5. Hybrid time-frequency partitioned techniques

This section is intended to provide a brief description of powerful circuit-block partitioning numerical simulation techniques operating in multivariate hybrid time-frequency frameworks. Section 5.1 introduces the fundaments of multivariate hybrid envelope following. Section 5.2 addresses some basic details of the simulation algorithms and finally, Section 5.3 describes the approach for automatic circuit-block partition.

The Newton iterative solver is usually utilized to solve (40), leading to

� � � � � � b Yð Þ t1,i ¼b Y ½ �r ð Þ t1,i

dPm Ybð Þ t1,i � �

dYblð Þ t1,i

þ jΩ

solve a linear system composed of n � ð Þ 2K þ 1 equations. The system of (41) involves the so-

of square submatrices (blocks), each one with dimensions 2ð Þ� K þ 1 ð Þ 2K þ 1 . The general

þ 1 h1:i

dQm Ybð Þ t1,i � �

dYblð Þ t1,i

vectors containing the Fourier coefficients of dpm by t1,i ð Þ ð Þ ; t2 =dbyl t1,i ð Þ ; t2 and dqm by t1,i ð Þ ð Þ ; t2 =

A very powerful technique has been proposed in the literature [18, 19] for solving (41) in an efficient way. This technique takes into account that, in some cases (e.g., RF heterogeneous systems), there are parts of the circuits in which there are no fluctuations dictated by the fast carrier. As a consequence, bidimensional forms by tð Þ 1; t2 of voltages and currents in those parts have no dependence on t2. This means that for each time line t1,i � ½ � 0; T2 each signal by t1,i ð Þ ; t2 has a constant value that can be represented as a Fourier series with a unique k ¼ 0 coefficient. Thus, while quickly varying signals are represented in the frequency domain by a set of ð Þ 2K þ 1 Fourier coefficients, signals in latent (slowly varying) blocks are represented by a single coefficient. Having this in mind it is straightforward to conclude that the size of vector Ybð Þ t1,i will be significantly reduced, as well as the size (number of equations) of the HB system. Significant Jacobian matrix size reductions will also be achieved, since some of the submatrices will no longer be 2ð Þ� K þ 1 ð Þ 2K þ 1 matrices, but, instead, simple 1 � 1 scalar elements. For instance, let us suppose that the mth component of (40) is a slowly varying signal exclusively dependent on other slowly varying signals. Let us also suppose that the lth component is also a slowly varying signal. Then, the Jacobian matrix block of row m and column l will be a 1 � 1

> ¼ dpmð Þ by tð Þ 1,i dbylð Þ t1,i

þ 1 h1,i dqmð Þ by tð Þ 1,i dbylð Þ t1,i

: (43)

Yb½ � rþ1

Numerical Simulation of Electronic Systems Based on Circuit-Block Partitioning Strategies

ð Þ t1,i from the previous estimate Yb½ �r

� �, which has a block structure, consisting of an n � n matrix

dQm Ybð Þ t1,i � �

dYblð Þ t1,i

, l, m ¼ 1, 2, …, n,

� �=dYblð Þ t1,i denote the Toeplitz matrices [7] of the

ð Þ� t1,i Yb½ �r

� �

ð Þ t1,i

http://dx.doi.org/10.5772/intechopen.75490

¼ 0, (41)

37

ð Þ t1,i we have to

(42)

dF Ybð Þ t1,i � �

dYbð Þ t1,i

¼

F Yb½ �r

called Jacobian matrix of F Ybð Þ t1,i

where dPm Ybð Þ t1,i

block given by

dbyl t1,i ð Þ ; t2 , respectively.

ð Þ t1,i � �

which implies that for computing Yb½ � rþ1

block of row m and column l can be expressed as

dFm Ybð Þ t1,i � �

dYblð Þ t1,i

� �=dYblð Þ t1,i and dQm Ybð Þ t1,i

dFm Ybð Þ t1,i � �

dYblð Þ t1,i

þ

### 5.1. Multivariate hybrid envelope following

Let us once again consider the initial-boundary value problem of (32) characterizing the bivariate nature of an electronic circuit operating at two widely separated time scales. Let us also consider the semi-discretization of the 0; tFinal ½ �� ½ � 0; T2 rectangular domain, which has led to the set of periodic boundary value problems defined by (34). When waveforms are not excessively demanding on the quantity of harmonic components needed for an accurate frequency domain representation, we are able to use the HB method for efficiently computing the solution of (34). In such case we will obtain for each time line t1,i � ½ � 0; T2 the following HB system

$$\mathbf{P}\left(\hat{\mathbf{Y}}(t\_{1,i})\right) + \frac{\mathbf{3Q}\left(\hat{\mathbf{Y}}(t\_{1,i})\right) - 4\mathbf{Q}\left(\hat{\mathbf{Y}}(t\_{1,i-1})\right) + \mathbf{Q}\left(\hat{\mathbf{Y}}(t\_{1,i-2})\right)}{2h\_{1,i}} + j\mathbf{2Q}\left(\hat{\mathbf{Y}}(t\_{1,i})\right) = \hat{\mathbf{X}}(t\_{1,i}),\tag{39}$$

in which Xbð Þ t1,i is a 2ð Þ� K þ 1 n vector containing the Fourier coefficients of the stimuli (independent sources) and Ybð Þ t1,i a 2ð Þ� K þ 1 n vector containing the Fourier coefficients of the unknowns (node voltages and brunch currents' waveforms), at t1 ¼ t1,i. K is the maximum harmonic order and n is the number of unknowns. In order to obtain the solution in the entire 0; tFinal ½ �� ½ � 0; T2 rectangular domain a total of K1 HB systems have to be solved.

