$$\mathrm{Assume }\delta =center\_frequency/imagein{g}_{frequency}, and\omega =\left(TR\otimes TE\right), \mathrm{MR}=\mathrm{Image Definition}.$$

Image definition formula, diagonal matrix signal transmission and reception form. Therefore, to some extent, sometimes its magnetic resonance signals can be received and interpreted^{6}.

$${A}^{\left(x,y,z\right)}\to \frac{\delta }{\omega }\times {Matrix\left[\begin{array}{ccc}{E}_{x}& & \\ & {S}_{y}& \\ & & {M}_{z}\end{array}\right]},and {A}^{\left(x,y,z\right)}\to Imag{e}_{Definite}$$

(4)

The general formula of MRI image definition is as follows:

$$\begin{aligned} & \left( {A_{{\left( {x,y,z} \right)}}^{MR} ,\overline{{A_{{\left( {x,y,z} \right)}}^{MR} }} } \right)^{{H_{ij} Q_{i} H_{ji}^{H} }} = \\ & \quad \mathop \sum \limits_{i = 1}^{k} \frac{{\varvec{\delta}}}{{\omega_{i} }} \times log\left| {I + R^{ – 1} \times H_{ij} \times Matrix\left[ {\begin{array}{*{20}c} {E_{x} } & {} & {} \\ {} & {S_{y} } & {} \\ {} & {} & {M_{z} } \\ \end{array} } \right]_{i}^{Q} \left( {A_{{}}^{E,S,M} ,\overline{{A_{{}}^{E,S,M} }} } \right) \times H_{ji}^{H} } \right|,and \\ & \quad R^{ – 1} interference signal, \\ & \quad E_{x} = Excitions\_number,S_{y} = Spacing\_between\_slices,M_{z} = Magnet\_field\_strength, \\ & \quad \omega_{i} = \left( {TR \otimes TE} \right) \\ \end{aligned}$$

(5)

Therefore, the image definition of MR is directly related to the interference signal (\({R}^{-1}\)). It is also related to the performance of MR machine, that is, whether it is high-end MR. The image of high-dimensional signal (information polar coordinates) of MR DISCOVERY MR750w is as follows, and reference to Figs. 14, 15.

\({\omega }_{i}=\left(TR\otimes TE\right)\) is a constraint parameter. \(1/{\omega }_{i}\) controls the stability morphological characteristics of high-dimensional information distribution boundary, and its image is as above. The core energy and sub core energy structure Q of MR,\({Q}_{core}=E\left\{{X}_{k}{X}_{k}^{H}\right\}\)

$$\begin{aligned} & Q_{core}^{{}} \left( {A_{{}}^{{X_{E} ,X_{S} ,X_{M} }} ,\overline{{A_{{}}^{{X_{E} ,X_{S} ,X_{M} }} }} } \right) = Matrix\left[ {\begin{array}{*{20}c} {E_{{X_{E} }}^{k} \otimes X_{k}^{H} } & {} & {} \\ {} & {E_{{X_{S} }}^{k} \otimes X_{k}^{H} } & {} \\ {} & {} & {E_{{X_{M} }}^{k} \otimes X_{k}^{H} } \\ \end{array} } \right]_{i}^{Q} ,and E_{{X_{E} }}^{k} \otimes X_{k}^{H} ,E_{{X_{S} }}^{k} \otimes X_{k}^{H} ,E_{{X_{M} }}^{k} \\ & \quad \otimes X_{k}^{H} {\text{Sub core energy structure}} \\ \end{aligned}$$

(6)

The simplified general formula for MR image definition is as following:

$$\begin{aligned} & \left( {A_{{\left( {x,y,z} \right)}}^{core} ,\overline{{A_{{\left( {x,y,z} \right)}}^{core} }} } \right)_{MR}^{{H_{ij} Q_{i} H_{ji}^{H} }} = \mathop \sum \limits_{i = 1}^{k} \frac{\delta }{{\omega_{i} }} \times log\left| {I + R^{ – 1} \times H_{ij} \times Q_{core}^{{}} \left( {A_{{}}^{{X_{E} ,X_{S} ,X_{M} }} ,\overline{{A_{{}}^{{X_{E} ,X_{S} ,X_{M} }} }} } \right) \times H_{ji}^{H} } \right| \\ & \quad ,and R^{ – 1} Interference signal,\omega_{i} = \left( {TR \otimes TE} \right) \\ \end{aligned}$$

(7)

### When the \({{\varvec{R}}}^{-1}\) interference signal is strengthened, the clarity of MR image decreases and the comprehensive evaluation index decreases

The MR parameter is related to the machine parameter \(\upomega =\left(\mathrm{TR}\otimes \mathrm{TE}\right)\), excitions_number, spacing_between_slices, Magnet_field_strength, SAR. Reference to Figs. 16, 17 and 18.

### When \({\mathbf{R}}^{-1}\) interference signals decreases, MR image clarity increases and comprehensive evaluation index increases

Comprehensive evaluation indexes: 69.730%, 62.940%, 74.716%, its core boundary is 40.01%, and the image is more scientific. And reference to Figs. 19, 20, 21.

### MR peak SAR RF (similar to CT exposure time high-dimensional data heavy core clustering mathematical model)

If SAR > 11.2 then MR stops, when SAR drops down, start MR again. MR does not need to set the domain value, because AI Mathematical model risk control can dynamically find the domain value and boundary of various internal indicators of MR machine. This is the advantage of AI system, and adopts the most cutting-edge and advanced original innovative mathematics to combine with AI. Medical equipment management is characterized by high professionalism, high compliance requirements, diverse types and uses, scattered applicable standards and regulations, and large time and space span of equipment management^{7}.

AI Mathematical model risk control can automatically and dynamically find the domain values and boundaries of various medical equipment indexs, such as the domain values and boundaries of CT’s heat capacity and internal indexs of the machine. And reference to Figs. 22, 23.

AI Mathematical model risk control automatically and dynamically finds the index domain values and boundaries of various medical equipment. Such as MR peakSAR RF, image definition, internal index domain value and boundary of the machine. And reference to Figs. 24, 25.

### Application scenario of non super flat enhanced heavy core TANH equilibrium state

Analyze the stability of DISCOVERY MR750w equipment. AI Mathematical model risk control big data found that the ductility, generality and high reliability of MR equipment DISCOVERY MR750w are also an important basis for judging whether it is a high-end MR. The reliability boundary is 40.01%, and reference to Figs. 26, 27, 28, which also reflects another important basis for high-end MR. MR peak SAR RF (core data of heavy core clustering TANH equilibrium state is similar to CT exposure time), high-dimensional signal image, and AI Mathematical model risk control image similar to CT exposure time.

### New generations of medical AI big data platform based on heavy core clustering quasi thinking iterative planning

Capture the most important quasi thinking wave curve (signal), and through the vibration of random function and AI operation, iterate and determine the condition, namely domain value. If possible, the fluctuation curve of human (thinking) brain wave signal, that is, the iterative evolution of brain like AI form on the reliability of risk control of the above large medical equipment from weak to strong^{8}, can be used to provide a basis for obtaining risk control of CT large equipment. Reliability percentage data of risk control of large medical equipment are analyzed by long-time distribution curve. It can be learned and trained by KNN of AI neural network. Moreover, the heavy core data corresponding to this reliability < + [1, 10]—[1, 10] > is KNN of dual core neural network, and the correct risk control successful data are marked through unsupervised learning.