19]. Many researchers have exploited the complementary advantages of spectrum and texture information, which has significantly improved crop growth parameters and the inversion effect of disease severity [20,21]. For example, Guo et al. [22] used vegetation index (VI) and texture features (TF) data obtained using an unmanned aerial vehicle (UAV) platform to establish a wheat stripe rust monitoring model based on partial least squares regression (PLSR). TF can provide plant morphology data that could be applied in the monitoring of crop growth based on remote sensing technologies, which can address the saturation and low accuracy shortcomings associated with single spectral information source-based monitoring, and in turn enhance the robustness of a model and model inversion performance.

Infrared thermal imaging technologies have high sensitivity and early warning capacity. Wheat plants are infected by powdery mildew fungus, and the early symptoms are mostly manifested by changes in internal physiological reactions. Thermal infrared images can reveal temperature changes infected regions that cannot be discerned by visible light images [23]. Mahlein et al. [24] used an infrared thermal instrument (IRT) to measure wheat canopy temperature (CT) and found that the temperature of diseased spikelets was significantly higher than that of healthy spikelets. Therefore, infrared thermal imaging technologies can be used to monitor crop stress during growth and physiological conditions. Many researchers have begun to combine IRT with other remote sensing data sources in plant disease monitoring activities. For example, Zarco-Tejada et al. [25] confirmed that the combination of VI, sun induced fluorescence (SIF), and crop water stress index (CWSI) could be used to effectively monitor diseased trees, and the identification accuracy rate exceeds 80%. In addition, Poblete et al. [26] combined the spectrum, SIF and CWSI, which could effectively distinguish diseased and non-diseased olive trees, whereas Zhang et al. [27] used UAV multi-spectral VI in combination with CT information to estimate disease severity in disease-stressed chickpea, with significantly enhanced detection accuracy. The results of the above studies indicate that thermal infrared data can reliably reflect

abnormal conditions in the CT of stressed crops, and can facilitate disease identification and disease classification when combined with other remote sensing data sources.

In the wake of rapid advancements in modern electronic information science, numerous sensors are available for application in the detection of crop morphology and canopy structure, such as reflectance spectrometers, chlorophyll fluorescence meters, and IRT and RGB cameras, which detect crop morphology and growth status based on different factors and principles [28]. However, crop information associated with a single information source is often potentially biased and has certain limitations. Data from different sensor types can be deployed synergistically to enhance target detection and recognition capabilities [29]. Compared to a single sensor data source, multi-sensor data sources can enhance the reliability and robustness of real-time detection [30]. At present, few studies have reported on the monitoring of wheat powdery mildew disease based on a synergy of spectral data and thermal infrared temperature data; in particular, there is a dearth of studies on disease monitoring using approaches that synergize VI, TF and temperature parameters (TP).

To further explore the synergistic effects of multimodal data obtained from different sensors in disease monitoring, in the present study, multimodal data on the incidence of wheat powdery mildew was obtained using hyperspectral surface spectrometer and thermal infrared camera, and compared with ground disease investigations. Multimodal data were obtained using modern modeling and inversion algorithms, such as PLSR, support vector machine regression (SVR), and random forest regression (RFR). The results of the present study could provide a technical basis for the rapid and large-scale monitoring of wheat powdery mildew, and facilitate the prevention and precise control of wheat powdery mildew, in addition to the improvement of pesticide efficiency and food safety.

#### **2. Materials and Methods**

#### *2.1. Experimental Design*

Experiment 1 (EXP.1): The experiment was conducted in the 2020–2021 wheat growing season at the Science and Education Demonstration Park (34◦51 N, 113◦35 E) of Henan Agricultural University, Zhengzhou, China. The tested varieties were varieties susceptible to wheat powdery mildew: Aikang 58 and Yumai 49–198. The first crop was corn, and the stalks were crushed and returned to the field. The soil was loam, the 0~30-cm soil contained 0.99–1.18 g kg−1 of total nitrogen (N), 0.023–0.034 g kg−1 of available phosphorus, 0.114–0.116 g kg−1 of available potassium, and 11.4–15.3 g kg−1 of organic matter. In the experiments, relatively high water and N fertilizer amounts were used to create favorable conditions for powdery mildew. The amount of N applied was 270 kg·hm−2, and the irrigation amount during the wintering period-jointing stage was 900 m3·hm−2. Powdery mildew fungus was inoculated at the jointing stage, and the wheat was infected from the flowering stage, and the canopy spectrum data were obtained at the flowering and filling stages. Other field management approaches were similar to those applied locally.

Experiment 2 (EXP.2): Carried out simultaneously with experiment 1, experiment 2 was a variety comparison experiment in the field, involving Yanzhan 4110, Nongmai 18, Zhoumai 27, Jinfeng 205, Zhengmai 1342, Xumai 318, Bainong 207, and Xinmai 26. The amount of N applied was 225 kg·hm−2, and the irrigation amount during the wintering period-jointing stage was 675 m3·hm−2. The experimental area was close to fences and pig farms, and the terrain was low-lying. Due to the terrain, air humidity, rainfall, and diseases in previous years, the wheat growth environment was suitable for the occurrence and spread of wheat powdery mildew, without field inoculation. Disease emergence was natural and more severe. Other field management approaches were similar to those applied in EXP.1.

#### *2.2. Ground Data Collection*

#### 2.2.1. Investigation of Powdery Mildew

During the wheat flowering and filling periods, wheat powdery mildew incidence was investigated manually, and 77 and 37 samples were collected in EXP.1 and EXP.2, respectively. About 0.2 m2 of the experimental area was investigated at each point, and 20 representative wheat plants were selected to test for powdery mildew infection. The survey was conducted in strict accordance with the technical specifications for crop disease monitoring (Chinese Standard: NY/T 2738.2-2015) [31]. The ratio of the leaf area covered by the diseased mycelium layer on the diseased leaf to the total leaf area was expressed based on a grading method, with eight levels representing 1%, 5%, 10%, 20%, 40%, 60%, 80%, and 100% coverage. The grid method was used to calculate the ratio of the diseased spot area to the leaf area. The operation involved using grids to cover the leaves, recording the total number of grids with disease spots, to facilitate the calculation of the ratio of the diseased spot area to leaf area. The closest value between grades was selected as the actual level. For example, at onset with a severity of less than 1%, the coverage was considered 1%. The average severity of diseased leaves was calculated as follows (1):

$$D = \frac{\sum \left( \mathbf{D}i \times L\mathbf{i} \right)}{L} \times \mathbf{100} \tag{1}$$

where, *D* is the average disease severity in leaves, and the unit is percentage (%); *Di* is each severity value; *Li* is the number of diseased leaves corresponding to each severity value, and the unit is slice; and *L* is the total number of leaves under investigation, and the unit is slice.

On the basis of the severity of disease in leaves, the disease index (*DI*) is calculated to represent the average level of disease occurrence (Equation (2)).

$$DI = F \times D \times 100\tag{2}$$

where, *DI* is the disease index; *F* is the diseased leaf rate; *D* is the average severity of disease in leaves.