With this hybrid time-frequency approach we have an envelope following technique that handles the slow variations of the unknowns in the time domain and their fast variations in the frequency domain. This technique, usually denoted as multivariate envelope transient harmonic balance [20, 21], is able to exploit the existence of time-rate disparities in circuits operating under moderately nonlinear regimes of operation.

### 5.2. Partitioned algorithms for hybrid envelope following computation

The hybrid time-frequency envelope following technique presented earlier does not perform any distinction between nodes or blocks in the circuit. Although it has been widely used, especially by the RF and microwave community, only a few years ago other versions regarding circuit-block partition were proposed [18, 19] in way to take into account possible circuit's heterogeneities. The most important aspects of these partitioning techniques are briefly reviewed in the following.

Let us rewrite (39) as

$$\begin{split} \mathbf{F}\left(\widehat{\mathbf{Y}}(t\_{1,i})\right) &= \mathbf{P}\left(\widehat{\mathbf{Y}}(t\_{1,i})\right) + \frac{3\mathbf{Q}\left(\widehat{\mathbf{Y}}(t\_{1,i})\right) - 4\mathbf{Q}\left(\widehat{\mathbf{Y}}(t\_{1,i-1})\right) + \mathbf{Q}\left(\widehat{\mathbf{Y}}(t\_{1,i-2})\right)}{2h\_{1,i}} \\ &+ j\mathbf{D}\mathbf{Q}\left(\widehat{\mathbf{Y}}(t\_{1,i})\right) - \widehat{\mathbf{X}}(t\_{1,i}) = 0. \end{split} \tag{40}$$

The Newton iterative solver is usually utilized to solve (40), leading to

addresses some basic details of the simulation algorithms and finally, Section 5.3 describes the

Let us once again consider the initial-boundary value problem of (32) characterizing the bivariate nature of an electronic circuit operating at two widely separated time scales. Let us also consider the semi-discretization of the 0; tFinal ½ �� ½ � 0; T2 rectangular domain, which has led to the set of periodic boundary value problems defined by (34). When waveforms are not excessively demanding on the quantity of harmonic components needed for an accurate frequency domain representation, we are able to use the HB method for efficiently computing the solution of (34). In

in which Xbð Þ t1,i is a 2ð Þ� K þ 1 n vector containing the Fourier coefficients of the stimuli (independent sources) and Ybð Þ t1,i a 2ð Þ� K þ 1 n vector containing the Fourier coefficients of the unknowns (node voltages and brunch currents' waveforms), at t1 ¼ t1,i. K is the maximum harmonic order and n is the number of unknowns. In order to obtain the solution in the entire

With this hybrid time-frequency approach we have an envelope following technique that handles the slow variations of the unknowns in the time domain and their fast variations in the frequency domain. This technique, usually denoted as multivariate envelope transient harmonic balance [20, 21], is able to exploit the existence of time-rate disparities in circuits operat-

The hybrid time-frequency envelope following technique presented earlier does not perform any distinction between nodes or blocks in the circuit. Although it has been widely used, especially by the RF and microwave community, only a few years ago other versions regarding circuit-block partition were proposed [18, 19] in way to take into account possible circuit's heterogeneities. The most important aspects of these partitioning techniques are briefly

þ Q Ybð Þ t1,i�2 � �

þ jΩQ Ybð Þ t1,i � �

¼ Xbð Þ t1,i , (39)

such case we will obtain for each time line t1,i � ½ � 0; T2 the following HB system

2h1,i

0; tFinal ½ �� ½ � 0; T2 rectangular domain a total of K1 HB systems have to be solved.

5.2. Partitioned algorithms for hybrid envelope following computation

þ

þ jΩQ Ybð Þ t1,i � �

3Q Ybð Þ t1,i � �

� Xbð Þ¼ t1,i 0:

� 4Q Ybð Þ t1,i�1 � �

2h1,i

þ Q Ybð Þ t1,i�2 � �

(40)

� 4Q Ybð Þ t1,i�1 � �

approach for automatic circuit-block partition.

36 Numerical Simulations in Engineering and Science

5.1. Multivariate hybrid envelope following

3Q Ybð Þ t1,i � �

ing under moderately nonlinear regimes of operation.

¼ P Ybð Þ t1,i � �

P Ybð Þ t1,i � �

þ

reviewed in the following.

