Hi Sarah. You can try using the "morphological close" operation to close the cells before filling. You may need to experiment with the size of the structuring element for your use case.
A = imread("ניסוי1 חתוך.tif","tif");
A=rgb2gray(A);
t = 0.64;
BW1 = imbinarize(A,t);
BW2 = bwareaopen(BW1,50);
BW3 = medfilt2(BW2);
se = strel('disk',20);
BW4 = imclose(BW3,se);
BW5 = imfill(BW4,'holes');
figure; imshow(BW5); title("after");