## Editor's Corner: Smartphones, Traffic Lights, and the Mechanical Ventilator: A Circuitous Path

**Patrick Yu and Vincent Valentine**

University of Texas Medical Branch

Galveston, TX, USA

vgvalent@utmb.edu

Moore's law is an observation that technological power doubles with every year. The boom in technological advances has also affected our daily lives. The hallmark of the creative '60s was "tuned in, turned on and dropped out." Today we are simply "plugged in" from the start of our day to the finish, even "wirelessly." Try explaining that to ourselves in the 1960s. Today, we wake up to check our e-mail. We commute to work while listening to our pre-set radio stations. Even stopped at a traffic light, we reach for our smart phones to check for updates. Some of us are literally embedded with technology, ranging from pacemakers to being intubated on a mechanical ventilator in the ICU. There is no denying how linked we are to technology and each other.

What do traffic lights, cell phones, mechanical ventilators and pacemakers all have in common? Other than being electronic devices, these devices rely on a specific type of circuit to work known as the resistor/capacitor circuit, or RC [1]. Simply stated, an RC circuit is an electrical circuit comprising a resistor, or something that can resist electric flow, and a capacitor, an electrical element capable of building up a charge across two plates separated by a short distance [1]. These two elements are in series with one another so that electrical current produced by a power source provides an electrical potential difference, or voltage that passes through a resistor before charging the capacitor. The electrons flowing through this circuit generates a charge across the capacitor, storing energy. Capacitors can be seen in some of the smallest places, like the millions upon billions of 1's and 0's generated in a computer chip to the largest of places like the space between the earth and the atmosphere to produce a bolt of lightning. Generating charge in a capacitor takes time. The longer amount of time allowed to charge a capacitor, the more the potential charge across the capacitor plates increases. The charge across the capacitor can be expressed as:

V_{c} = Q/C

Where V_{c} is the potential difference across the capacitor. If one were to try to analyze V_{c} as a function of time, Kirchoff's loop rule would be required. There are two rules that Kirchoff created, one of which is the conservation of energy, so called the "loop rule". It states that the sum of all the changes in potential energy around a closed loop circuit must equal zero [1]. With this in mind, the electron motive force (emf) of a battery used to charge the capacitor in an RC circuit must equal the sum of all the voltage changes that occur throughout the circuit as the current flows through the resistor and the rest of the system as it tries to build up charge [1]:

Emf = IR + Q/C

Emf, R and C are kept constant while Q and I are functions of time [1]. In other words, the amount of charge that is built up into a capacitor is dependent on the rate at which charge flows through the RC circuit, or in calculus terms: I = dQ/dt. Substituting this into our previous equation, we get:

Emf = R(dQ/dt) + Q/C

By using integration (I will spare you the derivation) and assessing the time it takes from the beginning of capacitor charging (time 0) to the time it takes to fully charge the capacitor, we are left with an equation that looks like this:

V_{c} = Emf (1- e^{-t/RC})

The RC term that is seen in this equation is known as the time constant [2], or:

τ = RC

It represents the amount of time required for the capacitor to reach 1-e^{-1}, or 0.63, or 63% of its full charge and voltage. The graph below shows that 2 time constants charges the capacitor 86% towards full capacity and 3 time constants charge up to 95% [1].

(Giancoli, *Physics*, 4th Edition)

Now what do traffic lights, smart phones, pacemakers, and the lungs have in common? Though it is not intuitive to think of the lung as an RC circuit, the two have many similar properties in terms of function and mechanics. If one were to imagine a lung as an RC circuit, the capacitance would be analogous to the compliance of the lung and the resistance of the circuit equivalent to the resistance of the airways. Just like an RC circuit, the lung also functions as a time constant that will depend on both resistance and compliance [3].

Resistance = Pressure change / flow rate

Compliance = volume change/ pressure change

This time constant is especially important in the ICU when pertaining to ventilator-dependent patients. The longer the time that is allowed for a lung to "charge up" like a capacitor, the more percentage of air will equilibrate within the lungs. In order for there to be adequate delivery and distribution of air (ventilation), a minimum of 3 time constants is needed. This corresponds to "charging up" the lung with gas to about 95% its capacity [4]. Therefore, in diseases where there are increases in resistance, compliance, or both the time constant increases thereby requiring a longer time to reach maximal "charge" of the lung, and vice versa (inflation/deflation). However in patients with ARDS, pulmonary edema or primary graft failure, they have highly elastic or stiff lungs with low compliances resulting in shorter time constants which mean that their lungs inflate and deflate at a faster rate than normal lungs leading to incomplete ventilation; rapid, shallow and ineffective ventilation. Also imagine a patient with obstructive pulmonary disease, where the conducting airways are constricted, leading to an increased resistance to flow. As a result, the time constant increases, therefore requiring a longer time constant in order to reach optimal lung ventilation [5].

(If one were to imagine the respiratory system as an RC circuit.)

One can apply this information in the ICU when managing a patient on a ventilator. How long should a patient's respiratory cycle be in relation to their current disease? Are their resistances increased or decreased? How about their compliance? All these aspects should be kept in mind when trying to properly ventilate and manage a patient requiring mechanical ventilation.

Who would have thought that an electrical physics concept would come to relate so perfectly to the respiratory system? Then again, medicine's relation to the physical and mathematical world has been present since the very beginning. As Neil deGrasse Tyson, a renowned astrophysicist, states, "We are all connected; to each other, biologically. To the earth, chemically. To the rest of the universe atomically." So in a sense, we have linked two seemingly unrelated concepts together.

Take a deep breath. Do you feel charged? ■

**Disclosure Statement:** the authors have no conflicts of interest to disclose.

**References:**

- Giancoli, D. (2000). Physics for scientists & engineers (3rd ed.). Upper Saddle River, N.J.: Prentice Hall.
- Butkov, N, Lee-Chiong, T. (2007). Fundamentals of Sleep Technology (pp. 78-80). Philadelphia, Pa.: Lippincott Williams & Wilkins.
- Benumof, J. (2007). Benumof's airway management: Principles and practice (2nd ed.). Philadelphia, Pa.: Mosby.
- Carlo, W, Ambalavanan, N. (1999). Conventional Mechanical Ventilation: Traditional and New Strategies.NeoReviews.
- Zhonghai, H, Zhenhe, M. (2013). Respiratory System Model Take into Account Pathology. Research Journal of Applied Sciences, Engineering and Technology, 6(1), 49-52.

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