Hi Everyone: I found some errors in Kaplan's MCAT review book (ISBN 0-7432-0186-8) <a href="http://www.kaptest.com/catalog/Product.jhtml;$sessionid$GUHPCGIDXPBW3LAQTEFXBNNMCCMQM2HB?PRODID=123228&CATID=8" target="_blank">]http://www.kaptest.com/catalog/Product.jhtml;$sessionid$GUHPCGI DXPBW3LAQTEFXBNNMCCMQM2HB?PRODID=123228&CATID=8</a> . I've been in contact with Kaplan and the person responsible (Scott - ask me and I can put you in touch with him) for errata got in touch with me, acknowledged there were some problems, was grateful for the input and said he did some work to ensure it gets fixed. I would put a link to an errata -->here<-- but Kaplan unfortunately hasn't created an on-line one (I recently searched 'errata' on Kaplan's web page). I suggested they make an errata and gave them a fair deal of time to do so (the letter I wrote them was dated September 6th 2001). If an errata is posted in the next little while I'll post a link. In the mean time, I have for the benefit of others, attached the gist of my letter. It is complete with references, if you don't want to trust me that I've got it right. Generally, I have a favorable opinion of the Kaplan Review book, despite of the errors in the one section. It is well organized and explains everything in a simple language. I found it especially useful for the writing section which, owing to my background in the physical sciences, wasn't a section I was confident I could do well in. Personally, I would recommend getting a couple of review books. One of my favorites is Baron's MCAT (ISBN 0-8120-9730-0). It, my opinion, is especially good for the physical sciences section and takes a somewhat more sophisticated approach than other books. It is also compact, concise and for those of you a bit weary about math -- it has a good math review section. In addition, it has four complete and tough practice tests. The Gold Standard prep book is also quite good. I'm not quite as familiar with it as the other two discussed above. In terms of the language and sophistication I'd say it lies somewhere between Baron's and Kaplan and is also well organized. Apologies that the post got a bit long. Nevertheless, I hope my explanations/corrections are informative, comprehensible and don't go totally overboard. Cheers! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Bits of My Letter to Kaplan (with a few little edits) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Dear Dr. Rochelle Rothstein: I have found a number of serious errors in the Solids and Fluids section of the Kaplan MCAT Comprehensive Review. They are described below along with corrections and suggestions. The presentation of the material in that section in my opinion only furthers misunderstanding. I hope my comments can help address this issue in a positive way. The cover of the book says good until 2003. Perhaps you can post an errata on <a href="http://www.kaplan.com." target="_blank">www.kaplan.com.</a> ... ERRORS 1. Streamlines "Streamlines are the paths followed by tiny fluid elements (sometimes called fluid particles) as they move." This statement (given on page 671) is simply not true. An excellent description of streamlines is given by Anderson (Anderson, JD Jr, Fundamentals of Aerodynamics, 2nd Edition, McGraw-Hill Inc., New York, 1991.). Paraphrasing Anderson (p. 123): A streamline is a curve whose tangent at any point is in the direction of the velocity vector at that point. In unsteady flow the streamline pattern is different at different times because the velocity vectors fluctuate with time in both magnitude and direction. Generally, streamlines are different from pathlines. A pathline can be visualized as a time-exposure photograph of a given fluid element, whereas a streamline pattern is like a single frame of a movie. When a flow is unsteady, the streamline pattern changes and each frame of the movie is different. SUGGESTION: Restrict the discussion to steady flow. Pathlines and streamlines are the same thing in steady flow. 2. Shear Stress The note on page 674 about shear stress is wrong. "Only solids can experience shear stresses, liquids and gases can't." Shear stresses exist in fluids and gases. In fluids they are of biological and pathological significance. The statement would be correct, in most cases, if it was specified that the fluid and gas are at rest. ------------------------------------ ASIDE ------------------------------------ GOING OVERBOARD ************************************ Technically speaking blood is thixotropic and can support a shear stress at rest. This is little known because it is not important under normal physiological conditions (at least for large vessels), as shown by Dutta and Tarbell and Gijsen et al. (Dutta A, Tarbell JM. Influence of non-Newtonian behavior of blood on flow in an elastic artery model. J Biomech Eng. 1996 Feb;118(1):111-9. Gijsen FJ, Allanic E, van de Vosse FN, Janssen JD. The influence of the non-Newtonian properties of blood on the flow in large arteries: unsteady flow in a 90 degrees curved tube. J Biomech. 1999 Jul;32(7):705-13.). ************************************ High shearing stress in the blood can lead to red blood cell break down. This is why high speed pumps (which impose high velocity gradients on the flow and thus high shearing stresses) can not be used to move blood. This is one of the many difficulties associated with the design of mechanical hearts, lung-heart machines and ventricular assist devices. Shear (among other things) keeps blood from clotting. The knowledge that shear prevents clotting and very low shear or stasis promotes clotting has been used in the treatment of aneurysms. (Mericle RA, Lanzino G, Wakhloo AK, Guterman LR, Hopkins LN. Stenting and secondary coiling of intracranial internal carotid artery aneurysm: technical case report. Neurosurgery. 