F Ybð Þ t1,i � �

Let us rewrite (39) as

$$\left| \mathbf{F} \left( \widehat{\mathbf{Y}}^{[r]} (t\_{1,i}) \right) + \frac{d \mathbf{F} \left( \widehat{\mathbf{Y}} (t\_{1,i}) \right)}{d \widehat{\mathbf{Y}} (t\_{1,i})} \right|\_{\widehat{\mathbf{Y}} (t\_{1,i}) = \widehat{\mathbf{Y}}^{[r]} (t\_{1,i})} \left[ \widehat{\mathbf{Y}}^{[r+1]} (t\_{1,i}) - \widehat{\mathbf{Y}}^{[r]} (t\_{1,i}) \right] = \mathbf{0},\tag{41}$$

which implies that for computing Yb½ � rþ1 ð Þ t1,i from the previous estimate Yb½ �r ð Þ t1,i we have to solve a linear system composed of n � ð Þ 2K þ 1 equations. The system of (41) involves the socalled Jacobian matrix of F Ybð Þ t1,i � �, which has a block structure, consisting of an n � n matrix of square submatrices (blocks), each one with dimensions 2ð Þ� K þ 1 ð Þ 2K þ 1 . The general block of row m and column l can be expressed as

$$\begin{split} \frac{d\mathbf{F}\_{m}\left(\widehat{\mathbf{Y}}(t\_{1,i})\right)}{d\widehat{\mathbf{Y}}\_{l}(t\_{1,i})} &= \frac{d\mathbf{P}\_{m}\left(\widehat{\mathbf{Y}}(t\_{1,i})\right)}{d\widehat{\mathbf{Y}}\_{l}(t\_{1,i})} + \frac{1}{h\_{1,i}} \frac{d\mathbf{Q}\_{m}\left(\widehat{\mathbf{Y}}(t\_{1,i})\right)}{d\widehat{\mathbf{Y}}\_{l}(t\_{1,i})} \\ &+ j\Omega \frac{d\mathbf{Q}\_{m}\left(\widehat{\mathbf{Y}}(t\_{1,i})\right)}{d\widehat{\mathbf{Y}}\_{l}(t\_{1,i})}, \qquad l, m = 1, 2, \dots, n, \end{split} \tag{42}$$

where dPm Ybð Þ t1,i � �=dYblð Þ t1,i and dQm Ybð Þ t1,i � �=dYblð Þ t1,i denote the Toeplitz matrices [7] of the vectors containing the Fourier coefficients of dpm by t1,i ð Þ ð Þ ; t2 =dbyl t1,i ð Þ ; t2 and dqm by t1,i ð Þ ð Þ ; t2 = dbyl t1,i ð Þ ; t2 , respectively.

A very powerful technique has been proposed in the literature [18, 19] for solving (41) in an efficient way. This technique takes into account that, in some cases (e.g., RF heterogeneous systems), there are parts of the circuits in which there are no fluctuations dictated by the fast carrier. As a consequence, bidimensional forms by tð Þ 1; t2 of voltages and currents in those parts have no dependence on t2. This means that for each time line t1,i � ½ � 0; T2 each signal by t1,i ð Þ ; t2 has a constant value that can be represented as a Fourier series with a unique k ¼ 0 coefficient. Thus, while quickly varying signals are represented in the frequency domain by a set of ð Þ 2K þ 1 Fourier coefficients, signals in latent (slowly varying) blocks are represented by a single coefficient. Having this in mind it is straightforward to conclude that the size of vector Ybð Þ t1,i will be significantly reduced, as well as the size (number of equations) of the HB system. Significant Jacobian matrix size reductions will also be achieved, since some of the submatrices will no longer be 2ð Þ� K þ 1 ð Þ 2K þ 1 matrices, but, instead, simple 1 � 1 scalar elements. For instance, let us suppose that the mth component of (40) is a slowly varying signal exclusively dependent on other slowly varying signals. Let us also suppose that the lth component is also a slowly varying signal. Then, the Jacobian matrix block of row m and column l will be a 1 � 1 block given by

$$\frac{d\mathbf{F}\_m(\widehat{\mathbf{Y}}(t\_{1,i}))}{d\widehat{\mathbf{Y}}\_l(t\_{1,i})} = \frac{d p\_m(\widehat{\mathbf{y}}(t\_{1,i}))}{d\widehat{\mathbf{y}}\_l(t\_{1,i})} + \frac{1}{h\_{1,i}} \frac{d q\_m(\widehat{\mathbf{y}}(t\_{1,i}))}{d\widehat{\mathbf{y}}\_l(t\_{1,i})}.\tag{43}$$

It may be noted that this 1 � 1 scalar block can be seen as a particular case of the general ð Þ� 2K þ 1 ð Þ 2K þ 1 block of (42), if K ¼ 0 is assumed as the maximum harmonic order. Actually, given that df m by t1,i ð Þ ð Þ ; t2 =dbyl t1,i ð Þ ; t2 is a constant function evidencing no fluctuations in the t2 fast time scale, the last term of (42) will vanish and there will be no more necessity of converting the right-hand side terms of (43) into the frequency domain.

Similar to what we have discussed for the method described in Section 4, the robustness of this partitioning strategy may be improved if more than one iteration in (41) is computed before the simulator decides which signals are slow and which signals are fast. The main drawback of such approach is the loss of some efficiency due to the extra computational effort required.

Numerical Simulation of Electronic Systems Based on Circuit-Block Partitioning Strategies

http://dx.doi.org/10.5772/intechopen.75490

39

As a final point of this section, we would like to point out that significant gains in computation speed have been reported in the scientific literature (e.g., [18, 19]) for the simulation of several illustrative examples of practical interest using these hybrid time-frequency envelope follow-

In this chapter, we have briefly reviewed some powerful numerical simulation techniques based on partitioned stratagems. Such techniques were especially designed to cope with the simulation challenges brought by emerging electronic technologies to the EDA community, as is the case of complex heterogeneous electronic systems composed of a combination of different kinds of circuit blocks (analog, mixed-signal and digital blocks, or even radio frequency blocks) containing node voltages and brunch currents of very distinct formats and running on widely separated time scales. With these partitioned techniques signals within different blocks of the circuits are computed with distinct algorithms and/or step sizes. Considerable reductions on the computational cost have been registered in several experiments published in the scientific literature (in comparison to previously recognized techniques) without compromising the accuracy of the results.

