Is it necessary to use the same cable brand and model for bi-wiring??

Yes, all cables have a "character". 
What might be a wonderful and expensive cable might not be the best choice for certain speakers or amplifier. 
Find a good dealer who is familiar with your speakers and electronics and ask for their advice. 
Also, Music Direct sells a variety of cables at various price points and you can try them for a few weeks and have the option to return them if you aren't happy with the sound. 
Thats what dealers are for. 

Yes, all cables have a "character".

Right, you're tone controlling by selecting a cable.   So what's the difference in using same or different cables for bi-wiring, still tone control?

BTW, I would use the same cable for bi-wiring.

What might be a wonderful and expensive cable might not be the best choice for certain speakers or amplifier.
Find a good dealer who is familiar with your speakers and electronics and ask for their advice.
Also, Music Direct sells a variety of cables at various price points and you can try them for a few weeks and have the option to return them if you aren't happy with the sound.
Thats what dealers are for.

How's this relevant to the discussion on tone control?   

All of audio is about tone control. What difference does it make if I change speaker around to suit my cables, or change cables around to suit my speakers?
People basically change gear/cables around to suit their personal tastes. It's nothing to make a fuss about.

Put 10 audiophiles in a room to discuss biwire, and they will emerge with at least 11 different theories.

The majority of speakers today have biwire connections, however only a minority have been specifically designed for this from the ground up. For the rest it's just an add-on to maintain audio fashion. The manufacturers of the speakers that are specifically designed for biwire only recommend using two separate runs of identical cable for the biwire. So it appears they think it is necessary.

I agree that changing cables can make a difference in tonal character of the sound, however IMHO it doesn't make common sense to try and change high and low inputs on a speaker separately. That could cause an imbalance of frequencies at the crossover point.

Thanks to all who have contributed to this thread.  Let me assure those who responded, I am not using cables as tone controls. I just want to see if there is a qualitative improvement in sound, and to find this out with moderate expense.   The single cables I currently use are the Grover Huffman "EZ"  ( not sure what that logo stands for. o bought the cables from a sound engineer who works for Warner Brothers. He raved about their sound, ands was pretty much on the mark. I also have a pair of Harmonic Technology Pro 11+ which were highly touted and rightfully so. The only probably they are thick fire hose girth and a 12 ft pair.  That is why I was asking about speaker cables for bi-wiring the Wharfdale  Denton monitors. which are excellent.