#### 2.2.2. Canopy Spectrum Data Measurement

From 10:00 to 14:00 (Beijing local time) with little wind and clear weather, a FieldSpec handheld spectrometer (FieldSpec Handheld 2, Analytical Spectral Devices, Boulder, CO, USA) was used to obtain wheat canopy spectrum data, and the probe was 1.0 m from the top of the wheat crop. The field of view of the spectrometer was 25◦, in the 325–1075 nm band, the spectral sampling interval was 1.4 nm, and the spectral resolution was 3.0 nm. A 0.4-m × 0.4-m BaSO4 calibration plate was used to calculate black and baseline reflectance. Ten spectral reflectance values were recorded at each sampling point as samples, and the average value was considered the spectral reflectance of the sampling area.

#### 2.2.3. Thermal Infrared Image and RGB Image Acquisition

An FLIR T650sc thermal infrared camera (FLIR Systems, Inc., Wilsonville, OR, USA) was used to obtain the wheat canopy temperature (CT) and RGB images. The device has dual thermal infrared and visible light sensors, and the image resolution is 640 × 480 pixels. Synchronous with the spectral reflectance measurement, the lens was 1.0 m from the top of the wheat crop, and the thermal infrared and RGB images were obtained vertically (Figure 1).

**Figure 1.** Wheat canopy RGB image (**a**) and thermal infrared image (**b**) obtained using thermal infrared camera.

#### *2.3. Data Processing Methods*

#### 2.3.1. Spectral Vegetation Index (VI)

Before extracting the VIs, the bands with high noise before 400 nm and after 1000 nm were removed, and then the Savitzky-Golay function was used to smoothen the spectra in MATLAB 7.0 (The MathWorks Inc., Natick, MA, USA). VIs associated with the disease were pre-selected by consulting relevant literatures (Table 1). Considering the potential existence of the collinearity problem among VIs, SPA was used to optimize VIs and reduce their multicollinearity. SPA is a forward variable selection method that selects characteristic variables by calculating the sizes of the projection vector of the remaining variables and the selected variables, which can ensure that the linear relationship between the selected variables is minimized, so as to eliminate redundant information between variables and reduce multicollinearity, to achieve the purpose of selecting sensitive variables [32].

**Table 1.** Spectral vegetation indices.

#### 2.3.2. RGB Image Texture Features (TF)

The gray level co-occurrence matrix (GLCM) method, proposed by Haralick in 1973 [50] is one of the most widely used texture extraction methods. The method has the advantages of rotation invariance, multi-scale characteristics, and low computational complexity, and is widely used in image processing, pattern recognition, and remote sensing monitoring [51,52]. In ENVI (Harris, Bloomfield, CO, USA), the gray level image of the RGB image was subjected to 3 × 3 sliding filtering using GLCM. Eight texture feature maps in the directions of 0◦, 45◦, 90◦ and 135◦ were extracted (Figure 2, Table 2), and the average of four directions was taken as the final texture feature map. To ensure that the extracted texture features are all based on canopy vegetation, a K-means clustering algorithm is used for bare soil rejection. The soil and vegetation mask is shown in Figure 3.

**Figure 2.** Eight texture feature maps of gray-level co-occurrence matrix from RGB image of wheat canopy in the 0◦ direction.

**Table 2.** Texture feature calculation formula.

Note: *i* and *j* indicate the row and column number of the images, respectively; *P*(*i*, *j*) is the relative frequency of two neighboring pixels.

**Figure 3.** A workflow diagram of feature extraction and modeling.

#### 2.3.3. Thermal Infrared Temperature Parameters (TP)

The thermal infrared image was annotated and combined with K-means clustering segmentation results (Figure 3) using FLIR Tools (FLIR Systems Inc., Wilsonville, OR, US), and the temperature parameters were extracted. Considering that CT changes with the daily change in atmospheric temperature, the canopy temperature difference (CTD), canopy temperature ratio (CTR), and normalized relative canopy temperature (NRCT) were extracted to eliminate the influence of atmospheric temperature on CT. The temperature parameter formula was as follows:

$$\text{CTD} = \text{CT}\_{\bar{l}} - AT \tag{3}$$

$$\text{CTR} = \frac{\text{CT}\_i}{\text{AT}}\tag{4}$$

$$\text{corr} = \text{corr}$$

$$\text{NRCT} = \frac{\text{CT}\_i - \text{CT}\_{\text{min}}}{\text{CT}\_{\text{max}} - \text{CT}\_{\text{min}}} \tag{5}$$

where, *AT* is the atmospheric temperature, *CTi* is the *CT* of the *i*-th pixel in the image, *CTmax* is the highest temperature measured in the entire experimental field, and *CTmin* is the lowest temperature measured in the entire experimental field.

#### 2.3.4. Estimation Model

(1) PLSR

PLSR is a classic modeling method, which includes the characteristics of principal component analysis (PCA), canonical correlation analysis, and multiple linear regression analysis, and is often used for quantitative analysis in remote sensing [53]. PLSR transforms the original variables with high data redundancy into a few variables by selecting the optimal latent variables, to describe the linear model of the relationship between the predicted value and the true value.

(2) SVR

The basic idea of SVR is to use training samples to establish a regression hyperplane, and to approximate the samples to the hyperplane to minimize the total deviation from the sample point to the plane [54]. The commonly used kernel functions of the SVR algorithm include the linear kernel function, radial basis function (RBF) kernel function, polynomial kernel function, and Sigmoid kernel function. Among them, the RBF kernel function can handle the complex nonlinear problem between the independent variable and the dependent variable.

(3) RFR

RFR is a machine learning algorithm based on a classification regression tree [55]. RFR uses the bootstrap resampling method to extract multiple samples from the original sample, models each bootstrap sample into a decision tree, combines them into multiple decision trees for prediction, and then applies the majority voting method to determine the final classification result of the joint prediction model. The advantage of the method is that the training speed is relatively fast and it does not require cross-validation. In addition, the randomness of sampling and feature selection make the random forest averts overfitting [56]. It is widely used in classification and prediction in remote sensing-based monitoring activities.

#### 2.3.5. Model Validation

With VI, TP and TF as independent variables, and DI as the dependent variable, a monitoring model for wheat powdery mildew disease index was established based on the three algorithms above. The workflow from feature extraction to model building and evaluation was demonstrated in Figure 3. To make the model evaluation results more objective, EXP.1 test data were used as the modeling set, and EXP.2 test data were used as the verification set. The accuracy of the wheat powdery mildew disease index monitoring model was evaluated based on three indicators: coefficient of determination (R2), root mean square error (RMSE), and relative error (RE). The closer *R*2 is to 1, the lower the *RMSE*, and the lower the *RE*, the higher the accuracy of the monitoring model. The formula was as follows:

$$\mathcal{R}^2 = \frac{\sum\_{i=1}^n (\mathbf{x}\_i - \overline{\mathbf{x}})^2 \times (y\_j - y)^2}{\sum\_{i=1}^n (\mathbf{x}\_i - \overline{\mathbf{x}})^2 \times \sum\_{i=1}^n (y\_j - y)^2} \tag{6}$$

$$\text{RMSE} = \sqrt{\frac{\sum\_{i=1}^{n} (y\_i - x\_i)^2}{n}} \tag{7}$$

$$\text{RE}\left(\%\right) = \sqrt{\frac{1}{n} \times \sum\_{i=1}^{n} \left(\frac{y\_i - x\_i}{x\_i}\right)^2} \times \mathbf{100} \tag{8}$$

where, *xi*, *x*, *yi* , and *y* are the measured *DI*, average *DI*, predicted *DI*, and average *DI*, respectively; *n* is the number of samples.