This work is funded by National Funds through FCT—Fundação para a Ciência e Tecnologia,

1 School of Technology and Management, Polytechnic Institute of Leiria, Leiria, Portugal

[1] Lambert J. Numerical Methods for Ordinary Differential Systems: The Initial Value Prob-

2 Institute of Telecommunications, University of Aveiro, Aveiro, Portugal

ing partitioned algorithms.

Acknowledgements

Author details

References

under the project UID/EEA/50008/2013.

Jorge dos Santos Freitas de Oliveira1,2\*

\*Address all correspondence to<EMAIL_ADDRESS>
lem. 1st ed. West Sussex: Wiley; 1991

6. Conclusions

Since only fast-varying signals are converted into the frequency domain, this partitioned technique can be seen as a combination of multivariate envelope transient harmonic balance (by treating the fast-varying signals in a hybrid time-frequency framework) with a pure time marching simulation engine (by treating some of the signals in a pure time domain scheme). Thus, beyond the notorious significant vector and matrix size reductions above mentioned, there is another important advantage brought by this partitioned technique. For example, in complex heterogeneous RF systems strongly nonlinear regimes of operation are in general associated to digital or baseband blocks, whereas moderately nonlinear regimes are typical of RF blocks. With this partitioned technique signals in digital and baseband blocks are appropriately computed in the time domain, while signals in RF blocks are treated in the hybrid time-frequency framework.

### 5.3. Circuit-block partitioning strategy

Similar to what we have mentioned for the methods discussed in the previous sections, it will be of great utility if the simulator is able to automatically distinguish the fast-varying variables from the slowly varying ones. We now briefly review the approach addressed in [19] for that purpose, which splits the circuit into distinct blocks according to the time rates of change of their voltages and currents.

Let us consider the HB system of (39). As stated earlier, this system has to be solved with the iterative scheme of (41) for each artificial time line t1,i � ½ � 0; T2 . The automatic partitioning strategy proposed in [19] consists in considering all the circuit's variables as fast on the first iteration of (41), that is, it consists in initially representing all the unknowns in the frequency domain as a set of 2ð Þ K þ 1 Fourier coefficients. This way, the algorithm starts by computing a single iteration in (41) to evaluate Yb½ � 1 ð Þ t1,i

$$\widehat{\mathbf{Y}}^{[1]}(t\_{1,i}) = \left[\widehat{\mathbf{Y}}\_1^{[1]}(t\_{1,i})^T, \widehat{\mathbf{Y}}\_2^{[1]}(t\_{1,i})^T, \dots, \widehat{\mathbf{Y}}\_n^{[1]}(t\_{1,i})^T\right]^T,\tag{44}$$

where each Ybvð Þ t1,i , v ¼ 1, …, n, is a 2ð Þ� K þ 1 1 vector defined as

$$\widehat{\mathbf{Y}}\_{v}^{[1]}(t\_{1,i}) = \left[Y\_{v,-K}{}^{[1]}(t\_{1,i}), \dots, Y\_{v,0}{}^{[1]}(t\_{1,i}), \dots, Y\_{v,K}{}^{[1]}(t\_{1,i})\right]^T. \tag{45}$$

Each of the Yb½ � 1 v ð Þ t1,i is then inspected. If its Fourier coefficients of order k 6¼ 0 are practically null (their absolute values stay under a very small prescribed tolerance) it will be classified as slow. Otherwise it will be classified as fast. After this classification, which will temporarily split the system into fast and slow subsystems, the simulator considers that signals in slow subsystems can be represented by a single Fourier coefficient for the remaining iterations needed to compute the solution of (41).

Similar to what we have discussed for the method described in Section 4, the robustness of this partitioning strategy may be improved if more than one iteration in (41) is computed before the simulator decides which signals are slow and which signals are fast. The main drawback of such approach is the loss of some efficiency due to the extra computational effort required.

As a final point of this section, we would like to point out that significant gains in computation speed have been reported in the scientific literature (e.g., [18, 19]) for the simulation of several illustrative examples of practical interest using these hybrid time-frequency envelope following partitioned algorithms.


**1. Introduction**

Reading is a complex process involving multiple regions in the brain communicating with each other to facilitate effective reading. Learning to read can play an important role in academic success. There is a reciprocal relationship between language and reading learning where improvements in one can lead to an increased understanding of the other [1, 2]. This chapter focuses on the concept of emergent reading and brain imaging evidence related to reading acquisition and aims to elucidate our understanding of emergent reading experience and its relationship with brain development.