1998 Nov;43(5):1229-34.). Most important biologically are the shear stresses the blood imposes on the artery wall. Atherosclerotic lesions are much more likely to form in regions of disturbed wall shear stress (e.g. carotid sinus). This has been known for some time. The landmark paper in this area was published in 1969 (Caro CG, Fitz-Gerald JM, Schroter RC. Arterial wall shear and distribution of early atheroma in man. Nature. 1969 Sep 13;223(211):1159-60.). ------------------------------------ ------------------------------------ SUGGESTION: Solids can support shearing stresses, fluids and gases when at rest can't. -- The above manages to keep it relatively simple and lies only a tiny bit. 3. Bernoulli's Equation. From the description of the Bernoulli's equation it is apparent the author of this section does NOT understand it properly. This becomes clear when one reads the "Real World Analogy" on page 672. The first part about how velocity varies with proximity to the wall is correct for a long straight tube and steady flow (which incidentally is not related to Bernoulli's equation). The second part (which claims Bernoulli's equation is valid between a point on the wall and a point in the center of the artery) is wrong. In reality (for a straight section of a blood vessel) there is a negligible pressure difference between the fluid at the wall of the blood vessel and the center of the blood vessel. This incidentally is an assumption in the famous Hagen-Poiseuille equation that relates pressure gradient, flow and vessel diameter. Bernoulli's equation, generally speaking, is not valid when applied across streamlines. This is the reason why the "Real World Analogy" is wrong. Bernoulli's equation can only be applied throughout the flow field if the flow is steady, incompressible and irrotational. A description of this exception, along with a derivation based on the irrotationality condition, is given by Roberson and Crowe (Roberson, JA, Crowe TC, Engineering Fluid Mechanics, 6th Edition, John Wiley & Sons Inc., New York, 1997. -- pp. 143-145). An excellent description of Bernoulli's equation complete with a list of six limitations is given by White (White, FM, Fluid Mechanics, 3rd Edition, McGraw-Hill Inc., New York, 1994. -- pp. 158-159). ------------------------------------ ASIDE ------------------------------------ Examples of how Bernoulli's equation can be applied are in the Pitot tube (used to measure wind speed) and Venturi meter (used to measure volumetric flow). It is my opinion that while Bernoulli's is useful in many cases it does not help one very much in describing blood flow. A good deal of the confusion about Bernoulli's equation rises when it is compared to the equation P=Q*R (P=pressure, Q=flow, R=resistance). This equation, it seems, is often taught to students in physiology courses. It is used because it is analogous to the familiar equation V=I*R (Ohm's law), and is useful for explaining the general concept of 'pressure drives flow'. This consideration aside it is often quite misleading. P=Q*R implicitly assumes a constant cross-sectional flow area and incorrectly suggests flows against an adverse pressure gradient (where the up-stream pressure is lower than the downstream pressure) are impossible. The equation also obscures the fact that gravity can drive the flow (P=Q*R ignores gravity). Rivers and waterfalls are not driven by a pressure gradient (they are driven by gravity). Furthermore, it should be noted that P=Q*R (where R is a constant) is only true for laminar flow in a long horizontal straight pipe (known as Hagen-Poiseuille flow). R is, generally speaking, a non-linear function of Q. In fully turbulent flow P is approximately proportional to Q^2 (i.e. R is approximately proportional to Q). ------------------------------------ ------------------------------------ SUGGESTION ---------- What I think a premed should understand about Bernoulli's equation: 1. The proper definition of a streamline (for steady flow). 2. Bernoulli's equation applies along a streamline. 3. Pressure, 'rho V squared divided by two' (rho*V^2/2) and 'rho g h' (rho*g*h) represent energies and their sum is constant (axially) along a pipe/or vessel of variable diameter if no energy losses (e.g. friction) or sources (e.g. pumps) are present ---(this is Bernoulli's equation in words). The energy explanation of Bernoulli's equation can be demonstrated by rewriting the dimensions of the individual terms. One can, for example, show that pressure is really work per volume (1 Pa = 1 N/m^2, 1 N/m^2=N*m/m^3, 1 N*m/m^3 = 1 J/m^3 - J (joule) is the unit for work and energy, m^3 is a volume).** 4. In a real system frictional losses are present. The sum P+rho*V^2/2+rho*g*h when traveling along a streamline is NOT a constant (it usually decreases due to friction). In most cases the frictional loss is apparent as a pressure loss (i.e. P downstream < P upstream --- in medical language: P distal < P proximal). 5. One does not always detect a pressure loss in a frictional flow. If the cross sectional area is increasing in the flow direction, it is possible that the pressure may be increasing in the flow direction (P distal > P proximal!).*** ** I think this is the easiest way of understanding Bernoulli's. There are a number of ways Bernoulli's equation can be understood. Anderson (Anderson, JD Jr, Fundamentals of Aerodynamics, 2nd Edition, McGraw-Hill Inc., New York, 1991.) discusses them shortly on page 159. *** P=Q*R (incorrectly) suggests this type of flow is impossible. Things I think a premed does NOT need to know: 1. Irrotational flow and when Bernoulli applies to the whole flow field (this requires a knowledge of calculus). 2. The magnitude of pressure loss due to friction and under exactly what conditions flow can proceed against an adverse (negative) pressure gradient (this requires an understanding of non-dimensional groups -- Reynolds number, roughness to diameter ratio and geometry associated loss coefficients).