CSF Infusion Study - ICP Curve Fitting & Differential Analysis

Patient ID / Hospital No.

Clinical Indication

Neurosurgeon / Clinician

Infusion Rate ($I_c$)

mL/min

ICP Safety Threshold

mmHg

⏱️ Time Intervals & ICP Recording Table 10 Data Points

#	Time Interval (min)	Measured ICP (mmHg)	Phase / Notes	Action

💡 Tip: Edit any time or ICP value in the table directly to update the curve fit and derivative graphs instantly. P(t) = calculating...

📈 1. ICP vs. Time with Curve Fitting Line

P(t) Fitted Curve

🔴 Discrete Recorded ICP Data Points 🔵 Continuous Polynomial Fitted Function P(t)

⚡ 2. First Derivative: Rate of ICP Change ($dP/dt$)

P'(t) = dP/dt [mmHg/min]

Represents the instantaneous velocity / slope of pressure rise. Peak slope marks maximum elastance. Max Slope: -- mmHg/min

🔄 3. Second Derivative: Acceleration of ICP ($d^2P/dt^2$)

P''(t) = d²P/dt² [mmHg/min²]

Represents curvature / transition dynamics. Zero-crossing identifies the inflection point (maximum rate of pressure rise). Inflection: -- min

Resistance to Outflow ($R_{out}$)

                --
                mmHg/(mL/min)
            
                Calculating...
            
                Derived from Plateau ICP ($P_p$), Baseline ($P_0$), and Infusion Rate ($I_c$).

Pressure Rise ($\Delta P = P_p - P_0$)

-- mmHg

Net elevation of CSF pressure above baseline under constant infusion.

Peak ICP Rate of Rise ($[dP/dt]_{max}$)

-- mmHg/min

Peak first derivative value during infusion ramp phase.

Outflow Conductance ($C_{out} = 1/R_{out}$)

-- (mL/min)/mmHg

Reciprocal of resistance. Normal resorption capacity is > 0.10.

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