#### **3. Results**

#### *3.1. Changes in Wheat Canopy Spectra under Different Powdery Mildew Severity Levels*

With an increase in DI, the spectral reflectance of the visible light band from 400 to 780 nm increased gradually, and the discrimination of DI was better (Figure 4a). The spectral reflectance of the near-infrared bands region across 780 nm–1000 nm was less distinguishable when the disease was mild; when the disease was more than moderate, the spectral reflectance increased gradually; and when the disease was severe (such as DI = 80), the spectral reflectance rose sharply due to severe damage to the canopy structure, even higher than the spectral reflectance of healthy wheat. From the perspective of the correlation between disease severity and reflectance (Figure 4b), there was a positive correlation in the visible light band from 400 to 730 nm, and a negative correlation in the near-infrared region from 730 to 1000 nm, especially at 600–700 nm (r = 0.373–0.431, probability value, *p* < 0.01) and 780–960 nm (r=−0.355–−0.294, *p* < 0.01), which can be considered as disease-sensitive bands for the real-time monitoring of disease progression.

**Figure 4.** Spectral reflectance changes (**a**) of wheat canopy and its correlation (**b**) with disease index.

#### *3.2. Selection of Vegetation Index*

Based on the reported VIs related to plant disease, the correlations between 20 VIs and DI were analyzed. The VI with the highest correlation was NSRI (r = 0.743) (Figure 5a), followed by GI and NPCI. Because VI is a combination of bands, and there is a certain degree of information duplication between bands, there is considerable multicollinearity among the spectral parameters. Therefore, the SPA algorithm is used to optimize the VI. The minimum number of sensitive variables extracted was two, and the maximum number of sensitive variables was twenty. RMSE decreased with an increase in the number of variables. RMSE was the minimum (RMSE = 15.575) when the number of variables was 10; however, with an increase in the number of variables, the RMSE increased gradually (Figure 5b). After SPA screening, there were 10 VIs, namely NSRI, NPCI, PSRI, PRI, ARI, SIPI, PMI, MSR, RVSI, and GNDVI. According to the results, when a single VI was used to estimate the DI, the linear R2 was low (R2 < 0.56), and the error in monitoring powdery mildew disease was relatively large (Figure 6).

**Figure 5.** Root mean square error (**a**) in the optimal variables selected using successive projections algorithm (SPA) and correlation (**b**) between vegetation index (VI) and disease index (DI).

**Figure 6.** Linear relationship of the optimal vegetation indices with wheat disease index (DI).

#### *3.3. Selection of Texture Feature Parameters*

Analysis of the correlation between TF parameters of canopy RGB images and DI showed that the correlation coefficients were all positive. Excluding the correlation coefficient between the correlation and DI, which was not significant, all the others were significant, among which entropy was the highest (r = 0.486, *p* < 0.01) (Figure 7a). The eight extracted TFs were all calculated from grayscale images, and considering the potential multicollinearity among TFs, the SPA algorithm was used to optimize the variables. The RMSE was the lowest (RMSE = 18.043) when the number of TF variables was five. Five TF parameters, mean, variance, homogeneity, entropy, and second moment, were selected as the input variables in the estimation model (Figure 7b).

**Figure 7.** Correlation (**a**) between texture feature parameter and disease index (DI) and the root mean square error (**b**) for the optimal variables selected using SPA.

#### *3.4. Selection of Thermal Infrared Temperature Parameters*

The TP parameters from thermal infrared images were extracted to analyze their correlation with DI, and the results showed that the correlation coefficient between CT and DI was 0.382, and was significant (*p* < 0.01) (Figure 8). Considering CT changes with daily atmospheric temperature changes, the CTD, CTR and NRCT were extracted to eliminate the influence of atmospheric temperature on CT. After eliminating the influence of atmospheric temperature, the significant level of correlation of TP was further improved, with a very significant level (*p* < 0.01) observed. Combining the principle of strong correlation and eliminating duplicate information, two TPs, CTD, and NRCT, were selected as input variables for the subsequent steps of modeling and analysis.

**Figure 8.** Correlation coefficient between temperature parameters and DI.

#### *3.5. Comparison of Different Model Algorithms Based on Single Data Sources*

With a single data source as an independent variable, three methods, including, PLSR, SVR and RFR, were used to invert the DI of wheat powdery mildew (Table 3, Figure 9). Comprehensive comparison revealed that the RFR model performed optimally, followed by the SVR and PLSR models. Based on the performance results of the three data sources, regardless of which method was used to estimate wheat DI, the performance of the VI was the best, followed by TP and TF. Based on combinations modeling methods and

independent variable data type, the RFR method with VI as the independent variable was the best combination, with R2, RMSE, and RE values of 0.690, 14.488, and 18.42%, respectively, in the calibration set, and R2, RMSE, and RE values of 0.680, 14.298, and 18.16%, respectively, in the validation set. The SVR method with VI as an independent variable was the second best combination, with R2, RMSE and RE values of 0.670, 14.757, and 18.69%, respectively, in the calibration set, and R2, RMSE, and RE values of 0.666, 15.578, and 18.16%, respectively, in the validation set.

**Table 3.** Estimation performance of single data source model based on different algorithms.

**Figure 9.** Prediction performance of different models with various input feature types.

#### *3.6. Comparison of Different Model Algorithms Based on Multi-Source Data Combination*

To fully exploit the information obtained from different data sources, TP, TF, and VI were combined to carry out a comparative analysis of three modeling methods (Table 4, Figure 9). After fusing TF on the basis of VI data, the average R2, RMSE, and RE values in the calibration set were 0.743, 12.91, and 17.57%, respectively, with the R2 value representing an average increase of 10% when compared with the R2 of single VI data source. The mean R2, RMSE, and RE values in the validation set were 0.742, 12.849, and 17.71%, respectively, and the R2 value represented a 11.6% increase when compared to the R2 of the single VI data source. The addition of TP based on VI data enhanced the accuracy of the combined model. The average R2 values in the validation and calibration sets were 0.779 and 0.772, respectively, the RMSE values were 12.823 and 12.467, respectively, and the RE values were 15.56% and 15.62%, respectively. The R2 values were 15.4% and 16% higher, respectively, than the R2 values based on the single VI data source. In addition, in the combined TP

and TF modelling, the estimation performance was superior to those of the single data sources, both TP or TF; however, the model was inferior to VI based on both the calibration and validation sets. The results indicate that when using single data source-based VI as a benchmark, TF has a minor positive effect on model accuracy when performing multi-data collaboration modeling, whereas TP has a relatively high positive effect on model improvement.