2.3.5. Determination of Free Sugars

A total of 1g of bee pollen was mixed with 20 mL of methanol and filled to 50 mL with water. The solution was centrifuged for 10 min at 5000 rpm; the supernatant was transferred into a 50 mL flask and filled with water. The solution was filtered using a 0.45 μm filter prior analysis. The separation of the free sugars (fructose, glucose, sucrose, melesitose and raffinose) was made on Schimadzu HPLC instrument (Kyoto, Japan) with RID (refractive index detector). A Phenomenex Luna® Omega 3 μm SUGAR 100 Å HPLC Column 150 × 4.6 mm (Torrance, CA, USA) was used for the separation. The mobile phases were acetonitrile and water in a mixture of 80:20 (*v*/*v*). The flow rate was set at 1.3 mL·min−1; column and detector temperature was 30 ◦C and the sample volume injection was 10 μL. The free sugars were expressed as % reported to dry mater. All the measurements were carried out in triplicate.


*Article* **Simultaneous Determination of 23 Mycotoxins in Broiler Tissues by Solid Phase Extraction UHPLC-Q/Orbitrap High Resolution Mass Spectrometry**

**Youyou Yang 1,\*,†, Zhuolin He 2,†, Lei Mu 3,4, Yunfeng Xie 3,4,\* and Liang Wang 2**

**Abstract:** Mycotoxins are a type of toxins harmful for not only animal but also human health. Cooccurrence of multi-mycotoxins could occur for food infected by several molds, producing multimycotoxins. It is necessary to develop corresponding determination methods, among which current mass spectrometry (MS) dominates. Currently, the accurate identification and quantitation of mycotoxins in complex matrices by MS with low resolution is still a challenge since false-positive results are typically obtained. Here, a method for the simultaneous determination of 23 mycotoxins in broiler tissues using ultra-high performance liquid chromatography-quadrupole/orbitrap HRMS was established. After the extraction by acetonitrile-water-formic acid (80:18:2, *v*/*v*/*v*), the purification by multifunctional purification solid phase extraction cartridges and the chromatographic separation on a C18 column, representative mycotoxins were determined by HRMS in full scan/data-dependent MS/MS acquisition mode. The quantitation was based on the external standard method. An MS/MS database of 23 mycotoxins was established to achieve qualitative screening and simultaneous quantification. Mycotoxins had a good linear relationship within a certain concentration range with correlation coefficients (r2) larger than 0.991 as well as the limit of quantitation of 1.80–300 μg/kg. The average recoveries at three different levels of low, medium and high fortification were 61–111% with relative standard deviations less than 13.5%. The method was fast, accurate, and suitable for the precise qualification of multiple mycotoxins in broiler tissues. 15 μg/kg zearalenone (ZEN) was detected in one liver sample among 30 samples from markets including chicken breast meat, liver, and gizzards. The result illustrated that the pollution of ZEN should not be neglected considering its harmful effect on the target organ of liver.

**Keywords:** broiler tissue; orbitrap high resolution mass spectrometry; mycotoxins; rapid screening; solid phase extraction

#### **1. Introduction**

Mycotoxins are secondary metabolites with low molecular weight, approximately of <1000 Da, produced by fungus species during growth and proliferation. The corresponding classification is difficult due to the complex structures and origins. Mycotoxins include group 1 and group 2B carcinogens (for example, aflatoxins (AFs)) are considered as the most toxic. In addition, there also exist modified and emerging mycotoxins. Mycotoxins which are harmful for animal liver and decrease animal' immunity and reproduction capacity can enter animal derived foods including meat, egg and milk and lead to residue through food chain, storage and processing, severely threatening human and animal

**Citation:** Yang, Y.; He, Z.; Mu, L.; Xie, Y.; Wang, L. Simultaneous Determination of 23 Mycotoxins in Broiler Tissues by Solid Phase Extraction UHPLC-Q/Orbitrap High Resolution Mass Spectrometry. *Separations* **2021**, *8*, 236. https:// doi.org/10.3390/separations8120236

Academic Editor: Erica Liberto

Received: 22 October 2021 Accepted: 22 November 2021 Published: 4 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/).

health [1,2]. Currently, there are more than 400 mycotoxins, only a few of which are daily regulated and routinely monitored [3]. The current research about the residue determination of mycotoxins paid more attention to feed, grain, and oil to prevent them from entering the food chain. However, the detection of mycotoxins in meat (especially animal derived organs) was seldom reported. It was determined that the elimination time of mycotoxin residue in liver and muscle reached the quantitative value within at least 11–18 d [4]. Zearalenone (ZEN) in chicken serum was completely eliminated after 7 d with oral administration of the feed polluted by mycotoxins. However, there existed ZEN in both liver and faeces [5,6]. Mycotoxin residue in liver, kidney, muscle and milk of animal derived from food was mainly due to oral intake of the feed polluted by mycotoxins. Through food chain, mycotoxins entered the human body, threatening the human health [7–9]. Mycotoxin pollution which was widespread and uncontrollable has become a crucial aspect of animal derived food safety.

Over the last two decades, considering the determination of mycotoxins, MS including tandem MS and HRMS dominated (as high as 55%). The determination methods of mycotoxins mainly included HPLC [10,11], GC [12,13], and LC-MS/MS [14–19]. Tandem MS for mycotoxins has been widely studied, focusing on multi-mycotoxin residue analysis and quantitation which was "golden standard". Tandem MS such as triple quadrupole (QQQ) of unit resolution MS selected multiple reaction monitoring (MRM) for the quantitation. The ion transitions and related parameters were necessary to be optimized sequentially, which were labor and time consuming when aiming at a large number of targets. The unit resolution MS was susceptible to the isobaric ion, allowing potential false positive phenomenon [19].

