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In this paper, the problem of wireless communications in human tissue is addressed for biosensor network applications. Today's offered solutions involve the usage of RF communication systems, which have shown to provide adequate performance to ensure proper network functionality. Yet they do not ensure that human tissue is not harmfully affected. In order to overcome this issue, we propose the use of ultrasonic waves for wireless communications in biosensor networks, motivated by the fact that, in contrast to electromagnetic waves, ultrasound has been used for almost a century now for medical purposes without any reported side effects. A simple propagation model is used to evaluate ultrasonic waves as a communication medium, study the feasibility of our proposal, the effective bit rates that may be achieved, the power efficiency of the scheme, as well as other system issues.