**Table 4.** Estimation performance of multi-source collaboration models based on different algorithms.

Three modeling methods were used to synergize three data sources, VI, TF, and TP. The R2 values of the calibration and validation sets were further improved compared with the R2 value following combination of the two data sources. The average R2 values of the calibration and validation sets in the model with the three data sources combined were 0.856 and 0.849, respectively, the RMSE values were 10.997 and 10.399, respectively, and the RE values were 13.42% and 13.16%, respectively. The R2 values were 26.8% and 27.6% higher, respectively, than the R2 values of the single VI data source model. Comparison of the modeling algorithm results showed that the RFR model had the highest R2, the lowest RMSE and RE, and the greatest DI predictive capacity, followed by the SVR model and PLSR models (Figure 10). The R2 values of the RFR fusion model of the three data sources were 0.872 and 0.862 in the calibration and validation sets, respectively, the RMSE values were 10.108 and 10.049, respectively, and the RE values were 12.54% and 12.31%, respectively. The above results indicate that collaborative modeling with multiple data sources is superior to single data source-based modeling, with the combined model exhibiting better fit, accuracy, and predictive ability (Figure 9).

**Figure 10.** Comparison of three data source fusion models based on (**a**) PLSR, (**b**) SVR and (**c**) RFR algorithm.

#### **4. Discussion**

#### *4.1. Combining VI and TF to Monitor Crop Diseases*

Previous literature has confirmed the importance of reflectance spectrum data in crop disease monitoring and its application prospects. The visible light and near-infrared regions are the sensitive bands for spectral identification of different crop diseases and insect pests; furthermore, the spectral sensitivity bands of different crops and different diseases vary. The sensitive bands of wheat powdery mildew are located at 490–780 nm [57], and wheat powdery mildew monitoring is mainly based on the sensitive band [58,59], and different forms of disease VI can be established according to the reflection characteristics of the disease [7–9]. Disease emergence involves gradual development that alters internal tissue physiology and biochemistry, and, in turn, the external morphological structure, and then manifests externally as disease that can be detected by remote sensing. Due to the combined effects of internal and external factors, such as mesophyll cells, water, chlorophyll, and leaf yellowing and dryness, the ability to extract disease information from a single band is often limited. The VIs with good performance in the present study were NSRI, NPCI, and CVI. Among them, NSRI performed optimally, with a linear R2 of only 0.552, which hardly meets the information requirements for accurate crop protection.

The onset of powdery mildew disease has a significant bottom-up characteristic. In the early and middle stages of the disease, the disease is mainly concentrated in the middle and lower levels of the plant. However, the canopy reflectance spectra data mainly originate from the upper level, which leads to lack of consistency between the collected canopy spectra data and disease characteristics, and increases the challenge of monitoring powdery mildew using canopy spectrum data only. Therefore, the use of multivariate analysis methods to identify and monitor disease has become a hotspot in quantitative remote sensing research.

In the present study, multiple VIs were used as independent variables, and three algorithms PLSR, SVR, and RFR were used to predict DI. The results showed that the RFR model had the highest monitoring accuracy; however, R2 was still lower than 0.7. From the perspective of precise crop protection and disease prevention and control, the spectral data could not be used to monitor wheat powdery mildew reliably. Some scholars have attempted to incorporate fluorescence data in modeling when using hyperspectral data for disease monitoring, and achieved good monitoring results [60]. When a pathogen infects plants, the canopy structure changes following physiological and biochemical responses, and the TF can reflect the change in canopy structure caused by pathogen infestation to a certain degree [61,62]. Researchers have used hyperspectral VI in combination with TF to monitor wheat stripe rust, and reported that the estimation results of the two combined data sources were significantly better than that of the single data source [22]. In the present study, the VI and TF were modeled together, and model accuracy improved when compared with when the VI from a single data source was used. However, the highest accuracy of the combined model in the validation set was only 0.761, the optimization effect was limited, and it did not satisfy the requirements of accurate monitoring, which could be due to the gradual senescence of wheat leaves after the flowering period, and the increased background complexity of withered plants. Furthermore, multiple factors in some plots, such as disease, drought, senescence, and atmospheric temperature, which make it impossible to accurately distinguish whether the withered leaves and structural changes are attributed to disease stress, could have adversely influenced the modelling findings.

#### *4.2. Combining VI and TP to Monitor Crop Disease*

Thermal infrared imaging technologies have great application potential in remote sensing monitoring activities [63–65]. After crops are infected by fungi and pathogens, cell membrane permeability increases, water is lost, and plants exhibit dehydration and wilting. In addition, stomata are closed and heat loss on the leaf surface changes, which leads to leaf surface temperature response. At the onset of crop disease, changes in heat

radiation energy caused by plant water loss, stomata closure, and increased respiration can be intuitively reflected in infrared heat maps; however, most studies have focused on disease classification and disease identification. Calderón et al. [66] demonstrated the capacity of using canopy temperature information and hyperspectral VI to identify olive trees with yellow dwarf disease; however, they did not estimate disease severity. In the previous monitoring research on wheat powdery mildew, no studies have reported the combination of VI and TP. The correlation analyses carried out in the present study showed that the thermal infrared temperature was sensitive to disease, and it was more effective to convert CT into CTD, CTR, and NRCT. Compared to canopy TF, temperature information had a greater role in disease monitoring. The RFR model performed best (R2 = 0.577) and was slightly more accurate than the TF-RFR model; however, it was significantly less accurate than the VI-RFR model. VI as a single data source was more suitable for monitoring wheat powdery mildew, followed by canopy TP and canopy TF. To further improve the information limitations of single data sources, VI and canopy TP were modeled together (VI&TP). Model accuracies of different algorithms were higher than that of VI&TF on the whole, indicating that canopy temperature information has great application potential in disease monitoring.

Previous studies have also demonstrated that spectral information, texture information, and thermal infrared information have the ability to monitor crop diseases [22,24,26]; however, no study has reported their joint application in wheat powdery mildew monitoring. To that end, the present study conducted fusion modeling based on VI, TF, and TP (VI&TF&TP). According to the results, the combination of the three data sources had obvious advantages over single data sources or two combined data sources. Among them, the R2 values of the three data source models based on the RFR algorithm was 0.862, which provides technical support and a reference method for the prevention and precise control of wheat powdery mildew.

#### *4.3. Machine Learning Algorithms in Disease Monitoring*

In the wake of rapid advancements in computer modeling science, machine learning technology has been applied extensively in crop disease monitoring, with the achievement of remarkable results [67,68]. Jiang et al. [69] demonstrated the high estimation capacity of the RFR model in the monitoring of mangrove disease and insect pests. In addition, Zhang et al. [70] demonstrated the good classification performance of the RFR model in the identification of wheat grains infected with *Fusarium*. In the present study, three modeling methods (PLSR, SVR, RFR) were used to monitor wheat powdery mildew DI. The RFR model performed best, regardless of whether it was based on single data source modeling or multi-source data modeling. This is mainly because the RFR algorithm has good anti-noise ability and does not easily exhibit over-fitting [71]. In the present study, SVR was used to integrate information from three data sources, and the average accuracy that the model achieved was 0.77. Considering the operation efficiency and prediction accuracy of the model, the method is effective for monitoring the disease. In contrast, the performance of the PLSR model was slightly worse, which might be because PLSR was better at addressing multicollinearity between parameters [72], and the parameters used in the present study were optimized by the SPA algorithm, which eliminated the influence of multicollinearity, resulting in an inability to maximize the performance of the PLSR model.