Recently, HRMS including Q/orbitrap and time of flight has been utilized in the determination of mycotoxins, which mainly focused on method development for avoiding matrix interference and accurate identification. Previous research work was more focused on the determination of single or a type of mycotoxins with a relative narrow covering range. Q/orbitrap HRMS has lots of advantages such as high resolution and high accuracy, which can realize accurate screening. It can obtain accurate molecular weights of compounds as well as the fragment ions under high resolution and with relatively strong anti-interference capacity [20,21]. Its most attractive advantage is the feasibility with target, non-target, and retrospective analysis. The current reported research about the determination of mycotoxins in meat has been mainly based on the unit resolution MS. The combination of UHPLC-Q/orbitrap HRMS has been utilized in the determination of pollutants in animal derived food [21] and pesticide residue [22].

In addition, the pretreatment method of mycotoxins has been mainly coupled with tandem MS. The corresponding coupling with HRMS was seldom. Currently, only QuECh-ERS method has been coupled to HRMS. However, fumonisins (FBs) which were known to be difficult to analyze with QuEChERS, were not considered by HRMS [23].

Considering the dietary habit of eating chicken meat as well as liver and gizzard in China, it was crucial to develop methods for analyzing mycotoxins in different broiler tissues and organs. In this work, A total of 23 mycotoxins including AFs (AFTB1, AFTB2, AFTG1, AFTG2, AFTM1, AFTM2), deoxynivalenol (DON), 3-acetyldeoxynivalenol (3- ADON), 15-acetyldeoxynivalenol (15-ADON), de-epoxydeoxynivalenol (DOM), T-2 toxin (T-2), HT-2 toxin (HT-2), FBs (FB1, FB2, FB3), ochratoxin A (OTA), ochratoxin (OTB), zearalanone (ZAN), zearalenone (ZEN), α-zearalanol (α-ZAL), β-zearalanol (β-ZAL), αzearalenol (α-ZOL) and β-zearaalenol (β-ZOL) in broiler tissues were determined by solid phase extraction (SPE)-UHPLC-Q/orbitrap HRMS for rapid and accurate identification and quantitation, providing supports for animal derived food safety.

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

#### *2.1. Reagents*

AFTB1 (2 μg/mL), AFTB2 (0.5 μg/mL), AFTG1 (2 μg/mL), AFTG2 (0.5 μg/mL), AFTM1 (0.5 μg/mL), AFTM2 (0.5 μg/mL), FB1 (50 μg/mL), FB2 (50 μg/mL), FB3 (50 μg/mL), DON (100 μg/mL), DOM (25 μg/mL), 3-ADON (100 μg/mL), 15-ADON (100 μg/mL), T-2 toxin (100 μg/mL), HT-2 toxin (100 μg/mL), STC (50 μg/mL), OTA (10 μg/mL), OTB (10 μg/mL) were purchased from Romer Labs Co., Ltd. (Tulln, Austria). ZAN (100 μg/mL), ZEN (100 μg/mL), α-ZAL (100 μg/mL), α-ZEL (100 μg/mL), β-ZOL (100 μg/mL), and β-ZOL (100 μg/mL) were purchased from Anpel Co., Ltd. (Shanghai, China). Chicken breast, liver and kidneys were purchased from local super market.

Methanol and acetonitrile were all HPLC grade and purchased from Fisher Scientific (Pittsburgh, PA, USA). Water was purified by a Milli Q Advantaged A10 water purification system (Millipore, Bedford, MA, USA). Formic acid for UPLC/LC-MS were from Anpel Co., Ltd. (Shanghai, China). SPE columns with Captiva-EMR Lipid (600 mg, 6 mL,) and Oasis PRIME HLB (600 mg, 6 mL) were from Agilent Technologies (Santa Clara, CA, USA) and Waters (Shanghai, China).

#### *2.2. Instrument Conditions*

Separation and detection of mycotoxins performed in the Q-Exactive system combined with Ultimate 3000 LC (Thermofisher, San Jose, CA, USA). Separation was fulfilled using a CORTECS C18 column (2.1 × 100 mm, 1.6 μm; Waters, Wexford, Ireland). The injection volume was set at 10 μL and the flow rate was maintained at 0.2 mL/min. The mobile phase was composed of water (0.1% formic acid) as eluent A and methanol as eluent B. The gradient elution program was shown in Table 1. The mass spectrometer was equipped with a heated electrospray ionization (H-ESI) source. Data with positive and negative modes were acquired through data-dependent acquisition, respectively. The mass spectrometer parameters were as follows: spray voltage, 3000 V (±); auxiliary gas heater temperature, 350 ◦C; capillary temperature, 320 ◦C; sheath gas flow rate 40 Arb; auxiliary gas flow rate, 15 Arb; scan range, 50–600 *m*/*z*; collision energy (NCE): 20, 30, 40 V; the resolving power for MS1 and MS2, 70,000 and 17,500, respectively.

