$$mathrm{Assume }delta =center_frequency/imagein{g}_{frequency}, andomega =left(TRotimes TEright), mathrm{MR}=mathrm{Definition of picture}.$$

Image definition formula, form of transmission and reception of the diagonal array signal. Therefore, to some extent, its magnetic resonance signals can sometimes be received and interpreted6.

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

(4)

The general formula for defining the MRI image 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 logleft| {I + R^{ – 1} times H_{ij} times Matrixleft[ {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} = Excites_number,S_{y} = Spacing _between_slices, M_{z} = Magnet_field_force, & quad omega_{i} = left( {TR otimes TE} right) end{aligned}

(5)

Therefore, the image resolution of MR is directly related to the interference signal (({R}^{-1})). This is also related to the performance of the MR machine, i.e. if it is a high-end MR. The high-dimensional signal image (information polar coordinates) of the MR DISCOVERY MR750w is as follows, and reference to Figs. 14, 15.

({omega }_{i}=left(TRotimes TEright)) is a constraint parameter. (1/{omega }_{i}) controls the stability morphological characteristics of the high-dimensional information distribution boundary, and its image is as above. The central energy and the sub-central energy structure Q of MR,({Q}_{core}=Eleft{{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) = Matrixleft[ {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{Subnucleus energy structure}} end {aligned}

(6)

The simplified general formula for MR image definition is:

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 logleft| {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}

(seven)

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

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

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

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

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

If SAR > 11.2, then MR stops, when SAR decreases, restart MR. MR does not need to set the domain value, because the AI ​​math model risk control can dynamically find the domain value and limit of various internal indicators of the MR machine. It is the advantage of the AI ​​system, and adopts the most advanced 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 equipment management time and space.seven.

AI mathematical model risk control can automatically and dynamically find the domain values ​​and limits of various indexes of medical equipment, such as the domain values ​​and limits of CT heat capacity and machine internal indexes . And reference to Figs. 22, 23.

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

### Non super flat enhanced heavy core TANH steady state application scenario

Analyze the stability of the DISCOVERY MR750w equipment. The AI ​​mathematical model risk control big data revealed that the ductility, generality and high reliability of MR DISCOVERY MR750w equipment is also an important basis for judging whether it is a high-end MR. The confidence limit is 40.01%, and reference to Figs. 26, 27, 28, which also reflects another important base for the high-end MR. MR Peak SAR RF (heavy core TANH steady state basic data is similar to CT exposure time), high-dimensional signal image and AI math model risk control image similar to exposure time CT exposure. 