Although the overall performance of the RFR model in the present study was the best, the estimated value was lower than the actual value under more severe disease conditions, which was also observed in the other model algorithms. Generally, the greater the population density of wheat powdery mildew, the worse the air permeability, and the more severe the disease, which decreases the sensitivity of spectral and thermal imaging data to disease severity. Under the condition of multi-source data fusion, the saturation of the model was alleviated, which also demonstrates the effectiveness of multi-data source fusion.

When applying different model algorithms to monitor wheat powdery mildew in collaboration with VI, TF, and TP, the present study did not consider the contribution rates of different data source parameters to the model. How to use different algorithms to determine the weights of different data source parameters to further improve the accuracy of the model remains to be further studied. The occurrence and characteristics of powdery mildew are certainly associated with crop variety, growth period, and other diverse factors. Using targeted information extraction algorithms to clarify the effects and contribution levels of each influencing factor could facilitate the integration multiple effect factors to accurately monitor disease occurrence, and provide a theoretical basis for crop protection and precise operations.

#### **5. Conclusions**

Based on multi-source data fusion and machine learning, the present study explores the application potential of canopy spectral vegetation index, thermal infrared information, and texture feature information obtained using different sensors in wheat powdery mildew monitoring. In the case of wheat disease index prediction based on single data source, spectral information is better than thermal infrared information and texture features. Regardless of the modeling method, the results obtained following the fusion of data from multiple sources are more reliable than the data obtained from a single data source. When using the combination of vegetation index, thermal infrared information and texture features, higher prediction precision can be achieved. Regardless of whether single data source or multi-source data is used, the monitoring accuracy of the RFR model is higher than that of other algorithm models. Therefore, the combination of multi-source data fusion and the RFR model have broad application prospects in wheat powdery mildew monitoring, which could not only promote disease prevention and control but also reduce pesticide use and enhance the efficiency of disease prevention and control activities. However, the models identified should be tested under different crop types, growth stages, and environmental conditions, to further evaluate the robustness of the models.

**Author Contributions:** Conceptualization, W.F.; methodology, W.F.; software, Z.F.; validation, Z.F. and L.S.; formal analysis, J.D. and L.H.; investigation, Z.F. and L.S.; resources, Y.Z.; data curation, Y.W.; writing—original draft preparation, Z.F. and L.S.; writing—review and editing, Z.F. and L.S.; visualization, Y.Z.; supervision, Y.Z and Y.W.; project administration, J.D. and L.H.; funding acquisition, W.F. and L.H. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by National Natural Science Foundation of China under Grant Numbers 31971791.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** We gratefully acknowledge the College of Agronomy, and Information and Management Science College, Henan Agricultural University, for providing the laboratory of this study. We sincerely thank the reviewers and the editors for their helpful comments and supplementary proposal. We also thank the native English speakers who provided assistance with language correction.

**Conflicts of Interest:** The authors declare no conflict of interest.

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The first written documented report of a successful liver biopsy was made by Paul Ehr‐ lich in the book "On diabetes" published in 1884. He published an account of the proce‐ dure performed in 1880 in Berlin, along with graphical illustrations of the instruments and the liver samples collected. This came detailed account was based on previous theo‐ retical advantages of this technique discussed by the French physician AGM Vernois in 1844, who in turn based his assumption on successful procedures performed for punctur‐

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All modern percutaneous liver biopsy techniques have rapidity as a common denominator. Either cutting or suction needles can be used for transthoracic or subcostal biopsy, either af‐ ter palpation or imaging assessment of the puncturing zone, or, preferably, under continu‐ ous image guidance. The transthoracic approach is the preferred method used, under realtime US or (more rarely) CT guidance and after a thorough imaging investigation of the liver and puncture route. All percutaneous methods imply two phases, one extra-hepatic corresponding to the needle puncturing the skin and reaching the needle, and a hepatic stage in which the needle passes the liver capsule, collects the parenchyma material, and is swiftly extracted. It is considered a relatively safe procedure, complication rates varying be‐

Risks and Benefits of Liver Biopsy in Focal Liver Disease

http://dx.doi.org/10.5772/52620

87

Trucut needles and their modified versions driven by spring-loaded biopsy guns are in‐ creasingly used and are the instruments of choice in many centers worldwide, especially in Europe [7]. Needle diameters vary between 1.20 mm to 1.60 mm, smaller calibers being used

Suction needles are less expensive and their operation allows for rapid intra-hepatic han‐ dling, thus being easier to use and possibly imply less bleeding-related complications. The most widespread types are the Menghini, Jamshidi and Klatskin needles, which remained virtually unchanged since their introduction in the second half of the last century. The maxi‐ mum required time for a complete syringe suction of the cytological material and the con‐ secutive needle retraction is 0.5 seconds. The intrahepatic phase is reduced to as low as 0.1

Image guidance has become mandatory in centers where the gastroenterologist can perform his or her own US exam. Real-time surveillance of the procedure greatly decreases the risk of complications (such as bleeding) and minimizes post-procedural complaints such as pain or hypotension. Hepatologists in the United States usually prefer to have a radiologist per‐

The transjugular route is preferred when the risk for complications is high and therefore a percutaneous approach is not considered safe enough for the patient. Patients with clinical ascites, known hemostatic defect, cirrhotic liver with clinical signs of organ deficiency (smaller size and increased palpatory stiffness) or morbid obesity are usually prime candi‐ dates for this approach. Another situation when the transvenous approach is preferred is

The resources needed for this procedure are higher than percutaneous approaches; howev‐ er, complication rates are lower (2.5% up to 6.5%) according to some authors [9], with mor‐ tality rates of approximately 0.09% in high-risk patient groups [10]. The expertise of the

when additional pressure measurements in the hepatic vein are required [8].

**3.1. Percutaneous biopsy**

tween studies, from 0.75% up to 13.6% [6].

when a high risk of complications is suspected.

seconds when the needle is operated by an expert practitioner [8].

forming the procedure under CT or US guidance [8].

**3.2. Transjugular (transvenous) biopsy**

Other scarce accounts of successful procedures followed in the next couple of decades (Oli‐ vet, 1926; Huard 1935; Silverman, 1938; Baron, 1939; Kofler, 1940; Dible, 1943), using differ‐ ent aspiration techniques performed with different modified biopsy needles [1].

A new stage in modern liver biopsy techniques was reached when, in 1957 and repeated in the following year, Menghini performed and reported on the first "one-second needle biop‐ sy" performed with a special small caliber needle with no trocar and a sharp bevel. This was the first time needle liver biopsy was introduced worldwide as a praised diagnostic techni‐ que capable of providing enough histological material for an accurate interpretation of the pathological changes present in the parenchyma [1].

Following this radical advancement, liver biopsy became more spread and the technique evolved once modern imagistic methods allowed for better and safer puncturing of the liver parenchyma. Thus, the technique entered the image-guided age of investigation per‐ formed under computed tomography (CT) or ultrasound (US) real-time screening. Re‐ ports from Denmark, China, the United Kingdom, France or the United States of America populated the 1960–1980 literature, once the technique became widespread and fully acknowledged by the academic community. Its utility in diagnosing liver diseases and later on in staging hepatitis or malignancies was undisputed for entire decades of the 20th century [1].