**Table 1.** Gradient elution programs.

#### *2.3. Sample Preparation*

Weigh 2.00 ± 0.05 g of the minced sample into a 50 mL centrifuge tube. 10 mL acetonitrile/water/formic acid (80/18/2, *v*/*v*/*v*) were added. The mixture was vortexed for 1 min and processed the ultrasonication at 30 ◦C for 20 min, followed by centrifugation at 8000 rpm for 10 min. 5 mL of the supernatant was transferred to the Captiva-EMR Lipid and controlled at the eluting rate of 3 drops/s. Right after the solution flowed through the column, 1 mL acetonitrile/water (80/20, *v*/*v*) was added. Both of the elution solutions were collected and nearly dried through the nitrogen flow at 40 ◦C. The dried eluents were redissolved in a mixture of methanol/water/formic acid (250 μL, 30/70/0.1, *v*/*v*/*v*), vortexed for 1 min, ultrasonicated for 5 min, and centrifuged at 12,000 rpm for 10 min. The supernatant was transferred into a vial for analysis.

#### *2.4. Method Validation*

Linearity, sensitivity, accuracy, and precision were investigated according to Criterion on quality control of laboratories—chemical testing of food (GB 27404). Calibration curves were constructed through the responses versus the concentrations spiked in the blank ma-

trix. The limit of detection (LOD, S/N = 3) and the limit of quantification (LOQ, S/N = 10) were calculated in light of the blank matrix with the lowest spiking level. Recoveries and stability were investigated using blank samples fortified with three different levels. Samples of each level were prepared in six replicates. The recovery of each mycotoxin was calculated as the ratio of the mean peak areas between the samples spiked before extraction and the samples spiked after extraction. The relative standard deviation (RSD) of peak areas in six replicates for each mycotoxin at three spiking levels represented the stability of the method.

#### **3. Results and Discussion**

#### *3.1. The Optimization of LC-HRMS Conditions*

In the optimization procedure of the chromatography conditions, the column type and the mobile phase were investigated. Compared with Thermo Scientific Accucore C18 column (2.1 mm × 100 mm, 2.6 μm), the separation efficiency of CORTECS-UPLC-C18 (2.1 mm × 100 mm, 1.6 μm) was higher, which could guarantee the good peak shape of each target compound. Besides, the analysis time was shorter and the resolution was relatively higher. Thus, analysis of 23 mycotoxins could be fulfilled within a shorter time. In this experiment, methanol was selected as the organic phase. Modifiers of 0.1% formic acid and 5 mmol/L ammonium formate in aqueous phase were investigated. The addition of formic acid in aqueous phase resulted in better responses of target mycotoxins since the formic acid could facilitate the protonization of some mycotoxins. Thus, methanol-0.1% aqueous formic acid (*v*/*v*) was chosen as the mobile phase. The extracted ion chromatograms of mycotoxins were shown in Figure 1.

**Figure 1.** *Cont*.

**Figure 1.** Extracted ion chromatograms of the 23 mycotoxins at positive mode (**a**) and negative mode (**b**).

Different spray voltages of 2.8, 3.0, and 3.5 kV for heated ESI (HESI) were studied for the ionization of targets, illustrating that 3.0 kV led to better ionization efficiency of target compounds. According to accurate identification of HRMS, two ions of mass tolerance within 5 ppm are required. One of these ions is required to be a fragment ion while the second ion should be the (de-) protonated molecular ion or an adduct ion thereof. In this work, full MS/data dependent-MS2 (full MS/dd-MS2) mode would be chosen and would give the information of precursor ions and MS/MS spectra. Retention time, accurate *m*/*z* of molecular ion and accurate *m*/*z* of the fragment were listed in Table 2. Within 14.0 min, satisfactory separation and detection were realized. According to the structure and the properties of mycotoxins, both positive and negative ionization modes were used.

#### *3.2. The Optimization of SPE Pretreatment*

The extraction solvent directly influenced recoveries of compounds. To obtain higher recoveries and decrease matrix interference, considering characteristics of protein and lipid contents in broiler tissue, different extraction solutions were optimized in order to realize simultaneous extraction of 23 mycotoxins. Methanol/formic acid (98:2, *v*/*v*), acetonitrile/formic acid (98:2, *v*/*v*) and acetonitrile/water/methanol (80:18:2, *v*/*v*/*v*) were investigated for preparation of broiler tissues including chicken breast meat, gizzards, and liver. When acidified methanol was used, two phases of solid-liquid could not be well separated, and the extraction solution was also in the muddy state even after centrifugation. However, no such phenomenon would happen when acetonitrile was used. Thus, acidified acetonitrile was used to extract 23 mycotoxins. The recovery comparison of two extraction solutions were shown in Figure 2. Finally, acetonitrile/water/methanol (80:18:2, *v*/*v*/*v*) was selected.

