Study on salinity penetration process into fish meat by simulation and MRI

Abstract

The process of salt permeation into fish meat was studied using magnetic resonance imaging (MRI) and salt diffusion simulation. MRI measurements of a fish body rubbed with salt powder were carried out, using various echo times to calculate the relaxation time ¹H T₂ and construct a ¹H T₂ map. The ¹H T₂ values were measured for fish fillets immersed in various salt concentrations to obtain the relationship of ¹H T₂ to the salt concentration. This was used to convert the ¹H T₂ map to the salt distribution in the fish body. The results showed that the method of taking out the internal organs and rubbing salt into the fish body and the abdominal cavity led to a more homogeneous distribution of salt after a short incubation time than the method of only rubbing salt on the surface of the fish body. This result implies that applying salt into the abdominal cavity helps to increase salt penetration and produce a homogeneous salt concentration throughout the fish. Simulations of the salt permeation into the fish body were also carried out to provide insight into the salt distribution obtained by the MRI measurements.

Appendices

Appendix A

Source code for the calculation of water diffusion

(* ––- constant outside concentration ––- *).

ooDif4Cnst[mDat1_,dif_,outVal_,numNest_]: = Module[{mdif,mDat1Inv},

mdif = {{0,dif,0},{dif,1-4dif,dif},{0,dif,0}};

mDat1Inv = 1-mDat1;

Nest[(

ListConvolve[mdif,#,2,outVal]mDat1Inv + mDat1.

)&,mDat1,numNest]mDat1Inv.];

(*––- reflection at boundary ––- *).

ooooDifRflc[lldat_,dif_]: = Module[{mdif,len1,len2,mAllLarge,mAllAdrInLarge,lldatLrg,lRep,lldatLrgRfl},

mdif = {{0,dif,0},{dif,1-4dif,dif},{0,dif,0}};

{len1,len2} = Dimensions[lldat];

mAllLarge = ConstantArray[0,{len1 + 2,len2 + 2}];

mAllAdrInLarge = Outer[{#,#2}&,Range[2,len1 + 1],Range[2,len2 + 1]];

lldatLrg = ReplacePart[mAllLarge,MapThread[(#- > #2)&,{Flatten[mAllAdrInLarge,1],Flatten[lldat]}]];

lRep = Join[Table[{1,jj}- > lldatLrg[[2,jj]],{jj,len2 + 2}],

Table[{len1 + 2,jj}- > lldatLrg[[len1 + 1,jj]],{jj,len2 + 2}],

Table[{ii,1}- > lldatLrg[[ii,2]],{ii,len1 + 2}],

Table[{ii,len2 + 2}- > lldatLrg[[ii,len2 + 1]],{ii,len1 + 2}]];

lldatLrgRfl = ReplacePart[lldatLrg,lRep];(* reflection *).

ListConvolve[mdif,lldatLrgRfl]].

{dif,outVal} = {0.2,1};

{or1,or2} = {2,4};

{mDat1,dif,outVal} = {lmInv[[or1]],0.2,1};

lnNest = 3 60{1/15,1,3,6,18};

lmDat = Map[(numNest = #;

ooDif4Cnst[mDat1,dif,outVal,numNest]lmDatOrg[[or1]]lmInv[[or2]].

)&,lnNest];

mtn[n_, a_, dif_, ini_, inf_]: = Module[{\[Alpha]},

\[Alpha] = N[BesselJZero[0, Range[9]]/a];

ini + (inf—ini) (1 -

Total[(4/(a^2 \[Alpha]^2)(*Exp[-diff \[Alpha]^2t]*))])];

ldat1 = {{0,308.7},{1,306.9},{3,334.3},{6,360.6},{18,529.3}};

{a,diff,ini,inf} = {0.025,0.84 10^–9 3600,267,530};

mt91 = mtn[9,a,diff,ini,inf];

Show[Plot[mt91,{t,0,6}],ListPlot[ldat1]].

Appendix B

(See Fig. 6).

Fig. 6

Fitting to get the diffusion coefficient