Recent advancements, based on the advent of new imagistic high-accuracy techniques based on both US and CT/RM approaches, highly diminished the role played by this invasive in‐ vestigation. The term "virtual biopsy" became more and more present in recent literature, once both doctors and patients alike became more confident and were introduced to these high-yield methods, such as Transient or Acoustic Radiation Force Elastography. Moreover, advanced serum markers (such as, for example, the Fibrotest-Actitest battery of tests) allow for an accurate non-invasive staging in hepatitis. The introduction of arterial uptake con‐ trast-enhanced US and CT/RM techniques substantially decreased the role of biopsy in diag‐ nosing liver biopsy [2–4].

However, histology remains one of the most accurate methods for evaluating liver paren‐ chymal changes, and is always used in malignancies when the diagnosis is uncertain or when other non-invasive methods fail to provide an accurate staging for hepatitis. Along with these non-invasive techniques came a revolution in in-situ biopsy methods. Such is probe-based confocal laser endoscopy (pCLE), which uses miniaturized probes connected to a laser source through fiber optics, small enough to fit inside a biopsy needle, thus provid‐ ing rapid live assessment of liver architecture [5].


**Author details**

Nekpen Erhunse\* and Victor Okomayin Faculty of Life Sciences, Department of Biochemistry, University of Benin, Benin City, Nigeria

\*Address all correspondence to<EMAIL_ADDRESS>
© 2022 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Algorithm to Generate Liutex Core Lines Based on Forward Liutex Magnitude Gradient Lines

*Yifei Yu and Chaoqun Liu*

### **Abstract**

Vortex definition and identification are extremely important for the study of fluid dynamics research. Liutex is a newly proposed concept that correctly represents vortex. Liutex is a vector whose direction is the local rotation axis and whose magnitude is twice the angular speed. To identify the unique structure of a vortex, a method known as the Liutex Core Line method has been developed, which displays the rotational core axis of a vortex. However, the original method is a manual method, which is not practical for real application, and an automatic algorithm is required for practical usage. Xu et al. proposed an algorithm by selecting the best line from a group of candidate lines, which is an important progress. In this chapter, from another perspective to solve this problem, a new algorithm is introduced based on forward Liutex magnitude gradient lines. Since gradient lines have the feature that they advance to the local maximums, the route will still result in a unique line, which avoids the process to find the best line. This algorithm has achieved some success for the Lambda vortex in early boundary layer transition.

**Keywords:** Liutex, vortex, vortex core, vortex identification, Liutex lines, Liutex core line

#### **1. Introduction**

Defining and visualizing vortices have been a challenge in fluid mechanics for several decades, even though the vortex is the essential part of formulating the turbulent flow that consists of countless vortices in different sizes and strengths. Turbulence generation and sustenance are still a mystery after intensive research efforts of centuries. Kaczorowski et al. [1] and Xi et al. [2] performed deep theory and experiment research on this topic, especially the Rayleigh–Bénard (RB) convection. In 2019, Zhou et al. elaborated the hydrodynamic instabilities that induced turbulent mixing in wide areas including inertial confinement fusion, supernovae, and their transition criteria. Zhou [3, 4] described in detail Rayleigh–Taylor and Richtmyer–Meshkov instability and some related models. Zhou's analysis is systematical, comprehensive, and sophisticated for flow instability and vortex generation, covering long history and state-of-the-art advances in turbulence research, which has clearly shown guidance

for further and deeper scientific research. Since vortex is the sinus and muscles of turbulence, it is of great importance to find out the definition of vortex. Human's understanding of vortex has gone through three stages [5].

The first generation is vorticity-based methods which have several weaknesses. One severe weakness is the contamination by shear. This shear contamination can be easily seen in the near-wall laminar boundary layer where there are high levels of shear with small amounts of rotational motion. High vorticity magnitude is seen in areas of high shear and low rotation, while areas with stronger rotation can be found to have relatively lower vorticity magnitude values [6]. Though the misconception that a vortex is defined by vorticity is still being published in textbooks and research papers, we know this is not appropriate. Then, the second generation that uses eigenvalue-based vortex identification criteria was developed. The second generation of vortex identification methods mainly used the eigenvalues of the velocity gradient tensor. Among the second generation, there are some popular methods such as Q criterion [7], Δ criterion [8], *λci* criterion [9], *λ*2 criterion [10], and some other methods. Although these methods made advances over the first generation, they were still contaminated by shear in different degrees. Another problem is that they are all scalar-based. These methods require a user-specified threshold to draw an iso-surface. Since the threshold was somewhat arbitrary, there must be many different thresholds used to represent the vortical structure and different thresholds may give totally different vortical structures. These scalar-based methods also prevent us from determining the rotation axis except that in the paper of *λci* [9], Zhou et al. indicated the rotation axis direction aligns the eigenvector but *λci* was still defined as a scalar and it is contaminated by shear as well due to the fact that the non-orthogonal transformation is used in the definition. To find the proper definition of vortex, Liu et al. proposed Liutex [11], which is a vector, in 2018. The direction of Liutex is the local rotation axis, and the magnitude of Liutex represents twice the angular speed.

Since the invention of Liutex, many researchers have used and tested it and reported that it is a strictly mathematical vortex definition and the currently best vortex identification method. Cuissa et al. [12] found that Liutex matches the analytical result of Lamb-Osceen vortex. Shen et al. [13] commented that Liutex is the only method that fully identifies small-scale vortices in vertical slit fishways simulation. Xu et al. found Liutex similarity, i.e., both the frequency and wavenumber spectrum of Liutex match the -5/3 law [14–16]. More reports on Liutex application can be found from [17–29] and four published books [30–33]. Liutex is considered as the vortex definition in this chapter.

Since Liutex is a vector-based concept that provides the direction as well as the magnitude of the rigid rotation, we can integrate the Liutex vector passing through a point within the vortex region to obtain a special Liutex core line. The concept of Liutex core line was first proposed in [34]. In short, Liutex core lines are formed by points where local maximal Liutex magnitude is reached. When calculating Liutex core lines using computer programs, some numerical difficulties are raised. Because of the numerical errors, the points selected by Liutex core line definition are a cluster of points rather than a single point. To solve this problem, Xu et al. [35] proposed seed point selection method. Li et al. [36] further improved this method by choosing the best line among the candidate lines generated by seed points. In this chapter, a new method, from another perspective, is reported to calculate the Liutex core lines based on the idea that the forward Liutex magnitude gradient lines converge to the Liutex core lines. So, instead of drawing two-directional Liutex magnitude lines, we only draw the forward lines. This leads to one advantage that the converging lines are

unique so that people do not need to select one line from several candidate lines. This method achieves preliminary success for identifying Liutex core lines of the Lambda vortex in early boundary layer transition.

This chapter is organized as follows: The definitions of Liutex and Liutex core lines are introduced in Section 2 and 3, respectively. In Section 4, the manual method and Xu's algorithm are reviewed. Then, the new proposed algorithm is introduced in Section 5. In Section 6, the proposed automatic method is applied to find the Liutex core lines from the data obtained from a Direct Numerical Simulation (DNSUTA) [37] of flow transition in a boundary layer validated by researchers from UTA and NASA Langley. The results of the DNSUTA were also compared to other DNS results where the DNSUTA was shown to have remarkable consistency with [38]. Conclusions are made in Section 7.