**Table 2.** Qualification parameters of 23 mycotoxins.

**Figure 2.** The effect of different extracts on the recovery of each mycotoxin.

Chicken breast meat which was cheap and easily available were widely consumed. Chicken liver and gizzard were the characteristic Chinese food. Considering 1.4 billion Chinese people, the method development was of great importance. As for different matrices of chicken breast meat, liver and gizzard, a great certain of proteins, lipids and minerals would be retained in the extraction solution, which brought in interference to mycotoxin determination. Besides, different mycotoxins would have different physicochemical properties. Therefore, it would be of great necessity to develop the method which would be

suitable for multiple mycotoxins. In this study, two multifunctional purification cartridges were investigated for the purification effect of 23 mycotoxins, such as Oasis PRIME-HLB and Captiva-EMR Lipid purification cartridges, whose purification effects on mycotoxin recoveries were shown in Figure 3. Both of those two columns allowed direct sample loading without equilibrium and activation and belonging to filtering SPE cartridge for the impurity removal, which greatly simplified the procedures of SPE and effectively decreased sample treatment time [24,25]. Captiva-EMR Lipid purification cartridge also had a higher absorptive capacity and removal efficiency of lipids. According to the response after the purification by Captiva EMR Lipid and Oasis PRIME-HLB cartridges, recoveries of 23 mycotoxins with the pretreatment of Captiva EMP Lipid cartridge were acceptable, namely 61–111%, wherein FBs also demonstrated good results. Thus, in this work, the Captiva-EMR Lipid purification cartridge was chosen.

**Figure 3.** The influence of different purification columns on the recovery of each mycotoxin.

#### *3.3. Matrix Effect*

The matrix effect was mainly due to endogenous components in the sample as well as impurities introduced in the pretreatment process. In ESI, the response of different mycotoxins was easily influenced by matrices, which was represented by the slope ratio between linear regression equation in blank matrix and that in the solvent. As shown in Table 3, most of the mycotoxins demonstrated relatively strong matrix effect. Thus, the matrix-matched linearity was used in this study to make up for the influence of matrix effect, guaranteeing the stability and accuracy of MS results.

#### *3.4. The Method Validation*

The recovery and repeatability assays were processed in three different blank matrices (chicken breast meat, liver and gizzard), respectively. And they were investigated at three spiking levels in six replicates. As shown in Table 4, recoveries of 23 mycotoxins were between 61% and 111% with RSDs < 15%. The good recovery and repeatability verified that the established SPE-UHPLC Q/orbitrap HRMS method was suitable for routine risk monitoring of 23 mycotoxins in broiler tissues such as breast meat, liver, and gizzards.

**Table 3.** Evaluation of matrix effect.

**Table 4.** Recoveries of 23 mycotoxins at 3 levels (n = 6).

**Table 4.** *Cont*.

Mixed standard solutions of mycotoxins with different concentrations were obtained in blank matrix solution. The linear regression equation was plotted through y of peak area and x of concentration (μg/L) as shown in Table 5. Linearity of 23 mycotoxins with correlation coefficients (R2) larger than 0.991 was obtained. LODs were in the range of 0.40–130.00 μg/kg and LOQs ranged from 1.20 to 350.00 μg/kg in those three matrices.

#### *3.5. The Real Sample Analysis*

With the optimized method, 30 samples including breast meat, liver and gizzard purchased from different markets were determined. ZEN was detected in one of chicken liver samples with the concentration of 15.29 μg/kg. Other samples' determination results were below the corresponding LOD. The MS/MS spectra of ZEN in the contaminated liver sample was shown in Figure 4. The occurrence of the positive result was due to the polluted feeds, which resulted in mycotoxin residue in animal. In addition, the pollution during the processing, storage, and marketing processes of meat was also possible.

**Figure 4.** MS2 spectra of ZEN in the standard solution (**a**) and contaminated sample (**b**).

ZEN was one of the most important mycotoxins, which altered fertility and reproduction and influenced hepatic cellular immune response. After oral administration, ZEN was difficult to be detected in vivo, which was not appropriate as the biomarker. However, in this work, ZEN's concentration in the positive liver sample was relatively high, illustrating that liver was the target organ reported in some publications. Besides, in the risk assessment report of ZEN from European Food Scientific Agency (EFSA) in 2011, the tolerable daily intake (TDI) was 0.25 μg/kg body weight. According to the adult body weight of 60 kg, although the ZEN intake of this positive liver sample didn't exceed the standard, the long-term or large dose intake hazards had to be worried especially considering those susceptible groups such as pregnant women or children.

#### **Table 5.** Linear range, detection limit and quantification limit of 23 mycotoxins.

Thus, to ensure the quality of broiler tissue, besides the safeguard of broiler feeds, the possible mycotoxin pollution of broiler in the slaughter or storage process should also be paid attention to.

#### **4. Conclusions**

An SPE-UHPLC Q/orbitrap method was established for rapid screening, accurate identification and quantitation of 23 mycotoxins in broiler tissues. The screening database of 23 mycotoxins was established, including retention time, accurate precursor *m*/*z* and MS/MS fragment, and could facilitate the rapid screening of mycotoxins. In this work, new multi-functional EMR column was applied in the removal of the lipids. Good recoveries were obtained and were in the range of 61–111%. In addition, high accuracy and high anti-interference capacity could be achieved in this method. ZEN at the concentration of 15 μg/kg was detected in one liver sample among 30 real broiler meat and organ samples, showing the possible harmful effect on the target organ of liver.

**Author Contributions:** Conceptualization, Y.Y. and Y.X.; Methodology, Y.Y., Z.H. and L.M.; Project administration, Y.X. and Y.Y.; Supervision, Y.X. and L.W.; Validation, Z.H.; Writing–original draft, Z.H.; Writing–review & editing, Y.Y. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was funded by the Ministry of Science and Technology of the People's Republic of China (Granted by No. 2017YFC1601600).

**Conflicts of Interest:** The authors declare that they have no financial or personal relationships with other people or organizations that could inappropriately influence the work in this study.

#### **References**