#### **2. Liutex**

Liutex *R* ! is a vector such that

$$
\overrightarrow{R} = R\overrightarrow{r} \tag{1}
$$

where its direction *r* ! is the eigenvector of the velocity gradient tensor *gradv*! that satisfies *ω* ! � *r* ! > 0 where *ω* ! is the vorticity and the magnitude R can be calculated by the following equation:

$$R = \left(\overrightarrow{\boldsymbol{\phi}} \cdot \overrightarrow{\boldsymbol{r}}\right) - \sqrt{\left(\overrightarrow{\boldsymbol{\phi}} \cdot \overrightarrow{\boldsymbol{r}}\right)^2 - 4\lambda\_{ci}^{-2}}\tag{2}$$

*r* ! is the real eigenvector of the velocity gradient tensor matrix representing local rotation axis, and *R* refers to the twice angular speed.

#### **3. Liutex core line**

The Liutex core line [34] (or the vortex rotation axis) can be defined as a Liutex line passing through the points that satisfy the condition:

$$
\nabla \mathbf{R} \times \overrightarrow{r} = \mathbf{0}, \mathbf{R} > \mathbf{0} \tag{3}
$$

where ∇*R* represents the Liutex magnitude gradient vector and *r* ! represents the direction of the Liutex vector. The Liutex core lines can be colored according to the vortex strength (Liutex magnitude) and provide a unique representation of the vortex structure.

The Liutex core concept comes from the idea that Liutex core is located at the position where Liutex reaches the maximum in the plane perpendicular to the local Liutex direction as shown in **Figure 1**. Since it is the local maxima in the plane, the projection of the Liutex gradient in the plane is zero, and thus, its only possible direction is perpendicular to the plane, which is parallel to the local Liutex direction. So, Eq. (3) is used to define Liutex core.

**Figure 1.**

*Liutex magnitude gradient lines distribution for the local maximal Liutex magnitude in the plane perpendicular to the Liutex direction.*

### **4. Manual method and Xu's algorithm to calculate Liutex core lines**

After defining the Liutex core line in [34], a manual method was proposed simultaneously in the same paper based on visualization software, for instance, Tecplot, Paraview, and so forth. After loading data files into these software, slices, iso-surfaces, and streamlines can be drawn, which are used in the manual method. The steps of the manual method are listed below.

Manual method:

Step 1: Draw the iso-surface of Liutex to get a general idea of the vortex structure. Step 2: Set a slice that exhibits the contour of Liutex magnitude.

Step 3: Determine the concentration of line of some Liutex magnitude gradient lines passing through the slice.

Step 4: Find the intersection point of the concentration line and the slice and create a Liutex line passing through the intersection point.

Use Burgers vortex as an example. The Bugers vortex is an analytical solution of the Navier-Stokes governing equations and is a typical widely used vortex model. Its velocity field can be described in the cylindrical coordinates as follows:

$$v\_r = -ar\tag{4}$$

$$v\_x = 2a\mathbf{z} \tag{5}$$

$$v\_{\theta} = \frac{\Gamma}{2\pi r} \mathbf{g}(r) \tag{6}$$

where *α* >0 and Γ> 0 are constants, and *g r*ð Þ can be expressed as

$$\mathbf{g}(r) = \mathbf{1} - \mathbf{e}^{\left(-\frac{\mathbf{w}^2}{2}\right)} \tag{7}$$

Some streamlines of the Burgers vortex is shown in **Figure 2**. It can be seen that Burgers vortex is like an upside-down cyclone where the flow converges into the center and then stays in the center and is stretched. As stated in the step 1, the isosurface of Liutex is shown in **Figure 3**, which shows there is a vortex center inside the iso-surface. Then, according to step 2 and step 3, a slice cutting the iso-surface is created, and gradient of Liutex magnitude lines is drawn, as shown in **Figure 4**. Clearly, all gradient lines converge to one point, and that point is the seed point. Next, we draw the Liutex line passing through the seed point, and this line represents the vortex center, and the result is shown in **Figure 5**.

**Figure 2.** *Streamlines of the Burgers vortex.*

**Figure 3.** *Liutex iso-surface of the Burgers vortex.*

**Figure 4.** *Liutex magnitude distribution on a slice with Liutex gradient lines.*

The Burgers vortex is a simple vortex model. Then, a more complicated case is tested. We will use the direct numerical simulation of the flat plate boundary layer transition. Similarly, we can first draw the iso-surface of Liutex (shown in **Figure 6**) and find the vortex structures are much more complicated than the Burgers vortex. Next, we display Liutex gradient lines and find the intersection point of the lines and the slice as shown in **Figure 7**. Then, we draw the Liutex line passing through that point. In **Figure 8**, colors are used to represent the Liutex magnitude and we can see the rotation strengths.

Obviously, the manual method is low in efficiency and impractical for generating all Liutex core lines for complicated vortex. So, many scientists aim to find an automatic way. Li and Xu et al. proposed an algorithm to automatically calculate Liutex core lines in [36].

**Figure 5.** *Liutex core line of the Burgers vortex.*

**Figure 6.** *Liutex iso-surface of the flat plate boundary layer transition.*

**Figure 7.** *Liutex iso-surface, a slice, Liutex gradient lines, and the intersection point.*

Xu's algorithm: Step 1: Read position and velocity data. Step 2: Compute Liutex vector.

Step 3: Search vortex core points by the criterions ∇*R* � *r* ! <*ε* and Ω*R* > Ω0 where Ω*R* represents relative rotation strength and can be calculated by

$$\Omega\_{\rm R} = \frac{\left(\overrightarrow{\boldsymbol{w}} \cdot \overrightarrow{\boldsymbol{r}}\right)^{2}}{2\left[\left(\overrightarrow{\boldsymbol{w}} \cdot \overrightarrow{\boldsymbol{r}}\right)^{2} - 2\lambda\_{ci}^{2} + 2\lambda\_{cr}^{2} + \lambda\_{r}^{2}\right] + \varepsilon} \tag{8}$$

#### **Figure 8.** *Liutex iso-surface and Liutex core line.*

where *ε* is a small positive number, *λcr* and *λci* are the real and complex eigenvalues of the velocity gradient tensor, and *λr* is the real eigenvalue of the velocity gradient tensor.

Step 4: Compute vortex core lines based on selected points in step 3.

Step 5: Group the vortex core lines.

Step 6: Delete the false and inaccurate vortex core lines by the third criterion. Step 7: Output data of vortex core lines.

To make it simple, Xu's algorithm indeed proposes a series of criterions on how to select the seed points. His method first selects some seed point candidates by applying some criterions. And then, it groups the seed point candidates of the same vortex together. After that, it selects the best one from the seed point candidates in each

## **5. New algorithm to calculate Liutex core line**

As explained in Section 3, Liutex direction is parallel to Liutex magnitude gradient direction at vortex core positions, so theoretically, Liutex lines and Liutex gradient lines will be the same in the location where the Liutex core lines pass. However, in practice, due to numerical errors, the points that the numerical program finds will not be exactly located on the same single Liutex line, which requires selecting the best one by a specified algorithm in Xu's paper. Another perspective to solve this problem is to make use of the property of gradient lines. Gradient lines have a good property that they can converge to the local maximums. In **Figure 9**, people can see that even though the seed points are much away from the vortex center, the generated Liutex gradient lines will converge to a unique line finally. So, even though selected points have numerical errors, we will still get a unique line. Based on this idea, a new algorithm is proposed as follows.

group.

**Figure 9.** *Liutex iso-surface and Liutex gradient lines.*

Step 1: Set the Liutex threshold and exclude the non-vortex points whose Liutex magnitudes are below the threshold.

Step 2: Find all seed points satisfying

$$\left| \nabla \mathbf{R} \times \overrightarrow{r} \right| < \varepsilon \tag{9}$$

where *ε* is a small number. Originally, the Liutex core line definition is ∇*R* � *r* ! ¼ 0. Because computer has numerical errors, we set a small number *ε* rather than 0.

Step 3: Draw forward Liutex gradient lines starting from the selected seed points. The proposed method has the following merits. First, this method does not have a high demand on the accuracy of the seed points. Xu's method already shows that it is hard to get enough accurate seed points and to ensure a unique line, people need to pick one seed point from seed point candidates. But the proposed method can tolerate some errors on the seed point selection. Secondly, since the proposed method can tolerate some errors on the seed point selection, the parameters in this method are not case-sensitive because people do not rely on the criterions to filter out all fake seed

#### **6. Test case**

points.

In this section, the proposed automatic method is applied to find the Liutex core line for the data obtained from a Direct Numerical Simulation [6] (DNSUTA) of flow transition in a boundary layer, which has been validated by researchers from UTA and

**Table 1.** *Flow parameters.*

NASA Langley. The mesh of this simulation includes 1920 � 128 � 241 points in streamwise (x), spanwise (y), and wall normal (z) directions. The parameters of the flow are shown in **Table 1**. *M*∞ is the inflow Mach number; Re represents Reynolds number, which is defined as *Re* ¼ *ρ*∞*u*∞*δin μ*∞ using the inflow boundary layer displacement thickness as the length reference; *xin* is the distance between the leading edge of the flat plate and upstream boundary of the computational domain; *Lx* and *Ly* are the lengths of the computational domain along *x* and *y* directions, respectively; *Lzin* means the height at inflow boundary; *Tw* and *T*∞ represent the temperatures of wall and free stream, respectively. The illustration of the computational domain is shown in **Figure 10**.

Compact schemes are used to do the spatial discretization. It has the following form:

$$
\beta\_- f'\_{j-2} + a\_- f'\_{j-1} + f'\_j + a\_+ f'\_{j+1} + \beta\_+ f'\_{j+2} = \frac{1}{h} \left( b\_- f\_{j-2} + a\_- f\_{j-1} + c f\_j + a\_+ f\_{j+1} + b\_+ f\_{j+2} \right) \tag{14}
$$

where *f* 0 *j* is the derivative at point j. For the sixth-order scheme used in this simulation,

$$\beta\_- = 0, a\_- = \frac{1}{3}, \beta\_+ = 0, a\_+ = \frac{1}{3}, b\_- = -\frac{1}{36}, a\_- = -\frac{7}{9}, a\_+ = \frac{7}{9}, b\_+ = \frac{1}{36} \tag{15}$$

The total variation diminishing (TVD) third order Runge–Kuntta method is used for the time discretization. The equations are:

$$\mathbf{Q}^{(0)} = \mathbf{Q}^{(n)} \tag{16}$$

$$Q^{(1)} = Q^{(0)} + \Delta t R^{(0)} \tag{17}$$

$$\mathcal{Q}^{(2)} = \frac{3}{4}\mathcal{Q}^{(0)} + \frac{1}{4}\mathcal{Q}^{(1)} + \frac{1}{4}\Delta t \mathcal{R}^{(1)} \tag{18}$$

$$\mathbf{Q}^{(\text{n}+1)} = \frac{\mathbf{1}}{\mathbf{3}} \mathbf{Q}^{(0)} + \frac{\mathbf{2}}{\mathbf{3}} \mathbf{Q}^{(2)} + \frac{\mathbf{2}}{\mathbf{3}} \Delta t \mathbf{R}^2 \tag{19}$$

The simulation result is shown in **Figure 11**. Spanwise vortex appears first followed by the Lambda vortex. We will use the Lambda vortex region to test the proposed method.

Applying step 1 and step 2 of the proposed method, we can get the seed points as shown in **Figures 12**–**14**. Drawing forward Lituex gradient lines starting from these seed points, we get **Figures 15**–**17**. If we draw Liutex lines from these seed points, we will get several separate lines rather than a unique line as shown in **Figures 18**–**20**. The proposed new algorithm obtains the unique vortex core line and does not need to select the best line from a group of lines generated by the seed points. Even though the obtained seed points have numerical errors, the output will still be convergent to a

**Figure 11.** *DNS result of the flat plate boundary layer transition.*

**Figure 12.** *Selected seed points by step 1 and step 2.*

unique line. **Figures 21**–**23** show Liutex magnitudes at the vortex core positions by colors. They show the rotation strength of the vortex core line is not uniform and is varied at different locations. This is what people cannot get by using the isosurface methods as iso-surface is a surface where the magnitudes are equal to the threshold.

**Figure 13.** *(top view) Selected seed points by step 1 and step 2.*

**Figure 14.** *(side view) Selected seed points by step 1 and step 2.*

**Figure 15.** *Selected seed points and corresponding forward Liutex gradient lines.*

**Figure 16.** *(top view) Selected seed points and corresponding forward Liutex gradient lines.*

**Figure 17.** *(side view) Selected seed points and corresponding forward Liutex gradient lines.*

**Figure 18.** *Liutex lines generated by the same seed points.*

**Figure 19.** *(top view) Liutex lines generated by the same seed points.*

**Figure 20.** *(side view) Liutex lines generated by the same seed points.*

### **7. Conclusion**

This study reports a method to automatically draw Liutex core lines from a new perspective. The proposed method is based on the property of gradient lines that they are converging toward to the local maximum points. Instead of Liutex lines, Liutex gradient lines are used in the proposed method and give this method two major merits. Firstly, the uniqueness comes from the property of gradient lines. Secondly, the proposed method can tolerate some numerical errors as these errors can easily be eliminated during the process that gradient lines converge to the center. However, this is not a mature method, and some work still needs to be done in the future, for example, developing it into a universal method that works for different cases.

**Figure 21.** *Liutex iso-surface and colorful forward Liutex gradient lines.*

**Figure 22.** *(top view) Liutex iso-surface and colorful forward Liutex gradient lines.*

**Figure 23.**

*(side view) Liutex iso-surface and colorful forward Liutex gradient lines.*


**3.2 Difficulty delivering balloons and stents**

First step to recognize if the difficulty is related to the lesion itself or difficulty due to the target vessel (severe tortuosity or calcifications)

Use a buddy wire technique.

Deep guide intubation.

Use glide balloon.

Combination of above techniques is needed in difficult cases.